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Randomized controlled trial

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A randomized controlled trial (or randomized control trial;<a href="#cite_note-Chalmers-1981-2">[2]</a> RCT) is a form of <a href="Scientific_experiment" class="mw-redirect" title="Scientific experiment">scientific experiment</a> used to control factors not under direct experimental control. Examples of RCTs are <a href="Clinical_trial" title="Clinical trial">clinical trials</a> that compare the effects of drugs, surgical techniques, <a href="Medical_device" title="Medical device">medical devices</a>, <a href="Diagnostic_procedure" class="mw-redirect" title="Diagnostic procedure">diagnostic procedures</a>, diets or other medical treatments.<a href="#cite_note-nia-3">[3]</a><a href="#cite_note-fda-types-4">[4]</a>

Participants who enroll in RCTs differ from one another in known and unknown ways that can influence study outcomes, and yet cannot be directly controlled. By <a href="Random_assignment" title="Random assignment">randomly allocating</a> participants among compared treatments, an RCT enables statistical control over these influences. Provided it is designed well, conducted properly, and enrolls enough participants, an RCT may achieve sufficient control over these <a href="Confounding_factor" class="mw-redirect" title="Confounding factor">confounding factors</a> to deliver a useful comparison of the treatments studied.

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<div class="mw-heading mw-heading2"><h2 id="Definition_and_examples">Definition and examples</h2></div>

An RCT in <a href="Clinical_research" title="Clinical research">clinical research</a> typically compares a proposed new treatment against an existing <a href="Standard_of_care#Medical_standard_of_care" title="Standard of care">standard of care</a>; these are then termed the 'experimental' and 'control' treatments, respectively. When no such generally accepted treatment is available, a <a href="Placebo" title="Placebo">placebo</a> may be used in the control group so that participants are <a href="Blinded_experiment" title="Blinded experiment">blinded</a>, or not given information, about their treatment allocations. This blinding principle is ideally also extended as much as possible to other parties including researchers, technicians, data analysts, and evaluators. Effective blinding experimentally isolates the physiological effects of treatments from various psychological sources of <a href="Bias" title="Bias">bias</a>.

The randomness in the assignment of participants to treatments reduces <a href="Selection_bias" title="Selection bias">selection bias</a> and allocation bias, balancing both known and unknown prognostic factors, in the assignment of treatments.<a href="#cite_note-Moher-2010-5">[5]</a> Blinding reduces other forms of <a href="Observer-expectancy_effect" title="Observer-expectancy effect">experimenter and subject biases</a>.

A well-blinded RCT is considered the <a href="Gold_standard_(test)" title="Gold standard (test)">gold standard</a> for clinical trials. Blinded RCTs are commonly used to test the <a href="Efficacy#Medicine" title="Efficacy">efficacy</a> of medical <a href="Health_intervention" class="mw-redirect" title="Health intervention">interventions</a> and may additionally provide information about adverse effects, such as <a href="Adverse_drug_reactions" class="mw-redirect" title="Adverse drug reactions">drug reactions</a>. A randomized controlled trial can provide compelling evidence that the study treatment causes an effect on human health.<a href="#cite_note-hannan-6">[6]</a>

The terms "RCT" and "randomized trial" are sometimes used synonymously, but the latter term omits mention of controls and can therefore describe studies that compare multiple treatment groups with each other in the absence of a control group.<a href="#cite_note-Ranjith-2005-7">[7]</a> Similarly, the <a href="Initialism" class="mw-redirect" title="Initialism">initialism</a> is sometimes expanded as "randomized clinical trial" or "randomized comparative trial", leading to ambiguity in the <a href="Scientific_literature" title="Scientific literature">scientific literature</a>.<a href="#cite_note-Peto-1976-8">[8]</a><a href="#cite_note-Peto-1977-9">[9]</a> Not all RCTs are randomized controlled trials (and some of them could never be, as in cases where controls would be impractical or unethical to use). The term randomized controlled clinical trial is an alternative term used in clinical research;<a href="#cite_note-Wollert-2004-10">[10]</a> however, RCTs are also employed in other research areas, including <a href="#In_social_science">many of the social sciences</a>.

<div class="mw-heading mw-heading2"><h2 id="History">History</h2></div>

The first reported <a href="Clinical_trial" title="Clinical trial">clinical trial</a> was conducted by <a href="James_Lind" title="James Lind">James Lind</a> in 1747 to identify a treatment for <a href="Scurvy" title="Scurvy">scurvy</a>.<a href="#cite_note-11">[11]</a> The first blind experiment was conducted by the <a href="Royal_Commission_on_Animal_Magnetism" title="Royal Commission on Animal Magnetism">French Royal Commission on Animal Magnetism</a> in 1784 to investigate the claims of <a href="Animal_magnetism" title="Animal magnetism">mesmerism</a>. An early essay advocating the blinding of researchers came from <a href="Claude_Bernard" title="Claude Bernard">Claude Bernard</a> in the latter half of the 19th century. Bernard recommended that the observer of an experiment should not have knowledge of the hypothesis being tested. This suggestion contrasted starkly with the prevalent <a href="Age_of_Enlightenment" title="Age of Enlightenment">Enlightenment</a>-era attitude that scientific observation can only be objectively valid when undertaken by a well-educated, informed scientist.<a href="#cite_note-12">[12]</a> The first study recorded to have a blinded researcher was published in 1907 by <a href="W._H._R._Rivers" title="W. H. R. Rivers">W. H. R. Rivers</a> and H. N. Webber to investigate the effects of caffeine.<a href="#cite_note-pmid16992882-13">[13]</a>

<a href="Randomized_experiment" title="Randomized experiment">Randomized experiments</a> first appeared in <a href="Experimental_psychology" title="Experimental psychology">psychology</a>, where they were introduced by <a href="Charles_Sanders_Peirce" title="Charles Sanders Peirce">Charles Sanders Peirce</a> and <a href="Joseph_Jastrow" title="Joseph Jastrow">Joseph Jastrow</a> in the 1880s,<a href="#cite_note-14">[14]</a> and in <a href="School_of_education" title="School of education">education</a>.<a href="#cite_note-15">[15]</a><a href="#cite_note-16">[16]</a><a href="#cite_note-17">[17]</a> The earliest experiments comparing <a href="Treatment_and_control_groups" title="Treatment and control groups">treatment and control groups</a> were published by <a href="Robert_S._Woodworth" title="Robert S. Woodworth">Robert Woodworth</a> and <a href="Edward_Thorndike" title="Edward Thorndike">Edward Thorndike</a> in 1901,<a href="#cite_note-18">[18]</a> and by <a href="John_Edgar_Coover" title="John Edgar Coover">John E. Coover</a> and <a href="Frank_Angell" title="Frank Angell">Frank Angell</a> in 1907.<a href="#cite_note-19">[19]</a><a href="#cite_note-20">[20]</a>

In the early 20th century, randomized experiments appeared in agriculture, due to <a href="Jerzy_Neyman" title="Jerzy Neyman">Jerzy Neyman</a><a href="#cite_note-21">[21]</a> and <a href="Ronald_A._Fisher" class="mw-redirect" title="Ronald A. Fisher">Ronald A. Fisher</a>. Fisher's experimental research and his writings popularized randomized experiments.<a href="#cite_note-Conniffe-22">[22]</a>

The first published Randomized Controlled Trial in medicine appeared in the 1948 paper entitled "<a href="Streptomycin" title="Streptomycin">Streptomycin</a> treatment of pulmonary <a href="Tuberculosis" title="Tuberculosis">tuberculosis</a>", which described a <a href="Medical_Research_Council_(UK)" class="mw-redirect" title="Medical Research Council (UK)">Medical Research Council</a> investigation.<a href="#cite_note-MRC-1948-23">[23]</a><a href="#cite_note-Brown-1998-24">[24]</a><a href="#cite_note-Shikata-2006-25">[25]</a> One of the authors of that paper was <a href="Austin_Bradford_Hill" title="Austin Bradford Hill">Austin Bradford Hill</a>, who is credited as having conceived the modern RCT.<a href="#cite_note-Stolberg-2004-26">[26]</a>

Trial design was further influenced by the large-scale <a href="International_Studies_of_Infarct_Survival" title="International Studies of Infarct Survival">ISIS</a> trials on <a href="Heart_attack" class="mw-redirect" title="Heart attack">heart attack</a> treatments that were conducted in the 1980s.<a href="#cite_note-27">[27]</a>

By the late 20th century, RCTs were recognized as the standard method for "rational therapeutics" in medicine.<a href="#cite_note-Meldrum-2000-28">[28]</a> As of 2004, more than 150,000 RCTs were in the <a href="Cochrane_Library" title="Cochrane Library">Cochrane Library</a>.<a href="#cite_note-Stolberg-2004-26">[26]</a> To improve the reporting of RCTs in the medical literature, an international group of scientists and editors published <a href="Consolidated_Standards_of_Reporting_Trials" title="Consolidated Standards of Reporting Trials">Consolidated Standards of Reporting Trials</a> (CONSORT) Statements in 1996, 2001 and 2010, and these have become widely accepted.<a href="#cite_note-Schulz-2010-1">[1]</a><a href="#cite_note-Moher-2010-5">[5]</a> Randomization is the process of assigning trial subjects to treatment or control groups using an element of chance to determine the assignments in order to reduce the bias.

<div class="mw-heading mw-heading2"><h2 id="Ethics">Ethics</h2></div>

Although the principle of <a href="Clinical_equipoise" title="Clinical equipoise">clinical equipoise</a> ("genuine uncertainty within the expert medical community... about the preferred treatment") common to clinical trials<a href="#cite_note-Freedman-1987-29">[29]</a> has been applied to RCTs, the <a href="Ethics" title="Ethics">ethics</a> of RCTs have special considerations. For one, it has been argued that equipoise itself is insufficient to justify RCTs.<a href="#cite_note-Gifford-1995-30">[30]</a> For another, "collective equipoise" can conflict with a lack of personal equipoise (e.g., a personal belief that an intervention is effective).<a href="#cite_note-Edwards-1998-31">[31]</a> Finally, <a href="Zelen's_design" title="Zelen's design">Zelen's design</a>, which has been used for some RCTs, randomizes subjects before they provide informed consent, which may be ethical for RCTs of <a href="Screening_(medicine)" title="Screening (medicine)">screening</a> and selected therapies, but is likely unethical "for most therapeutic trials."<a href="#cite_note-Zelen-1979-32">[32]</a><a href="#cite_note-Torgerson-1998-33">[33]</a>

Although subjects almost always provide <a href="Informed_consent" title="Informed consent">informed consent</a> for their participation in an RCT, studies since 1982 have documented that RCT subjects may believe that they are certain to receive treatment that is best for them personally; that is, they do not understand the difference between research and treatment.<a href="#cite_note-Appelbaum-1982-34">[34]</a><a href="#cite_note-Henderson-2007-35">[35]</a> Further research is necessary to determine the prevalence of and ways to address this "<a href="Therapeutic_misconception" title="Therapeutic misconception">therapeutic misconception</a>".<a href="#cite_note-Henderson-2007-35">[35]</a>

The RCT method variations may also create cultural effects that have not been well understood.<a href="#cite_note-Jain-2010-36">[36]</a> For example, patients with terminal illness may join trials in the hope of being cured, even when treatments are unlikely to be successful.

<div class="mw-heading mw-heading3"><h3 id="Trial_registration">Trial registration</h3></div>

In 2004, the <a rel="nofollow" class="external text" href="http://www.icmje.org/">International Committee of Medical Journal Editors</a> (ICMJE) announced that all trials starting enrolment after July 1, 2005, must be registered prior to consideration for publication in one of the 12 member journals of the committee.<a href="#cite_note-pmid15356289-37">[37]</a> However, trial registration may still occur late or not at all.<a href="#cite_note-pmid22147862-38">[38]</a><a href="#cite_note-pmid19724045-39">[39]</a>

Medical journals have been slow in adapting policies requiring mandatory clinical trial registration as a prerequisite for publication.<a href="#cite_note-40">[40]</a>

<div class="mw-heading mw-heading2"><h2 id="Classifications">Classifications</h2></div>

<div class="mw-heading mw-heading3"><h3 id="By_study_design">By study design</h3></div>

One way to classify RCTs is by <a href="Study_design" class="mw-redirect" title="Study design">study design</a>. From most to least common in the healthcare literature, the major categories of RCT study designs are:<a href="#cite_note-Hopewell-2010-41">[41]</a>

<ul><li><a href="Parallel_study" title="Parallel study">Parallel-group</a> – each participant is randomly assigned to a group, and all the participants in the group receive (or do not receive) an intervention.<a href="#cite_note-42">[42]</a><a href="#cite_note-43">[43]</a></li>

<li><a href="Crossover_study" title="Crossover study">Crossover</a> – over time, each participant receives (or does not receive) an intervention in a random sequence.<a href="#cite_note-44">[44]</a><a href="#cite_note-45">[45]</a></li>

<li><a href="Stepped-wedge_trial" title="Stepped-wedge trial">Stepped-wedge trial</a> - " involves random and sequential crossover of clusters (of subjects) from control to intervention until all clusters are exposed."<a href="#cite_note-pmid25662947-46">[46]</a> In the past, this design has been called a “waiting list designs” or “phased implementations.”<a href="#cite_note-pmid25662947-46">[46]</a></li></ul>

<ul><li><a href="Cluster_randomised_controlled_trial" class="mw-redirect" title="Cluster randomised controlled trial">Cluster</a> – pre-existing groups of participants (e.g., villages, schools) are randomly selected to receive (or not receive) an intervention.<a href="#cite_note-47">[47]</a><a href="#cite_note-48">[48]</a></li>

<li><a href="Factorial_experiment" title="Factorial experiment">Factorial</a> – each participant is randomly assigned to a group that receives a particular combination of interventions or non-interventions (e.g., group 1 receives vitamin X and vitamin Y, group 2 receives vitamin X and placebo Y, group 3 receives placebo X and vitamin Y, and group 4 receives placebo X and placebo Y).</li></ul>

An analysis of the 616 RCTs indexed in <a href="PubMed" title="PubMed">PubMed</a> during December 2006 found that 78% were parallel-group trials, 16% were crossover, 2% were split-body, 2% were cluster, and 2% were factorial.<a href="#cite_note-Hopewell-2010-41">[41]</a>

<div class="mw-heading mw-heading3"><h3 id="By_outcome_of_interest_(efficacy_vs._effectiveness)">By outcome of interest (efficacy vs. effectiveness)</h3></div>

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</style><div role="note" class="hatnote navigation-not-searchable">Main article: <a href="Pragmatic_clinical_trial" title="Pragmatic clinical trial">Pragmatic clinical trial</a></div>

RCTs can be classified as "explanatory" or "pragmatic."<a href="#cite_note-Zwarenstein-2008-49">[49]</a> Explanatory RCTs test <a href="Efficacy#Medicine" title="Efficacy">efficacy</a> in a research setting with highly selected participants and under highly controlled conditions.<a href="#cite_note-Zwarenstein-2008-49">[49]</a> In contrast, pragmatic RCTs (pRCTs) test <a href="Effectiveness#Usage" title="Effectiveness">effectiveness</a> in everyday practice with relatively unselected participants and under flexible conditions; in this way, pragmatic RCTs can "inform decisions about practice."<a href="#cite_note-Zwarenstein-2008-49">[49]</a>

<div class="mw-heading mw-heading3"><h3 id="By_hypothesis_(superiority_vs._noninferiority_vs._equivalence)">By hypothesis (superiority vs. noninferiority vs. equivalence)</h3></div>

<div role="note" class="hatnote navigation-not-searchable">Main article: <a href="Equivalence_test" title="Equivalence test">Equivalence test</a></div>

Another classification of RCTs categorizes them as "superiority trials", "noninferiority trials", and "equivalence trials", which differ in methodology and reporting.<a href="#cite_note-Piaggio-2006-50">[50]</a> Most RCTs are superiority trials, in which one intervention is hypothesized to be superior to another in a <a href="Statistical_significance" title="Statistical significance">statistically significant</a> way.<a href="#cite_note-Piaggio-2006-50">[50]</a> Some RCTs are noninferiority trials "to determine whether a new treatment is no worse than a reference treatment."<a href="#cite_note-Piaggio-2006-50">[50]</a> Other RCTs are equivalence trials in which the hypothesis is that two interventions are indistinguishable from each other.<a href="#cite_note-Piaggio-2006-50">[50]</a>

<div class="mw-heading mw-heading2"><h2 id="Randomization">Randomization</h2></div>

The advantages of proper <a href="Randomized_experiment" title="Randomized experiment">randomization</a> in RCTs include:<a href="#cite_note-SchulzGrimes2002-51">[51]</a>

<ul><li>"It eliminates bias in treatment assignment," specifically <a href="Selection_bias" title="Selection bias">selection bias</a> and <a href="Confounding" title="Confounding">confounding</a>.</li>

<li>"It facilitates blinding (masking) of the identity of treatments from investigators, participants, and assessors."</li>

<li>"It permits the use of probability theory to express the likelihood that any difference in outcome between treatment groups merely indicates chance."</li></ul>

There are two processes involved in randomizing patients to different interventions. First is choosing a randomization procedure to generate an unpredictable sequence of allocations; this may be a simple random assignment of patients to any of the groups at equal probabilities, may be "restricted", or may be "adaptive." A second and more practical issue is allocation concealment, which refers to the stringent precautions taken to ensure that the group assignment of patients are not revealed prior to definitively allocating them to their respective groups. Non-random "systematic" methods of group assignment, such as alternating subjects between one group and the other, can cause "limitless contamination possibilities" and can cause a breach of allocation concealment.<a href="#cite_note-Schulz-2002-52">[52]</a>

However empirical evidence that adequate randomization changes outcomes relative to inadequate randomization has been difficult to detect.<a href="#cite_note-Howick-2014-53">[53]</a>

<div class="mw-heading mw-heading3"><h3 id="Procedures">Procedures</h3></div>

The treatment allocation is the desired proportion of patients in each treatment arm.

An ideal randomization procedure would achieve the following goals:<a href="#cite_note-Lachin-1988a-54">[54]</a>

<ul><li>Maximize <a href="Statistical_power" class="mw-redirect" title="Statistical power">statistical power</a>, especially in <a href="Subgroup_analysis" title="Subgroup analysis">subgroup analyses</a>. Generally, equal group sizes maximize statistical power, however, unequal groups sizes may be more powerful for some analyses (e.g., multiple comparisons of placebo versus several doses using Dunnett's procedure<a href="#cite_note-55">[55]</a> ), and are sometimes desired for non-analytic reasons (e.g., patients may be more motivated to enroll if there is a higher chance of getting the test treatment, or regulatory agencies may require a minimum number of patients exposed to treatment).<a href="#cite_note-Avins-1998-56">[56]</a></li>

<li>Minimize selection bias. This may occur if investigators can consciously or unconsciously preferentially enroll patients between treatment arms. A good randomization procedure will be unpredictable so that investigators cannot guess the next subject's group assignment based on prior treatment assignments. The risk of selection bias is highest when previous treatment assignments are known (as in unblinded studies) or can be guessed (perhaps if a drug has distinctive side effects).</li>

<li>Minimize allocation bias (or confounding). This may occur when <a href="Covariate" class="mw-redirect" title="Covariate">covariates</a> that affect the outcome are not equally distributed between treatment groups, and the treatment effect is confounded with the effect of the covariates (i.e., an "accidental bias"<a href="#cite_note-SchulzGrimes2002-51">[51]</a><a href="#cite_note-Buyse-1989-57">[57]</a>). If the randomization procedure causes an imbalance in covariates related to the outcome across groups, estimates of effect may be <a href="Bias_of_an_estimator" title="Bias of an estimator">biased</a> if not adjusted for the covariates (which may be unmeasured and therefore impossible to adjust for).</li></ul>

However, no single randomization procedure meets those goals in every circumstance, so researchers must select a procedure for a given study based on its advantages and disadvantages.

<div class="mw-heading mw-heading4"><h4 id="Simple">Simple</h4></div>

This is a commonly used and intuitive procedure, similar to "repeated fair coin-tossing."<a href="#cite_note-SchulzGrimes2002-51">[51]</a> Also known as "complete" or "unrestricted" randomization, it is <a href="Robust_statistics" title="Robust statistics">robust</a> against both selection and accidental biases. However, its main drawback is the possibility of imbalanced group sizes in small RCTs. It is therefore recommended only for RCTs with over 200 subjects.<a href="#cite_note-Lachin-1988b-58">[58]</a>

<div class="mw-heading mw-heading4"><h4 id="Restricted">Restricted</h4></div>

To balance group sizes in smaller RCTs, some form of <a href="Restricted_randomization" title="Restricted randomization">"restricted" randomization</a> is recommended.<a href="#cite_note-Lachin-1988b-58">[58]</a> The major types of restricted randomization used in RCTs are:

<ul><li><a href="Randomized_block_design" class="mw-redirect" title="Randomized block design">Permuted-block randomization</a> or blocked randomization: a "block size" and "allocation ratio" (number of subjects in one group versus the other group) are specified, and subjects are allocated randomly within each block.<a href="#cite_note-Schulz-2002-52">[52]</a> For example, a block size of 6 and an allocation ratio of 2:1 would lead to random assignment of 4 subjects to one group and 2 to the other. This type of randomization can be combined with "<a href="Stratified_randomization" title="Stratified randomization">stratified randomization</a>", for example by center in a <a href="Multicenter_trial" title="Multicenter trial">multicenter trial</a>, to "ensure good balance of participant characteristics in each group."<a href="#cite_note-Moher-2010-5">[5]</a> A special case of permuted-block randomization is random allocation, in which the entire sample is treated as one block.<a href="#cite_note-Schulz-2002-52">[52]</a> The major disadvantage of permuted-block randomization is that even if the block sizes are large and randomly varied, the procedure can lead to selection bias.<a href="#cite_note-Lachin-1988a-54">[54]</a> Another disadvantage is that "proper" analysis of data from permuted-block-randomized RCTs requires stratification by blocks.<a href="#cite_note-Lachin-1988b-58">[58]</a></li>

<li>Adaptive biased-coin randomization methods (of which urn randomization is the most widely known type): In these relatively uncommon methods, the probability of being assigned to a group decreases if the group is overrepresented and increases if the group is underrepresented.<a href="#cite_note-Schulz-2002-52">[52]</a> The methods are thought to be less affected by selection bias than permuted-block randomization.<a href="#cite_note-Lachin-1988b-58">[58]</a></li></ul>

<div class="mw-heading mw-heading4"><h4 id="Adaptive">Adaptive</h4></div>

At least two types of "adaptive" randomization procedures have been used in RCTs, but much less frequently than simple or restricted randomization:

<ul><li>Covariate-adaptive randomization, of which one type is <a href="Minimisation_(clinical_trials)" title="Minimisation (clinical trials)">minimization</a>: The probability of being assigned to a group varies in order to minimize "covariate imbalance."<a href="#cite_note-Lachin-1988b-58">[58]</a> Minimization is reported to have "supporters and detractors"<a href="#cite_note-Schulz-2002-52">[52]</a> because only the first subject's group assignment is truly chosen at random, the method does not necessarily eliminate bias on unknown factors.<a href="#cite_note-Moher-2010-5">[5]</a></li>

<li>Response-adaptive randomization, also known as outcome-adaptive randomization: The probability of being assigned to a group increases if the responses of the prior patients in the group were favorable.<a href="#cite_note-Lachin-1988b-58">[58]</a> Although arguments have been made that this approach is more ethical than other types of randomization when the probability that a treatment is effective or ineffective increases during the course of an RCT, ethicists have not yet studied the approach in detail.<a href="#cite_note-Rosenberger-1993-59">[59]</a></li></ul>

<div class="mw-heading mw-heading3"><h3 id="Allocation_concealment">Allocation concealment</h3></div>

<div role="note" class="hatnote navigation-not-searchable">Main article: <a href="Allocation_concealment" title="Allocation concealment">Allocation concealment</a></div>

"Allocation concealment" (defined as "the procedure for protecting the randomization process so that the treatment to be allocated is not known before the patient is entered into the study") is important in RCTs.<a href="#cite_note-Forder-2005-60">[60]</a> In practice, clinical investigators in RCTs often find it difficult to maintain impartiality. Stories abound of investigators holding up sealed envelopes to lights or ransacking offices to determine group assignments in order to dictate the assignment of their next patient.<a href="#cite_note-Schulz-2002-52">[52]</a> Such practices introduce selection bias and <a href="Lurking_variable" class="mw-redirect" title="Lurking variable">confounders</a> (both of which should be minimized by randomization), possibly distorting the results of the study.<a href="#cite_note-Schulz-2002-52">[52]</a> Adequate allocation concealment should defeat patients and investigators from discovering treatment allocation once a study is underway and after the study has concluded. Treatment related side-effects or adverse events may be specific enough to reveal allocation to investigators or patients thereby introducing bias or influencing any subjective parameters collected by investigators or requested from subjects.

Some standard methods of ensuring allocation concealment include sequentially numbered, opaque, sealed envelopes (SNOSE); sequentially numbered containers; pharmacy controlled randomization; and central randomization.<a href="#cite_note-Schulz-2002-52">[52]</a> It is recommended that allocation concealment methods be included in an RCT's <a href="Clinical_trial_protocol" class="mw-redirect" title="Clinical trial protocol">protocol</a>, and that the allocation concealment methods should be reported in detail in a publication of an RCT's results; however, a 2005 study determined that most RCTs have unclear allocation concealment in their protocols, in their publications, or both.<a href="#cite_note-Pildal-2005-61">[61]</a> On the other hand, a 2008 study of 146 <a href="Meta-analysis" title="Meta-analysis">meta-analyses</a> concluded that the results of RCTs with inadequate or unclear allocation concealment tended to be biased toward beneficial effects only if the RCTs' outcomes were <a href="Subjectivity" class="mw-redirect" title="Subjectivity">subjective</a> as opposed to <a href="Objectivity_(philosophy)" class="mw-redirect" title="Objectivity (philosophy)">objective</a>.<a href="#cite_note-Wood-2008-62">[62]</a>

<div class="mw-heading mw-heading3"><h3 id="Sample_size">Sample size</h3></div>

<div role="note" class="hatnote navigation-not-searchable">Main article: <a href="Sample_size_determination" title="Sample size determination">Sample size determination</a></div>

The number of treatment units (subjects or groups of subjects) assigned to control and treatment groups, affects an RCT's reliability. If the effect of the treatment is small, the number of treatment units in either group may be insufficient for rejecting the null hypothesis in the respective <a href="Statistical_hypothesis_testing" class="mw-redirect" title="Statistical hypothesis testing">statistical test</a>. The failure to reject the <a href="Null_hypothesis" title="Null hypothesis">null hypothesis</a> would imply that the treatment shows no statistically significant effect on the treated in a given test. But as the sample size increases, the same RCT may be able to demonstrate a significant effect of the treatment, even if this effect is small.<a href="#cite_note-Glennerster-2013-63">[63]</a>

<div class="mw-heading mw-heading2"><h2 id="Blinding">Blinding</h2></div>

<div role="note" class="hatnote navigation-not-searchable">Further information: <a href="Blinded_experiment" title="Blinded experiment">Blinded experiment</a></div>

An RCT may be blinded, (also called "masked") by "procedures that prevent study participants, caregivers, or outcome assessors from knowing which intervention was received."<a href="#cite_note-Wood-2008-62">[62]</a> Unlike allocation concealment, blinding is sometimes inappropriate or impossible to perform in an RCT; for example, if an RCT involves a treatment in which active participation of the patient is necessary (e.g., <a href="Physical_therapy" title="Physical therapy">physical therapy</a>), participants cannot be blinded to the intervention.

Traditionally, blinded RCTs have been classified as "single-blind", "double-blind", or "triple-blind"; however, in 2001 and 2006 two studies showed that these terms have different meanings for different people.<a href="#cite_note-Devereaux-2001-64">[64]</a><a href="#cite_note-Haahr-2006-65">[65]</a> The 2010 <a href="Consolidated_Standards_of_Reporting_Trials" title="Consolidated Standards of Reporting Trials">CONSORT Statement</a> specifies that authors and editors should not use the terms "single-blind", "double-blind", and "triple-blind"; instead, reports of blinded RCT should discuss "If done, who was blinded after assignment to interventions (for example, participants, care providers, those assessing outcomes) and how."<a href="#cite_note-Moher-2010-5">[5]</a>

RCTs without blinding are referred to as "unblinded",<a href="#cite_note-Marson-2007-66">[66]</a> "open",<a href="#cite_note-Chan-1995-67">[67]</a> or (if the intervention is a medication) "<a href="Open-label_trial" title="Open-label trial">open-label</a>".<a href="#cite_note-Fukase-2008-68">[68]</a> In 2008 a study concluded that the results of unblinded RCTs tended to be biased toward beneficial effects only if the RCTs' outcomes were subjective as opposed to objective;<a href="#cite_note-Wood-2008-62">[62]</a> for example, in an RCT of treatments for <a href="Multiple_sclerosis" title="Multiple sclerosis">multiple sclerosis</a>, unblinded neurologists (but not the blinded neurologists) felt that the treatments were beneficial.<a href="#cite_note-Noseworthy-1994-69">[69]</a> In pragmatic RCTs, although the participants and providers are often unblinded, it is "still desirable and often possible to blind the assessor or obtain an objective source of data for evaluation of outcomes."<a href="#cite_note-Zwarenstein-2008-49">[49]</a>

<div class="mw-heading mw-heading2"><h2 id="Analysis_of_data">Analysis of data</h2></div>

The types of statistical methods used in RCTs depend on the characteristics of the data and include:

<ul><li>For <a href="Dichotomous" class="mw-redirect" title="Dichotomous">dichotomous</a> (binary) outcome data, <a href="Logistic_regression" title="Logistic regression">logistic regression</a> (e.g., to predict sustained virological response after receipt of <a href="Peginterferon_alfa-2a" title="Peginterferon alfa-2a">peginterferon alfa-2a</a> for <a href="Hepatitis_C" title="Hepatitis C">hepatitis C</a><a href="#cite_note-Manns-2001-70">[70]</a>) and other methods can be used.</li>

<li>For continuous outcome data, <a href="Analysis_of_covariance" title="Analysis of covariance">analysis of covariance</a> (e.g., for changes in blood lipid levels after receipt of <a href="Atorvastatin" title="Atorvastatin">atorvastatin</a> after <a href="Acute_coronary_syndrome" title="Acute coronary syndrome">acute coronary syndrome</a><a href="#cite_note-Schwartz-2001-71">[71]</a>) tests the effects of predictor variables.</li>

<li>For time-to-event outcome data that may be <a href="Censoring_(statistics)" title="Censoring (statistics)">censored</a>, <a href="Survival_analysis" title="Survival analysis">survival analysis</a> (e.g., <a href="Kaplan%E2%80%93Meier_estimator" title="Kaplan–Meier estimator">Kaplan–Meier estimators</a> and <a href="Cox_proportional_hazards_model" class="mw-redirect" title="Cox proportional hazards model">Cox proportional hazards models</a> for time to <a href="Coronary_heart_disease" class="mw-redirect" title="Coronary heart disease">coronary heart disease</a> after receipt of <a href="Hormone_replacement_therapy_(menopause)" class="mw-redirect" title="Hormone replacement therapy (menopause)">hormone replacement therapy in menopause</a><a href="#cite_note-Rossouw-2002-72">[72]</a>) is appropriate.</li></ul>

Regardless of the statistical methods used, important considerations in the analysis of RCT data include:

<ul><li>Whether an RCT should be stopped early due to interim results. For example, RCTs may be stopped early if an intervention produces "larger than expected benefit or harm", or if "investigators find evidence of no important difference between experimental and control interventions."<a href="#cite_note-Moher-2010-5">[5]</a></li>

<li>The extent to which the groups can be analyzed exactly as they existed upon randomization (i.e., whether a so-called "<a href="Intention-to-treat_analysis" title="Intention-to-treat analysis">intention-to-treat analysis</a>" is used). A "pure" intention-to-treat analysis is "possible only when complete outcome data are available" for all randomized subjects;<a href="#cite_note-Hollis-1999-73">[73]</a> when some outcome data are missing, options include analyzing only cases with known outcomes and using <a href="Imputation_(statistics)" title="Imputation (statistics)">imputed</a> data.<a href="#cite_note-Moher-2010-5">[5]</a> Nevertheless, the more that analyses can include all participants in the groups to which they were randomized, the less bias that an RCT will be subject to.<a href="#cite_note-Moher-2010-5">[5]</a></li>

<li>Whether <a href="Subgroup_analysis" title="Subgroup analysis">subgroup analysis</a> should be performed. These are "often discouraged" because <a href="Multiple_comparisons" class="mw-redirect" title="Multiple comparisons">multiple comparisons</a> may produce false positive findings that cannot be confirmed by other studies.<a href="#cite_note-Moher-2010-5">[5]</a></li></ul>

<div class="mw-heading mw-heading2"><h2 id="Reporting_of_results">Reporting of results</h2></div>

The <a href="Consolidated_Standards_of_Reporting_Trials" title="Consolidated Standards of Reporting Trials">CONSORT 2010 Statement</a> is "an evidence-based, minimum set of recommendations for reporting RCTs."<a href="#cite_note-CONSORT-74">[74]</a> The CONSORT 2010 checklist contains 25 items (many with sub-items) focusing on "individually randomised, two group, parallel trials" which are the most common type of RCT.<a href="#cite_note-Schulz-2010-1">[1]</a>

For other RCT study designs, "<a href="Consolidated_Standards_of_Reporting_Trials" title="Consolidated Standards of Reporting Trials">CONSORT extensions</a>" have been published, some examples are:

<ul><li>Consort 2010 Statement: Extension to Cluster Randomised Trials<a href="#cite_note-CONSORT2010-EXTENSION-CLUSTER-75">[75]</a></li>

<li>Consort 2010 Statement: Non-Pharmacologic Treatment Interventions<a href="#cite_note-CONSORT2010-EXTENSION-NON-PHARMACOLOGIC-1-76">[76]</a><a href="#cite_note-CONSORT2010-EXTENSION-NON-PHARMACOLOGIC-2-77">[77]</a></li>

<li>"Reporting of surrogate endpoints in randomised controlled trial reports (CONSORT-Surrogate): extension checklist with explanation and elaboration"<a href="#cite_note-CONSORT-SURROGATE-78">[78]</a></li></ul>

<div class="mw-heading mw-heading3"><h3 id="Relative_importance_and_observational_studies">Relative importance and observational studies</h3></div>

Two studies published in <a href="The_New_England_Journal_of_Medicine" title="The New England Journal of Medicine">The New England Journal of Medicine</a> in 2000 found that <a href="Observational_study" title="Observational study">observational studies</a> and RCTs overall produced similar results.<a href="#cite_note-Benson-2000-79">[79]</a><a href="#cite_note-Concato-2000-80">[80]</a> The authors of the 2000 findings questioned the belief that "observational studies should not be used for defining evidence-based medical care" and that RCTs' results are "evidence of the highest grade."<a href="#cite_note-Benson-2000-79">[79]</a><a href="#cite_note-Concato-2000-80">[80]</a> However, a 2001 study published in <a href="Journal_of_the_American_Medical_Association" class="mw-redirect" title="Journal of the American Medical Association">Journal of the American Medical Association</a> concluded that "discrepancies beyond chance do occur and differences in estimated magnitude of treatment effect are very common" between observational studies and RCTs.<a href="#cite_note-Ioannidis-2001-81">[81]</a> According to a 2014 (updated in 2024) Cochrane review, there is little evidence for significant effect differences between observational studies and randomized controlled trials.<a href="#cite_note-:0-82">[82]</a> To evaluate differences it is necessary to consider things other than design, such as heterogeneity, population, intervention or comparator.<a href="#cite_note-:0-82">[82]</a>

Two other lines of reasoning question RCTs' contribution to scientific knowledge beyond other types of studies:

<ul><li>If study designs are ranked by their potential for new discoveries, then <a href="Anecdotal_evidence#Scientific_context" title="Anecdotal evidence">anecdotal evidence</a> would be at the top of the list, followed by observational studies, followed by RCTs.<a href="#cite_note-Vandenbroucke-2008-83">[83]</a></li>

<li>RCTs may be unnecessary for treatments that have dramatic and rapid effects relative to the expected stable or progressively worse natural course of the condition treated.<a href="#cite_note-Black-1996-84">[84]</a><a href="#cite_note-Glasziou-2007-85">[85]</a> One example is <a href="History_of_cancer_chemotherapy#Combination_chemotherapy" title="History of cancer chemotherapy">combination chemotherapy</a> including <a href="Cisplatin" title="Cisplatin">cisplatin</a> for <a href="Metastasis" title="Metastasis">metastatic</a> <a href="Testicular_cancer" title="Testicular cancer">testicular cancer</a>, which increased the cure rate from 5% to 60% in a 1977 non-randomized study.<a href="#cite_note-Glasziou-2007-85">[85]</a><a href="#cite_note-Einhorn-2002-86">[86]</a></li></ul>

<div class="mw-heading mw-heading3"><h3 id="Interpretation_of_statistical_results">Interpretation of statistical results</h3></div>

Like all statistical methods, RCTs are subject to both <a href="Type_I_and_type_II_errors" title="Type I and type II errors">type I ("false positive") and type II ("false negative") statistical errors</a>. Regarding Type I errors, a typical RCT will use 0.05 (i.e., 1 in 20) as the probability that the RCT will falsely find two equally effective treatments significantly different.<a href="#cite_note-Wittes-2002-87">[87]</a> Regarding Type II errors, despite the publication of a 1978 paper noting that the <a href="Sample_size" class="mw-redirect" title="Sample size">sample sizes</a> of many "negative" RCTs were too small to make definitive conclusions about the negative results,<a href="#cite_note-Freiman-1978-88">[88]</a> by 2005-2006 a sizeable proportion of RCTs still had inaccurate or incompletely reported sample size calculations.<a href="#cite_note-Charles-2009-89">[89]</a>

<div class="mw-heading mw-heading3"><h3 id="Peer_review">Peer review</h3></div>

<a href="Peer_review" title="Peer review">Peer review</a> of results is an important part of the <a href="Scientific_method" title="Scientific method">scientific method</a>. Reviewers examine the study results for potential problems with design that could lead to unreliable results (for example by creating a <a href="Systematic_bias" class="mw-redirect" title="Systematic bias">systematic bias</a>), evaluate the study in the context of related studies and other evidence, and evaluate whether the study can be reasonably considered to have proven its conclusions. To underscore the need for peer review and the danger of overgeneralizing conclusions, two Boston-area medical researchers performed a randomized controlled trial in which they randomly assigned either a parachute or an empty backpack to 23 volunteers who jumped from either a biplane or a helicopter. The study was able to accurately report that parachutes fail to reduce injury compared to empty backpacks. The key context that limited the general applicability of this conclusion was that the aircraft were parked on the ground, and participants had only jumped about two feet.<a href="#cite_note-90">[90]</a>

<div class="mw-heading mw-heading2"><h2 id="Advantages">Advantages</h2></div>

RCTs are considered to be the most reliable form of <a href="Scientific_method" title="Scientific method">scientific evidence</a> in the <a href="Hierarchy_of_evidence" title="Hierarchy of evidence">hierarchy of evidence</a> that influences healthcare policy and practice because RCTs reduce spurious causality and bias. Results of RCTs may be combined in <a href="Systematic_review" title="Systematic review">systematic reviews</a> which are increasingly being used in the conduct of <a href="Evidence-based_practice" title="Evidence-based practice">evidence-based practice</a>. Some examples of scientific organizations' considering RCTs or systematic reviews of RCTs to be the highest-quality evidence available are:

<ul><li>As of 1998, the <a href="National_Health_and_Medical_Research_Council" title="National Health and Medical Research Council">National Health and Medical Research Council</a> of Australia designated "Level I" evidence as that "obtained from a <a href="Systematic_review" title="Systematic review">systematic review</a> of all relevant randomised controlled trials" and "Level II" evidence as that "obtained from at least one properly designed randomised controlled trial."<a href="#cite_note-91">[91]</a></li>

<li>Since at least 2001, in making <a href="Clinical_practice_guideline" class="mw-redirect" title="Clinical practice guideline">clinical practice guideline</a> recommendations the <a href="United_States_Preventive_Services_Task_Force" title="United States Preventive Services Task Force">United States Preventive Services Task Force</a> has considered both a study's design and its <a href="Internal_validity" title="Internal validity">internal validity</a> as indicators of its quality.<a href="#cite_note-Harris-2001-92">[92]</a> It has recognized "evidence obtained from at least one properly randomized controlled trial" with good <a href="Internal_validity" title="Internal validity">internal validity</a> (i.e., a rating of "I-good") as the highest quality evidence available to it.<a href="#cite_note-Harris-2001-92">[92]</a></li>

<li>The <a href="Evidence-based_medicine#Grade_Working_Group" title="Evidence-based medicine">GRADE Working Group</a> concluded in 2008 that "randomised trials without important limitations constitute high quality evidence."<a href="#cite_note-Guyatt-2008-93">[93]</a></li>

<li>For issues involving "Therapy/Prevention, Aetiology/Harm", the <a href="Oxford_Centre_for_Evidence-based_Medicine" class="mw-redirect" title="Oxford Centre for Evidence-based Medicine">Oxford Centre for Evidence-based Medicine</a> as of 2011 defined "Level 1a" evidence as a systematic review of RCTs that are consistent with each other, and "Level 1b" evidence as an "individual RCT (with narrow <a href="Confidence_Interval" class="mw-redirect" title="Confidence Interval">Confidence Interval</a>)."<a href="#cite_note-94">[94]</a></li></ul>

Notable RCTs with unexpected results that contributed to changes in clinical practice include:

<ul><li>After <a href="Food_and_Drug_Administration" title="Food and Drug Administration">Food and Drug Administration</a> approval, the <a href="Antiarrhythmic_agents" class="mw-redirect" title="Antiarrhythmic agents">antiarrhythmic agents</a> <a href="Flecainide" title="Flecainide">flecainide</a> and <a href="Encainide" title="Encainide">encainide</a> came to market in 1986 and 1987 respectively.<a href="#cite_note-Anderson-1997-95">[95]</a> The non-randomized studies concerning the drugs were characterized as "glowing",<a href="#cite_note-Rubin-2006-96">[96]</a> and their sales increased to a combined total of approximately 165,000 prescriptions per month in early 1989.<a href="#cite_note-Anderson-1997-95">[95]</a> In that year, however, a preliminary report of an RCT concluded that the two drugs increased mortality.<a href="#cite_note-CAST-1989-97">[97]</a> Sales of the drugs then decreased.<a href="#cite_note-Anderson-1997-95">[95]</a></li>

<li>Prior to 2002, based on observational studies, it was routine for physicians to prescribe hormone replacement therapy for post-menopausal women to prevent <a href="Myocardial_infarction" title="Myocardial infarction">myocardial infarction</a>.<a href="#cite_note-Rubin-2006-96">[96]</a> In 2002 and 2004, however, published RCTs from the <a href="Women's_Health_Initiative" title="Women's Health Initiative">Women's Health Initiative</a> claimed that women taking hormone replacement therapy with estrogen plus progestin had a higher rate of myocardial infarctions than women on a placebo, and that estrogen-only hormone replacement therapy caused no reduction in the incidence of coronary heart disease.<a href="#cite_note-Rossouw-2002-72">[72]</a><a href="#cite_note-Anderson-2004-98">[98]</a> Possible explanations for the discrepancy between the observational studies and the RCTs involved differences in methodology, in the hormone regimens used, and in the populations studied.<a href="#cite_note-Grodstein-2003-99">[99]</a><a href="#cite_note-Vandenbroucke-2009-100">[100]</a> The use of hormone replacement therapy decreased after publication of the RCTs.<a href="#cite_note-Hsu-2009-101">[101]</a></li></ul>

<div class="mw-heading mw-heading2"><h2 id="Disadvantages">Disadvantages</h2></div>

Many papers discuss the disadvantages of RCTs.<a href="#cite_note-Black-1996-84">[84]</a><a href="#cite_note-Bell_&_Peck-2012-102">[102]</a><a href="#cite_note-Sanson-Fisher-2007-103">[103]</a> Among the most frequently cited drawbacks are:

<div class="mw-heading mw-heading3"><h3 id="Time_and_costs">Time and costs</h3></div>

RCTs can be expensive;<a href="#cite_note-Sanson-Fisher-2007-103">[103]</a> one study found 28 <a href="Phase_III_clinical_trials" class="mw-redirect" title="Phase III clinical trials">Phase III</a> RCTs funded by the <a href="National_Institute_of_Neurological_Disorders_and_Stroke" title="National Institute of Neurological Disorders and Stroke">National Institute of Neurological Disorders and Stroke</a> prior to 2000 with a total cost of US$335 million,<a href="#cite_note-Johnston-2006-104">[104]</a> for a <a href="Mean" title="Mean">mean</a> cost of US$12 million per RCT. Nevertheless, the <a href="Return_on_investment" title="Return on investment">return on investment</a> of RCTs may be high, in that the same study projected that the 28 RCTs produced a "net benefit to society at 10-years" of 46 times the cost of the trials program, based on evaluating a <a href="Quality-adjusted_life_year" title="Quality-adjusted life year">quality-adjusted life year</a> as equal to the prevailing mean <a href="Per_capita" title="Per capita">per capita</a> <a href="Gross_domestic_product" title="Gross domestic product">gross domestic product</a>.<a href="#cite_note-Johnston-2006-104">[104]</a>

The conduct of an RCT takes several years until being published; thus, data is restricted from the medical community for long years and may be of less relevance at time of publication.<a href="#cite_note-CaseReport-105">[105]</a>

It is costly to maintain RCTs for the years or decades that would be ideal for evaluating some interventions.<a href="#cite_note-Black-1996-84">[84]</a><a href="#cite_note-Sanson-Fisher-2007-103">[103]</a>

Interventions to prevent events that occur only infrequently (e.g., <a href="Sudden_infant_death_syndrome" class="mw-redirect" title="Sudden infant death syndrome">sudden infant death syndrome</a>) and uncommon adverse outcomes (e.g., a rare side effect of a drug) would require RCTs with extremely large sample sizes and may, therefore, best be assessed by observational studies.<a href="#cite_note-Black-1996-84">[84]</a>

Due to the costs of running RCTs, these usually only inspect one variable or very few variables, rarely reflecting the full picture of a complicated medical situation; whereas the <a href="Case_report" title="Case report">case report</a>, for example, can detail many aspects of the patient's <a href="Medicine" title="Medicine">medical</a> situation (e.g. <a href="Patient_history" class="mw-redirect" title="Patient history">patient history</a>, <a href="Physical_examination" title="Physical examination">physical examination</a>, <a href="Diagnosis" title="Diagnosis">diagnosis</a>, <a href="Psychosocial" title="Psychosocial">psychosocial</a> aspects, follow up).<a href="#cite_note-CaseReport-105">[105]</a>

<div class="mw-heading mw-heading3"><h3 id="Conflict_of_interest_dangers">Conflict of interest dangers</h3></div>

A 2011 study done to disclose possible <a href="Conflicts_of_interest" class="mw-redirect" title="Conflicts of interest">conflicts of interests</a> in underlying research studies used for medical meta-analyses reviewed 29 meta-analyses and found that conflicts of interests in the studies underlying the meta-analyses were rarely disclosed. The 29 meta-analyses included 11 from general medicine journals; 15 from specialty medicine journals, and 3 from the <a href="Cochrane_Collaboration" class="mw-redirect" title="Cochrane Collaboration">Cochrane</a> Database of Systematic Reviews. The 29 meta-analyses reviewed an aggregate of 509 randomized controlled trials (RCTs). Of these, 318 RCTs reported funding sources with 219 (69%) industry funded. 132 of the 509 RCTs reported author conflict of interest disclosures, with 91 studies (69%) disclosing industry financial ties with one or more authors. The information was, however, seldom reflected in the meta-analyses. Only two (7%) reported RCT funding sources and none reported RCT author-industry ties. The authors concluded "without acknowledgment of COI due to industry funding or author industry financial ties from RCTs included in meta-analyses, readers' understanding and appraisal of the evidence from the meta-analysis may be compromised."<a href="#cite_note-106">[106]</a>

Some RCTs are fully or partly funded by the health care industry (e.g., the <a href="Pharmaceutical_industry" title="Pharmaceutical industry">pharmaceutical industry</a>) as opposed to government, nonprofit, or other sources. A systematic review published in 2003 found four 1986–2002 articles comparing industry-sponsored and nonindustry-sponsored RCTs, and in all the articles there was a correlation of industry sponsorship and positive study outcome.<a href="#cite_note-Bekelman-2003-107">[107]</a> A 2004 study of 1999–2001 RCTs published in leading medical and surgical journals determined that industry-funded RCTs "are more likely to be associated with statistically significant pro-industry findings."<a href="#cite_note-Bhandari-2004-108">[108]</a> These results have been mirrored in trials in surgery, where although industry funding did not affect the rate of trial discontinuation it was however associated with a lower odds of publication for completed trials.<a href="#cite_note-Chapman-2014-109">[109]</a> One possible reason for the pro-industry results in industry-funded published RCTs is <a href="Publication_bias" title="Publication bias">publication bias</a>.<a href="#cite_note-Bhandari-2004-108">[108]</a> Other authors have cited the differing goals of academic and industry sponsored research as contributing to the difference. Commercial sponsors may be more focused on performing trials of drugs that have already shown promise in early stage trials, and on replicating previous positive results to fulfill regulatory requirements for drug approval.<a href="#cite_note-110">[110]</a>

<div class="mw-heading mw-heading3"><h3 id="Ethics_2">Ethics</h3></div>

If a <a href="Disruptive_innovation" title="Disruptive innovation">disruptive innovation</a> in medical technology is developed, it may be difficult to test this ethically in an RCT if it becomes "obvious" that the control subjects have poorer outcomes—either due to other foregoing testing, or within the initial phase of the RCT itself. Ethically it may be necessary to abort the RCT prematurely, and getting ethics approval (and patient agreement) to withhold the innovation from the control group in future RCTs may not be feasible.

Historical control trials (HCT) exploit the data of previous RCTs to reduce the sample size; however, these approaches are controversial in the scientific community and must be handled with care.<a href="#cite_note-111">[111]</a>

<div class="mw-heading mw-heading2"><h2 id="In_social_science">In social science</h2></div>

Due to the recent emergence of RCTs in social science, the use of RCTs in social sciences is a contested issue. Some writers from a medical or health background have argued that existing research in a range of social science disciplines lacks rigour, and should be improved by greater use of randomized control trials.<a href="#cite_note-112">[112]</a>

<div class="mw-heading mw-heading3"><h3 id="Transport_science">Transport science</h3></div>

Researchers in transport science argue that public spending on programmes such as school travel plans could not be justified unless their efficacy is demonstrated by randomized controlled trials.<a href="#cite_note-Rowland_et_al_(2003)-113">[113]</a> Graham-Rowe and colleagues<a href="#cite_note-Graham-Rowe_et_al_(2011)-114">[114]</a> reviewed 77 evaluations of transport interventions found in the literature, categorising them into 5 "quality levels". They concluded that most of the studies were of low quality and advocated the use of randomized controlled trials wherever possible in future transport research.

Dr. Steve Melia<a href="#cite_note-Melia_2011-115">[115]</a> took issue with these conclusions, arguing that claims about the advantages of RCTs, in establishing causality and avoiding bias, have been exaggerated. He proposed the following eight criteria for the use of RCTs in contexts where interventions must change human behaviour to be effective:

The intervention:

<ol><li>Has not been applied to all members of a unique group of people (e.g. the population of a whole country, all employees of a unique organisation etc.)</li>

<li>Is applied in a context or setting similar to that which applies to the control group</li>

<li>Can be isolated from other activities—and the purpose of the study is to assess this isolated effect</li>

<li>Has a short timescale between its implementation and maturity of its effects</li></ol>

And the causal mechanisms:

<ol><li value="5">Are either known to the researchers, or else all possible alternatives can be tested</li>

<li>Do not involve significant feedback mechanisms between the intervention group and external environments</li>

<li>Have a stable and predictable relationship to exogenous factors</li>

<li>Would act in the same way if the control group and intervention group were reversed</li></ol>

<div class="mw-heading mw-heading3"><h3 id="Criminology">Criminology</h3></div>

A 2005 review found 83 randomized experiments in criminology published in 1982–2004, compared with only 35 published in 1957–1981.<a href="#cite_note-Farrington-2005-116">[116]</a> The authors classified the studies they found into five categories: "policing", "prevention", "corrections", "court", and "community".<a href="#cite_note-Farrington-2005-116">[116]</a> Focusing only on offending behavior programs, Hollin (2008) argued that RCTs may be difficult to implement (e.g., if an RCT required "passing sentences that would randomly assign offenders to programmes") and therefore that experiments with <a href="Quasi-experimental_design" class="mw-redirect" title="Quasi-experimental design">quasi-experimental design</a> are still necessary.<a href="#cite_note-117">[117]</a>

<div class="mw-heading mw-heading3"><h3 id="Education">Education</h3></div>

RCTs have been used in evaluating a number of educational interventions. Between 1980 and 2016, over 1,000 reports of RCTs have been published.<a href="#cite_note-118">[118]</a> For example, a 2009 study randomized 260 elementary school teachers' classrooms to receive or not receive a program of behavioral screening, classroom intervention, and parent training, and then measured the behavioral and academic performance of their students.<a href="#cite_note-119">[119]</a> Another 2009 study randomized classrooms for 678 first-grade children to receive a classroom-centered intervention, a parent-centered intervention, or no intervention, and then followed their academic outcomes through age 19.<a href="#cite_note-120">[120]</a>

<div class="mw-heading mw-heading2"><h2 id="Criticism">Criticism</h2></div>

A 2018 review of the 10 most cited randomised controlled trials noted poor distribution of background traits, difficulties with blinding, and discussed other assumptions and biases inherent in randomised controlled trials. These include the "unique time period assessment bias", the "background traits remain constant assumption", the "average treatment effects limitation", the "simple treatment at the individual level limitation", the "all preconditions are fully met assumption", the "quantitative variable limitation" and the "placebo only or conventional treatment only limitation".<a href="#cite_note-121">[121]</a>

<ul><li><a href="Drug_development" title="Drug development">Drug development</a></li>

<li><a href="Hypothesis_testing" class="mw-redirect" title="Hypothesis testing">Hypothesis testing</a></li>

<li><a href="Impact_evaluation" title="Impact evaluation">Impact evaluation</a></li>

<li><a href="Jadad_scale" title="Jadad scale">Jadad scale</a></li>

<li><a href="Pipeline_planning" title="Pipeline planning">Pipeline planning</a></li>

<li><a href="Patient_and_public_involvement" title="Patient and public involvement">Patient and public involvement</a></li>

<li><a href="Observational_study" title="Observational study">Observational study</a></li>

<li><a href="Blinded_experiment" title="Blinded experiment">Blinded experiment</a></li>

<li><a href="Statistical_inference" title="Statistical inference">Statistical inference</a></li>

<li><a href="Royal_Commission_on_Animal_Magnetism" title="Royal Commission on Animal Magnetism">Royal Commission on Animal Magnetism</a> – 1784 French scientific bodies' investigations involving systematic controlled trials</li></ul>

<div class="mw-heading mw-heading2"><h2 id="References">References</h2></div>

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According to Denis Conniffe:

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.mw-parser-output .templatequote{overflow:hidden;margin:1em 0;padding:0 32px}.mw-parser-output .templatequotecite{line-height:1.5em;text-align:left;margin-top:0}@media(min-width:500px){.mw-parser-output .templatequotecite{padding-left:1.6em}}

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</style><blockquote class="templatequote">

Ronald A. Fisher was "interested in application and in the popularization

of statistical methods and his early book <a href="Statistical_Methods_for_Research_Workers" title="Statistical Methods for Research Workers">Statistical Methods for Research Workers</a>, published in 1925, went through many editions and

motivated and influenced the practical use of statistics in many fields of

study. His Design of Experiments (1935) [promoted] statistical technique and application. In that book he

emphasized examples and how to design experiments systematically from

a statistical point of view. The mathematical justification of the methods

described was not stressed and, indeed, proofs were often barely sketched

or omitted altogether ..., a fact which led <a href="Henry_Mann" title="Henry Mann">H. B. Mann</a> to fill the gaps with a rigorous mathematical treatment in his well known treatise, <a href="#CITEREFMann1949">Mann (1949)</a>."

</blockquote>

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<li id="cite_note-118"><a href="#cite_ref-118">^</a> <cite id="CITEREFConnollyKeenanUrbanska2018" class="citation journal cs1">Connolly P, Keenan C, Urbanska K (2018-07-09). <a rel="nofollow" class="external text" href="https://pure.qub.ac.uk/portal/en/publications/the-trials-of-evidencebased-practice-in-education-a-systematic-review-of-randomised-controlled-trials-in-education-research-19802016(34e5d239-e91a-4807-96eb-a926022cbb14).html">"The trials of evidence-based practice in education: a systematic review of randomised controlled trials in education research 1980–2016"</a>. Educational Research. 60 (3): 276–291. <a href="Doi_(identifier)" class="mw-redirect" title="Doi (identifier)">doi</a>:<a rel="nofollow" class="external text" href="https://doi.org/10.1080%2F00131881.2018.1493353">10.1080/00131881.2018.1493353</a>. <a href="ISSN_(identifier)" class="mw-redirect" title="ISSN (identifier)">ISSN</a> <a rel="nofollow" class="external text" href="https://search.worldcat.org/issn/0013-1881">0013-1881</a>.</cite>

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</ol></div>

<div class="mw-heading mw-heading2"><h2 id="Further_reading">Further reading</h2></div>

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<ul><li><cite id="CITEREFBland2008" class="citation web cs1">Bland M (19 March 2008). <a rel="nofollow" class="external text" href="http://www-users.york.ac.uk/~mb55/guide/randsery.htm">"Directory of randomisation software and services"</a>. University of York.</cite></li>

<li><cite id="CITEREFEvansThorntonChalmers2010" class="citation book cs1">Evans I, Thornton H, Chalmers I (2010). <a rel="nofollow" class="external text" href="https://web.archive.org/web/20101225093331/http://www.jameslindlibrary.org/pdf/testing-treatments.pdf">Testing treatments: better research for better health care</a> (PDF). London: Pinter & Martin. <a href="ISBN_(identifier)" class="mw-redirect" title="ISBN (identifier)">ISBN</a> <bdi>978-1-905177-35-6</bdi>. Archived from <a rel="nofollow" class="external text" href="http://www.jameslindlibrary.org/pdf/testing-treatments.pdf">the original</a> (PDF) on 2010-12-25.</cite></li>

<li><cite id="CITEREFGelband1983" class="citation book cs1">Gelband H (1983). <a rel="nofollow" class="external text" href="https://web.archive.org/web/20160303191654/http://www.fas.org/ota/reports/8310.pdf">The impact of randomized clinical trials on health policy and medical practice: background paper</a> (PDF). Washington, DC: U.S. Congress, Office of Technology Assessment. OTA-BP-H-22. Archived from <a rel="nofollow" class="external text" href="https://fas.org/ota/reports/8310.pdf">the original</a> (PDF) on 2016-03-03.</cite></li>

<li><cite class="citation web cs1"><a rel="nofollow" class="external text" href="http://reflect-statement.org/">"REFLECT (Reporting guidElines For randomized controLled trials for livEstoCk and food safeTy) Statement"</a>.</cite></li>

<li><cite id="CITEREFWathenCook2006" class="citation web cs1">Wathen JK, Cook JD (12 July 2006). <a rel="nofollow" class="external text" href="http://www.mdanderson.org/education-and-research/departments-programs-and-labs/departments-and-divisions/division-of-quantitative-sciences/research/biostats-utmdabtr-002-06.pdf">"Power and bias in adaptively randomized clinical trials"</a> (PDF). M.D. Anderson Cancer Center, University of Texas.</cite></li></ul>

</div>

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</style><div id="Clinical_research_and_experimental_design505" style="font-size:114%;margin:0 4em"><a href="Clinical_research" title="Clinical research">Clinical research</a> and <a href="Design_of_experiments" title="Design of experiments">experimental design</a></div></th></tr><tr><th scope="row" class="navbox-group" style="width:1%">Overview</th><td class="navbox-list-with-group navbox-list navbox-odd" style="width:100%;padding:0"><div style="padding:0 0.25em">

<ul><li><a href="Clinical_trial" title="Clinical trial">Clinical trial</a>

<ul><li><a href="Protocol_(science)" title="Protocol (science)">Trial protocols</a></li>

<li><a href="Adaptive_clinical_trial" class="mw-redirect" title="Adaptive clinical trial">Adaptive clinical trial</a></li></ul></li>

<li><a href="Academic_clinical_trials" class="mw-redirect" title="Academic clinical trials">Academic clinical trials</a></li>

<li><a href="Clinical_study_design" title="Clinical study design">Clinical study design</a></li>

<li><a href="Evidence-based_medicine" title="Evidence-based medicine">Evidence-based medicine</a></li>

<li><a href="Real_world_evidence" title="Real world evidence">Real world evidence</a></li>

<li><a href="Patient_and_public_involvement" title="Patient and public involvement">Patient and public involvement</a></li></ul>

</div></td></tr><tr><th scope="row" class="navbox-group" style="width:1%"><a href="Scientific_control" title="Scientific control">Controlled study</a> (<a href="Hierarchy_of_evidence#USA" title="Hierarchy of evidence">EBM I to II-1</a>)</th><td class="navbox-list-with-group navbox-list navbox-even" style="width:100%;padding:0"><div style="padding:0 0.25em">

<ul><li><a href="Experiment" title="Experiment">Scientific experiment</a></li>

<li><a href="Blind_experiment" class="mw-redirect" title="Blind experiment">Blind experiment</a></li>

<li><a href="Open-label_trial" title="Open-label trial">Open-label trial</a></li></ul></li>

<li><a href="Adaptive_clinical_trial" class="mw-redirect" title="Adaptive clinical trial">Adaptive clinical trial</a>

<ul><li><a href="Platform_trial" title="Platform trial">Platform trial</a></li></ul></li></ul>

</div></td></tr><tr><th scope="row" class="navbox-group" style="width:1%"><a href="Observational_study" title="Observational study">Observational study</a> (<a href="Hierarchy_of_evidence#USA" title="Hierarchy of evidence">EBM II-2 to II-3</a>)</th><td class="navbox-list-with-group navbox-list navbox-odd" style="width:100%;padding:0"><div style="padding:0 0.25em">

<ul><li><a href="Cross-sectional_study" title="Cross-sectional study">Cross-sectional study</a> vs. <a href="Longitudinal_study" title="Longitudinal study">Longitudinal study</a>, <a href="Ecological_study" title="Ecological study">Ecological study</a></li>

<li><a href="Cohort_study" title="Cohort study">Cohort study</a>

<ul><li><a href="Retrospective_cohort_study" title="Retrospective cohort study">Retrospective</a></li>

<li><a href="Prospective_cohort_study" title="Prospective cohort study">Prospective</a></li></ul></li>

<li><a href="Case%E2%80%93control_study" title="Case–control study">Case–control study</a> (<a href="Nested_case%E2%80%93control_study" title="Nested case–control study">Nested case–control study</a>)</li>

<li><a href="Case_series" title="Case series">Case series</a></li>

<li><a href="Case_study" title="Case study">Case study</a></li>

<li><a href="Case_report" title="Case report">Case report</a></li></ul>

</div></td></tr><tr><th scope="row" class="navbox-group" style="width:1%"><a href="Outcome_measure" title="Outcome measure">Measures</a></th><td class="navbox-list-with-group navbox-list navbox-odd" style="width:100%;padding:0"><div style="padding:0 0.25em"></div><table class="nowraplinks navbox-subgroup" style="border-spacing:0"><tbody><tr><th scope="row" class="navbox-group" style="width:1%"><a href="Epidemiological_methods" class="mw-redirect" title="Epidemiological methods">Occurrence</a></th><td class="navbox-list-with-group navbox-list navbox-even" style="width:100%;padding:0"><div style="padding:0 0.25em"><a href="Incidence_(epidemiology)" title="Incidence (epidemiology)">Incidence</a>, <a href="Cumulative_incidence" class="mw-redirect" title="Cumulative incidence">Cumulative incidence</a>, <a href="Prevalence" title="Prevalence">Prevalence</a>, <a href="Point_prevalence" class="mw-redirect" title="Point prevalence">Point prevalence</a>, <a href="Period_prevalence" class="mw-redirect" title="Period prevalence">Period prevalence</a></div></td></tr><tr><th scope="row" class="navbox-group" style="width:1%"><a href="Epidemiological_methods" class="mw-redirect" title="Epidemiological methods">Association</a></th><td class="navbox-list-with-group navbox-list navbox-odd" style="width:100%;padding:0"><div style="padding:0 0.25em"><a href="Risk_difference" title="Risk difference">Risk difference</a>, <a href="Number_needed_to_treat" title="Number needed to treat">Number needed to treat</a>, <a href="Number_needed_to_harm" title="Number needed to harm">Number needed to harm</a>, <a href="Risk_ratio" class="mw-redirect" title="Risk ratio">Risk ratio</a>, <a href="Relative_risk_reduction" title="Relative risk reduction">Relative risk reduction</a>, <a href="Odds_ratio" title="Odds ratio">Odds ratio</a>, <a href="Hazard_ratio" title="Hazard ratio">Hazard ratio</a></div></td></tr><tr><th scope="row" class="navbox-group" style="width:1%"><a href="Population_impact_measure" title="Population impact measure">Population impact</a></th><td class="navbox-list-with-group navbox-list navbox-even" style="width:100%;padding:0"><div style="padding:0 0.25em"><a href="Attributable_fraction_among_the_exposed" title="Attributable fraction among the exposed">Attributable fraction among the exposed</a>, <a href="Attributable_fraction_for_the_population" title="Attributable fraction for the population">Attributable fraction for the population</a>, <a href="Preventable_fraction_among_the_unexposed" title="Preventable fraction among the unexposed">Preventable fraction among the unexposed</a>, <a href="Preventable_fraction_for_the_population" title="Preventable fraction for the population">Preventable fraction for the population</a></div></td></tr><tr><th scope="row" class="navbox-group" style="width:1%"><a href="Epidemiological_methods" class="mw-redirect" title="Epidemiological methods">Other</a></th><td class="navbox-list-with-group navbox-list navbox-odd" style="width:100%;padding:0"><div style="padding:0 0.25em"><a href="Clinical_endpoint" title="Clinical endpoint">Clinical endpoint</a>, <a href="Virulence" title="Virulence">Virulence</a>, <a href="Infectivity" title="Infectivity">Infectivity</a>, <a href="Mortality_rate" title="Mortality rate">Mortality rate</a>, <a href="Morbidity" class="mw-redirect" title="Morbidity">Morbidity</a>, <a href="Case_fatality_rate" title="Case fatality rate">Case fatality rate</a>, <a href="Specificity_and_sensitivity" class="mw-redirect" title="Specificity and sensitivity">Specificity and sensitivity</a>, <a href="Likelihood_ratios_in_diagnostic_testing" title="Likelihood ratios in diagnostic testing">Likelihood-ratios</a>, <a href="Pre-_and_post-test_probability" title="Pre- and post-test probability">Pre- and post-test probability</a></div></td></tr></tbody></table><div></div></td></tr><tr><th scope="row" class="navbox-group" style="width:1%">Trial/test types</th><td class="navbox-list-with-group navbox-list navbox-even" style="width:100%;padding:0"><div style="padding:0 0.25em">

<ul><li><a href="In_vitro" title="In vitro">In vitro</a></li>

<li><a href="Animal_testing" title="Animal testing">Animal testing</a></li>

<li><a href="Animal_testing_on_non-human_primates" title="Animal testing on non-human primates">Animal testing on non-human primates</a></li>

<li><a href="First-in-man_study" class="mw-redirect" title="First-in-man study">First-in-man study</a></li>

<li><a href="Multicenter_trial" title="Multicenter trial">Multicenter trial</a></li>

<li><a href="Seeding_trial" title="Seeding trial">Seeding trial</a></li>

<li><a href="Vaccine_trial" title="Vaccine trial">Vaccine trial</a></li></ul>

</div></td></tr><tr><th scope="row" class="navbox-group" style="width:1%"><a href="Analysis_of_clinical_trials" title="Analysis of clinical trials">Analysis of clinical trials</a></th><td class="navbox-list-with-group navbox-list navbox-odd" style="width:100%;padding:0"><div style="padding:0 0.25em">

<ul><li><a href="Risk%E2%80%93benefit_ratio" title="Risk–benefit ratio">Risk–benefit ratio</a></li>

<li><a href="Systematic_review" title="Systematic review">Systematic review</a></li>

<li><a href="Reproducibility" title="Reproducibility">Replication</a></li>

<li><a href="Meta-analysis" title="Meta-analysis">Meta-analysis</a></li>

<li><a href="Intention-to-treat_analysis" title="Intention-to-treat analysis">Intention-to-treat analysis</a></li></ul>

</div></td></tr><tr><th scope="row" class="navbox-group" style="width:1%">Interpretation of results</th><td class="navbox-list-with-group navbox-list navbox-even" style="width:100%;padding:0"><div style="padding:0 0.25em">

<ul><li><a href="Selection_bias" title="Selection bias">Selection bias</a></li>

<li><a href="Survivorship_bias" title="Survivorship bias">Survivorship bias</a></li>

<li><a href="Correlation_does_not_imply_causation" title="Correlation does not imply causation">Correlation does not imply causation</a></li>

<li><a href="Null_result" title="Null result">Null result</a></li>

<li><a href="Sex_as_a_biological_variable" title="Sex as a biological variable">Sex as a biological variable</a></li></ul>

</div></td></tr><tr><td class="navbox-abovebelow" colspan="2"><div>

<ul><li>Category</li>

<li><a href="Glossary_of_clinical_research" title="Glossary of clinical research">Glossary</a></li>

<li><a href="List_of_clinical_research_topics" class="mw-redirect" title="List of clinical research topics">List of topics</a></li></ul>

</div></td></tr></tbody></table></div>

<div class="navbox-styles"></div><div role="navigation" class="navbox" aria-labelledby="Design_of_experiments708" style="padding:3px"><table class="nowraplinks hlist mw-collapsible autocollapse navbox-inner" style="border-spacing:0;background:transparent;color:inherit"><tbody><tr><th scope="col" class="navbox-title" colspan="2"><div id="Design_of_experiments708" style="font-size:114%;margin:0 4em"><a href="Design_of_experiments" title="Design of experiments">Design of experiments</a></div></th></tr><tr><th scope="row" class="navbox-group" style="width:1%"><a href="Scientific_method" title="Scientific method">Scientific method</a></th><td class="navbox-list-with-group navbox-list navbox-odd" style="width:100%;padding:0"><div style="padding:0 0.25em">

<ul><li><a href="Experiment" title="Experiment">Scientific experiment</a></li>

<li><a href="Design_of_experiments" title="Design of experiments">Statistical design</a></li>

<li><a href="Scientific_control" title="Scientific control">Control</a></li>

<li><a href="Internal_validity" title="Internal validity">Internal</a> and <a href="External_validity" title="External validity">external</a> <a href="Validity_(statistics)" title="Validity (statistics)">validity</a></li>

<li><a href="Experimental_unit" class="mw-redirect" title="Experimental unit">Experimental unit</a></li>

<li><a href="Blind_experiment" class="mw-redirect" title="Blind experiment">Blinding</a></li></ul>

<ul><li><a href="Optimal_design" class="mw-redirect" title="Optimal design">Optimal design</a>: <a href="Bayesian_experimental_design" title="Bayesian experimental design">Bayesian</a></li>

<li><a href="Random_assignment" title="Random assignment">Random assignment</a></li>

<li><a href="Randomization" title="Randomization">Randomization</a></li>

<li><a href="Restricted_randomization" title="Restricted randomization">Restricted randomization</a></li>

<li><a href="Replication_(statistics)" title="Replication (statistics)">Replication versus subsampling</a></li>

<li><a href="Sample_size" class="mw-redirect" title="Sample size">Sample size</a></li></ul>

</div></td></tr><tr><th scope="row" class="navbox-group" style="width:1%"><a href="Glossary_of_experimental_design" title="Glossary of experimental design">Treatment</a> and <a href="Blocking_(statistics)" title="Blocking (statistics)">blocking</a></th><td class="navbox-list-with-group navbox-list navbox-even" style="width:100%;padding:0"><div style="padding:0 0.25em">

<ul><li><a href="Glossary_of_experimental_design" title="Glossary of experimental design">Treatment</a></li>

<li><a href="Effect_size" title="Effect size">Effect size</a></li>

<li><a href="Contrast_(statistics)" title="Contrast (statistics)">Contrast</a></li>

<li><a href="Interaction_(statistics)" title="Interaction (statistics)">Interaction</a></li>

<li><a href="Confounding" title="Confounding">Confounding</a></li>

<li><a href="Orthogonality#Statistics,_econometrics,_and_economics" title="Orthogonality">Orthogonality</a></li>

<li><a href="Blocking_(statistics)" title="Blocking (statistics)">Blocking</a></li>

<li><a href="Covariate" class="mw-redirect" title="Covariate">Covariate</a></li>

<li><a href="Nuisance_variable" title="Nuisance variable">Nuisance variable</a></li></ul>

</div></td></tr><tr><th scope="row" class="navbox-group" style="width:1%"><a href="Statistical_model" title="Statistical model">Models</a> and <a href="Statistical_inference" title="Statistical inference">inference</a></th><td class="navbox-list-with-group navbox-list navbox-odd" style="width:100%;padding:0"><div style="padding:0 0.25em">

<ul><li><a href="Linear_regression" title="Linear regression">Linear regression</a></li>

<li><a href="Ordinary_least_squares" title="Ordinary least squares">Ordinary least squares</a></li>

<li><a href="Bayesian_linear_regression" title="Bayesian linear regression">Bayesian</a></li></ul>

<ul><li><a href="Random_effect" class="mw-redirect" title="Random effect">Random effect</a></li>

<li><a href="Mixed_model" title="Mixed model">Mixed model</a></li>

<li><a href="Hierarchical_linear_modeling" class="mw-redirect" title="Hierarchical linear modeling">Hierarchical model:</a> <a href="Hierarchical_Bayes_model" class="mw-redirect" title="Hierarchical Bayes model">Bayesian</a></li></ul>

<ul><li><a href="Analysis_of_variance" title="Analysis of variance">Analysis of variance (Anova)</a></li>

<li><a href="Cochran's_theorem" title="Cochran's theorem">Cochran's theorem</a></li>

<li><a href="Multivariate_analysis_of_variance" title="Multivariate analysis of variance">Manova (multivariate)</a></li>

<li><a href="Analysis_of_covariance" title="Analysis of covariance">Ancova (covariance)</a></li></ul>

<ul><li><a href="Comparing_means" class="mw-redirect" title="Comparing means">Compare means</a></li>

<li><a href="Multiple_comparison" class="mw-redirect" title="Multiple comparison">Multiple comparison</a></li></ul>

</div></td></tr><tr><th scope="row" class="navbox-group" style="width:1%"><a href="Design_of_experiments" title="Design of experiments">Designs</a> <a href="Completely_randomized_design" title="Completely randomized design">Completely randomized</a></th><td class="navbox-list-with-group navbox-list navbox-even" style="width:100%;padding:0"><div style="padding:0 0.25em">

<ul><li><a href="Factorial_experiment" title="Factorial experiment">Factorial</a></li>

<li><a href="Fractional_factorial_design" title="Fractional factorial design">Fractional factorial</a></li>

<li><a href="Plackett-Burman_design" class="mw-redirect" title="Plackett-Burman design">Plackett–Burman</a></li>

<li><a href="Taguchi_methods" title="Taguchi methods">Taguchi</a></li></ul>

<ul><li><a href="Response_surface_methodology" title="Response surface methodology">Response surface methodology</a></li>

<li><a href="Polynomial_and_rational_function_modeling" title="Polynomial and rational function modeling">Polynomial and rational modeling</a></li>

<li><a href="Box%E2%80%93Behnken_design" title="Box–Behnken design">Box–Behnken</a></li>

<li><a href="Central_composite_design" title="Central composite design">Central composite</a></li></ul>

<ul><li><a href="Randomized_block_design" class="mw-redirect" title="Randomized block design">Block</a></li>

<li><a href="Generalized_randomized_block_design" title="Generalized randomized block design">Generalized randomized block design</a> (GRBD)</li>

<li><a href="Latin_square" title="Latin square">Latin square</a></li>

<li><a href="Graeco-Latin_square" class="mw-redirect" title="Graeco-Latin square">Graeco-Latin square</a></li>

<li><a href="Orthogonal_array" title="Orthogonal array">Orthogonal array</a></li>

<li><a href="Latin_hypercube_sampling" title="Latin hypercube sampling">Latin hypercube</a> <a href="Repeated_measures_design" title="Repeated measures design">Repeated measures design</a></li>

<li><a href="Crossover_study" title="Crossover study">Crossover study</a></li></ul>

<li><a href="Sequential_analysis" title="Sequential analysis">Sequential analysis</a></li>

<li><a href="Sequential_probability_ratio_test" title="Sequential probability ratio test">Sequential probability ratio test</a></li></ul>

</div></td></tr><tr><td class="navbox-abovebelow" colspan="2"><div>

<ul><li><a href="Glossary_of_experimental_design" title="Glossary of experimental design">Glossary</a></li>

<li>Category</li>

<li> <a href="Portal%3AMathematics" title="Portal:Mathematics">Mathematics portal</a></li>

<li><a href="Outline_of_statistics" title="Outline of statistics">Statistical outline</a></li>

<li><a href="List_of_statistics_articles" title="List of statistics articles">Statistical topics</a></li></ul>

</div></td></tr></tbody></table></div>

<div class="navbox-styles"></div><div role="navigation" class="navbox" aria-labelledby="Statistics654" style="padding:3px"><table class="nowraplinks hlist mw-collapsible mw-collapsed navbox-inner" style="border-spacing:0;background:transparent;color:inherit"><tbody><tr><th scope="col" class="navbox-title" colspan="2"><div id="Statistics654" style="font-size:114%;margin:0 4em"><a href="Statistics" title="Statistics">Statistics</a></div></th></tr><tr><td class="navbox-abovebelow" colspan="2"><div>

<ul><li><a href="Outline_of_statistics" title="Outline of statistics">Outline</a></li>

<li><a href="List_of_statistics_articles" title="List of statistics articles">Index</a></li></ul>

</div></td></tr><tr><td colspan="2" class="navbox-list navbox-odd" style="width:100%;padding:0"><div style="padding:0 0.25em"></div><table class="nowraplinks mw-collapsible mw-collapsed navbox-subgroup" style="border-spacing:0"><tbody><tr><th scope="col" class="navbox-title" colspan="2"><div id="Descriptive_statistics654" style="font-size:114%;margin:0 4em"><a href="Descriptive_statistics" title="Descriptive statistics">Descriptive statistics</a></div></th></tr><tr><td colspan="2" class="navbox-list navbox-odd" style="width:100%;padding:0"><div style="padding:0 0.25em"></div><table class="nowraplinks navbox-subgroup" style="border-spacing:0"><tbody><tr><th scope="row" class="navbox-group" style="width:12.5em"><a href="Continuous_probability_distribution" class="mw-redirect" title="Continuous probability distribution">Continuous data</a></th><td class="navbox-list-with-group navbox-list navbox-odd" style="padding:0"><div style="padding:0 0.25em"></div><table class="nowraplinks navbox-subgroup" style="border-spacing:0"><tbody><tr><th scope="row" class="navbox-group" style="width:1%;font-weight:normal;"><a href="Central_tendency" title="Central tendency">Center</a></th><td class="navbox-list-with-group navbox-list navbox-odd" style="width:100%;padding:0"><div style="padding:0 0.25em">

<ul><li><a href="Arithmetic_mean" title="Arithmetic mean">Arithmetic</a></li>

<li><a href="Arithmetic%E2%80%93geometric_mean" title="Arithmetic–geometric mean">Arithmetic-Geometric</a></li>

<li><a href="Contraharmonic_mean" title="Contraharmonic mean">Contraharmonic</a></li>

<li><a href="Cubic_mean" title="Cubic mean">Cubic</a></li>

<li><a href="Generalized_mean" title="Generalized mean">Generalized/power</a></li>

<li><a href="Geometric_mean" title="Geometric mean">Geometric</a></li>

<li><a href="Harmonic_mean" title="Harmonic mean">Harmonic</a></li>

<li><a href="Heronian_mean" title="Heronian mean">Heronian</a></li>

<li><a href="Heinz_mean" title="Heinz mean">Heinz</a></li>

<li><a href="Lehmer_mean" title="Lehmer mean">Lehmer</a></li></ul></li>

<li><a href="Median" title="Median">Median</a></li>

</div></td></tr><tr><th scope="row" class="navbox-group" style="width:1%;font-weight:normal;"><a href="Statistical_dispersion" title="Statistical dispersion">Dispersion</a></th><td class="navbox-list-with-group navbox-list navbox-even" style="width:100%;padding:0"><div style="padding:0 0.25em">

<ul><li><a href="Average_absolute_deviation" title="Average absolute deviation">Average absolute deviation</a></li>

<li><a href="Coefficient_of_variation" title="Coefficient of variation">Coefficient of variation</a></li>

<li><a href="Interquartile_range" title="Interquartile range">Interquartile range</a></li>

<li><a href="Percentile" title="Percentile">Percentile</a></li>

<li><a href="Range_(statistics)" title="Range (statistics)">Range</a></li>

<li><a href="Standard_deviation" title="Standard deviation">Standard deviation</a></li>

<li><a href="Variance#Sample_variance" title="Variance">Variance</a></li></ul>

</div></td></tr><tr><th scope="row" class="navbox-group" style="width:1%;font-weight:normal;"><a href="Shape_of_the_distribution" class="mw-redirect" title="Shape of the distribution">Shape</a></th><td class="navbox-list-with-group navbox-list navbox-odd" style="width:100%;padding:0"><div style="padding:0 0.25em">

<ul><li><a href="Central_limit_theorem" title="Central limit theorem">Central limit theorem</a></li>

<li><a href="Moment_(mathematics)" title="Moment (mathematics)">Moments</a>

<ul><li><a href="Kurtosis" title="Kurtosis">Kurtosis</a></li>

<li><a href="L-moment" title="L-moment">L-moments</a></li>

<li><a href="Skewness" title="Skewness">Skewness</a></li></ul></li></ul>

</div></td></tr></tbody></table><div></div></td></tr><tr><th scope="row" class="navbox-group" style="width:12.5em"><a href="Count_data" title="Count data">Count data</a></th><td class="navbox-list-with-group navbox-list navbox-even" style="padding:0"><div style="padding:0 0.25em">

<ul><li><a href="Index_of_dispersion" title="Index of dispersion">Index of dispersion</a></li></ul>

</div></td></tr><tr><th scope="row" class="navbox-group" style="width:12.5em">Summary tables</th><td class="navbox-list-with-group navbox-list navbox-odd" style="padding:0"><div style="padding:0 0.25em">

<ul><li><a href="Contingency_table" title="Contingency table">Contingency table</a></li>

<li><a href="Frequency_distribution" class="mw-redirect" title="Frequency distribution">Frequency distribution</a></li>

<li><a href="Grouped_data" title="Grouped data">Grouped data</a></li></ul>

</div></td></tr><tr><th scope="row" class="navbox-group" style="width:12.5em"><a href="Correlation_and_dependence" class="mw-redirect" title="Correlation and dependence">Dependence</a></th><td class="navbox-list-with-group navbox-list navbox-even" style="padding:0"><div style="padding:0 0.25em">

<ul><li><a href="Partial_correlation" title="Partial correlation">Partial correlation</a></li>

<li><a href="Pearson_correlation_coefficient" title="Pearson correlation coefficient">Pearson product-moment correlation</a></li>

<li><a href="Rank_correlation" title="Rank correlation">Rank correlation</a>

<ul><li><a href="Kendall_rank_correlation_coefficient" title="Kendall rank correlation coefficient">Kendall's τ</a></li>

<li><a href="Spearman's_rank_correlation_coefficient" title="Spearman's rank correlation coefficient">Spearman's ρ</a></li></ul></li>

<li><a href="Scatter_plot" title="Scatter plot">Scatter plot</a></li></ul>

</div></td></tr><tr><th scope="row" class="navbox-group" style="width:12.5em"><a href="Statistical_graphics" title="Statistical graphics">Graphics</a></th><td class="navbox-list-with-group navbox-list navbox-odd" style="padding:0"><div style="padding:0 0.25em">

<ul><li><a href="Bar_chart" title="Bar chart">Bar chart</a></li>

<li><a href="Biplot" title="Biplot">Biplot</a></li>

<li><a href="Control_chart" title="Control chart">Control chart</a></li>

<li><a href="Correlogram" title="Correlogram">Correlogram</a></li>

<li><a href="Fan_chart_(statistics)" title="Fan chart (statistics)">Fan chart</a></li>

<li><a href="Forest_plot" title="Forest plot">Forest plot</a></li>

<li><a href="Histogram" title="Histogram">Histogram</a></li>

<li><a href="Pie_chart" title="Pie chart">Pie chart</a></li>

<li><a href="Radar_chart" title="Radar chart">Radar chart</a></li>

<li><a href="Run_chart" title="Run chart">Run chart</a></li>

<li><a href="Scatter_plot" title="Scatter plot">Scatter plot</a></li>

<li><a href="Stem-and-leaf_display" title="Stem-and-leaf display">Stem-and-leaf display</a></li>

<li><a href="Violin_plot" title="Violin plot">Violin plot</a></li></ul>

</div></td></tr></tbody></table><div></div></td></tr></tbody></table><div></div></td></tr><tr><td colspan="2" class="navbox-list navbox-odd" style="width:100%;padding:0"><div style="padding:0 0.25em"></div><table class="nowraplinks mw-collapsible mw-collapsed navbox-subgroup" style="border-spacing:0"><tbody><tr><th scope="col" class="navbox-title" colspan="2"><div id="Data_collection654" style="font-size:114%;margin:0 4em"><a href="Data_collection" title="Data collection">Data collection</a></div></th></tr><tr><td colspan="2" class="navbox-list navbox-odd" style="width:100%;padding:0"><div style="padding:0 0.25em"></div><table class="nowraplinks navbox-subgroup" style="border-spacing:0"><tbody><tr><th scope="row" class="navbox-group" style="width:12.5em"><a href="Design_of_experiments" title="Design of experiments">Study design</a></th><td class="navbox-list-with-group navbox-list navbox-odd" style="padding:0"><div style="padding:0 0.25em">

<ul><li><a href="Effect_size" title="Effect size">Effect size</a></li>

<li><a href="Missing_data" title="Missing data">Missing data</a></li>

<li><a href="Optimal_design" class="mw-redirect" title="Optimal design">Optimal design</a></li>

<li><a href="Statistical_population" title="Statistical population">Population</a></li>

<li><a href="Replication_(statistics)" title="Replication (statistics)">Replication</a></li>

<li><a href="Sample_size_determination" title="Sample size determination">Sample size determination</a></li>

<li><a href="Statistic" title="Statistic">Statistic</a></li>

<li><a href="Statistical_power" class="mw-redirect" title="Statistical power">Statistical power</a></li></ul>

</div></td></tr><tr><th scope="row" class="navbox-group" style="width:12.5em"><a href="Survey_methodology" title="Survey methodology">Survey methodology</a></th><td class="navbox-list-with-group navbox-list navbox-even" style="padding:0"><div style="padding:0 0.25em">

<ul><li><a href="Sampling_(statistics)" title="Sampling (statistics)">Sampling</a>

<ul><li><a href="Cluster_sampling" title="Cluster sampling">Cluster</a></li>

<li><a href="Stratified_sampling" title="Stratified sampling">Stratified</a></li></ul></li>

<li><a href="Opinion_poll" title="Opinion poll">Opinion poll</a></li>

<li><a href="Questionnaire" title="Questionnaire">Questionnaire</a></li>

<li><a href="Standard_error" title="Standard error">Standard error</a></li></ul>

</div></td></tr><tr><th scope="row" class="navbox-group" style="width:12.5em"><a href="Experiment" title="Experiment">Controlled experiments</a></th><td class="navbox-list-with-group navbox-list navbox-odd" style="padding:0"><div style="padding:0 0.25em">

<ul><li><a href="Blocking_(statistics)" title="Blocking (statistics)">Blocking</a></li>

<li><a href="Factorial_experiment" title="Factorial experiment">Factorial experiment</a></li>

<li><a href="Interaction_(statistics)" title="Interaction (statistics)">Interaction</a></li>

<li><a href="Random_assignment" title="Random assignment">Random assignment</a></li>

<li><a href="Randomized_experiment" title="Randomized experiment">Randomized experiment</a></li>

<li><a href="Scientific_control" title="Scientific control">Scientific control</a></li></ul>

</div></td></tr><tr><th scope="row" class="navbox-group" style="width:12.5em">Adaptive designs</th><td class="navbox-list-with-group navbox-list navbox-even" style="padding:0"><div style="padding:0 0.25em">

<ul><li><a href="Adaptive_clinical_trial" class="mw-redirect" title="Adaptive clinical trial">Adaptive clinical trial</a></li>

<li><a href="Stochastic_approximation" title="Stochastic approximation">Stochastic approximation</a></li>

<li><a href="Up-and-Down_Designs" class="mw-redirect" title="Up-and-Down Designs">Up-and-down designs</a></li></ul>

</div></td></tr><tr><th scope="row" class="navbox-group" style="width:12.5em"><a href="Observational_study" title="Observational study">Observational studies</a></th><td class="navbox-list-with-group navbox-list navbox-odd" style="padding:0"><div style="padding:0 0.25em">

<ul><li><a href="Cohort_study" title="Cohort study">Cohort study</a></li>

<li><a href="Cross-sectional_study" title="Cross-sectional study">Cross-sectional study</a></li>

<li><a href="Natural_experiment" title="Natural experiment">Natural experiment</a></li>

<li><a href="Quasi-experiment" title="Quasi-experiment">Quasi-experiment</a></li></ul>

</div></td></tr></tbody></table><div></div></td></tr></tbody></table><div></div></td></tr><tr><td colspan="2" class="navbox-list navbox-odd" style="width:100%;padding:0"><div style="padding:0 0.25em"></div><table class="nowraplinks mw-collapsible mw-collapsed navbox-subgroup" style="border-spacing:0"><tbody><tr><th scope="col" class="navbox-title" colspan="2"><div id="Statistical_inference654" style="font-size:114%;margin:0 4em"><a href="Statistical_inference" title="Statistical inference">Statistical inference</a></div></th></tr><tr><td colspan="2" class="navbox-list navbox-odd" style="width:100%;padding:0"><div style="padding:0 0.25em"></div><table class="nowraplinks navbox-subgroup" style="border-spacing:0"><tbody><tr><th scope="row" class="navbox-group" style="width:12.5em"><a href="Statistical_theory" title="Statistical theory">Statistical theory</a></th><td class="navbox-list-with-group navbox-list navbox-odd" style="padding:0"><div style="padding:0 0.25em">

<ul><li><a href="Population_(statistics)" class="mw-redirect" title="Population (statistics)">Population</a></li>

<li><a href="Statistic" title="Statistic">Statistic</a></li>

<li><a href="Probability_distribution" title="Probability distribution">Probability distribution</a></li>

<li><a href="Sampling_distribution" title="Sampling distribution">Sampling distribution</a>

<ul><li><a href="Order_statistic" title="Order statistic">Order statistic</a></li></ul></li>

<li><a href="Empirical_distribution_function" title="Empirical distribution function">Empirical distribution</a>

<ul><li><a href="Density_estimation" title="Density estimation">Density estimation</a></li></ul></li>

<li><a href="Statistical_model" title="Statistical model">Statistical model</a>

<ul><li><a href="Model_specification" class="mw-redirect" title="Model specification">Model specification</a></li>

<li><a href="Lp_space" title="Lp space">Lp space</a></li></ul></li>

<li><a href="Statistical_parameter" title="Statistical parameter">Parameter</a>

<ul><li><a href="Location_parameter" title="Location parameter">location</a></li>

<li><a href="Scale_parameter" title="Scale parameter">scale</a></li>

<li><a href="Shape_parameter" title="Shape parameter">shape</a></li></ul></li>

<li><a href="Parametric_statistics" title="Parametric statistics">Parametric family</a>

<ul><li><a href="Likelihood_function" title="Likelihood function">Likelihood</a> <a href="Monotone_likelihood_ratio" title="Monotone likelihood ratio">(monotone)</a></li>

<li><a href="Location%E2%80%93scale_family" title="Location–scale family">Location–scale family</a></li>

<li><a href="Exponential_family" title="Exponential family">Exponential family</a></li></ul></li>

<li><a href="Completeness_(statistics)" title="Completeness (statistics)">Completeness</a></li>

<li><a href="Sufficient_statistic" title="Sufficient statistic">Sufficiency</a></li>

<li><a href="Plug-in_principle" class="mw-redirect" title="Plug-in principle">Statistical functional</a>

<ul><li><a href="Bootstrapping_(statistics)" title="Bootstrapping (statistics)">Bootstrap</a></li>

<li><a href="Optimal_decision" title="Optimal decision">Optimal decision</a>

<ul><li><a href="Loss_function" title="Loss function">loss function</a></li></ul></li>

<li><a href="Efficiency_(statistics)" title="Efficiency (statistics)">Efficiency</a></li>

<li><a href="Statistical_distance" title="Statistical distance">Statistical distance</a>

<ul><li><a href="Divergence_(statistics)" title="Divergence (statistics)">divergence</a></li></ul></li>

<li><a href="Asymptotic_theory_(statistics)" title="Asymptotic theory (statistics)">Asymptotics</a></li>

<li><a href="Robust_statistics" title="Robust statistics">Robustness</a></li></ul>

</div></td></tr><tr><th scope="row" class="navbox-group" style="width:12.5em"><a href="Frequentist_inference" title="Frequentist inference">Frequentist inference</a></th><td class="navbox-list-with-group navbox-list navbox-odd" style="padding:0"><div style="padding:0 0.25em"></div><table class="nowraplinks navbox-subgroup" style="border-spacing:0"><tbody><tr><th scope="row" class="navbox-group" style="width:1%;font-weight:normal;"><a href="Point_estimation" title="Point estimation">Point estimation</a></th><td class="navbox-list-with-group navbox-list navbox-even" style="width:100%;padding:0"><div style="padding:0 0.25em">

<ul><li><a href="Estimating_equations" title="Estimating equations">Estimating equations</a>

<ul><li><a href="Maximum_likelihood" class="mw-redirect" title="Maximum likelihood">Maximum likelihood</a></li>

<li><a href="Method_of_moments_(statistics)" title="Method of moments (statistics)">Method of moments</a></li>

<li><a href="M-estimator" title="M-estimator">M-estimator</a></li>

<li><a href="Minimum_distance_estimation" class="mw-redirect" title="Minimum distance estimation">Minimum distance</a></li></ul></li>

<li><a href="Bias_of_an_estimator" title="Bias of an estimator">Unbiased estimators</a>

<ul><li><a href="Minimum-variance_unbiased_estimator" title="Minimum-variance unbiased estimator">Mean-unbiased minimum-variance</a>

<ul><li><a href="Rao%E2%80%93Blackwell_theorem" title="Rao–Blackwell theorem">Rao–Blackwellization</a></li>

<li><a href="Lehmann%E2%80%93Scheff%C3%A9_theorem" title="Lehmann–Scheffé theorem">Lehmann–Scheffé theorem</a></li></ul></li>

<li><a href="Median-unbiased_estimator" class="mw-redirect" title="Median-unbiased estimator">Median unbiased</a></li></ul></li>

</div></td></tr><tr><th scope="row" class="navbox-group" style="width:1%;font-weight:normal;"><a href="Interval_estimation" title="Interval estimation">Interval estimation</a></th><td class="navbox-list-with-group navbox-list navbox-odd" style="width:100%;padding:0"><div style="padding:0 0.25em">

<ul><li><a href="Confidence_interval" title="Confidence interval">Confidence interval</a></li>

<li><a href="Pivotal_quantity" title="Pivotal quantity">Pivot</a></li>

<li><a href="Likelihood_interval" class="mw-redirect" title="Likelihood interval">Likelihood interval</a></li>

<li><a href="Prediction_interval" title="Prediction interval">Prediction interval</a></li>

<li><a href="Tolerance_interval" title="Tolerance interval">Tolerance interval</a></li>

<li><a href="Resampling_(statistics)" title="Resampling (statistics)">Resampling</a>

<ul><li><a href="Bootstrapping_(statistics)" title="Bootstrapping (statistics)">Bootstrap</a></li>

<li><a href="Jackknife_resampling" title="Jackknife resampling">Jackknife</a></li></ul></li></ul>

</div></td></tr><tr><th scope="row" class="navbox-group" style="width:1%;font-weight:normal;"><a href="Statistical_hypothesis_testing" class="mw-redirect" title="Statistical hypothesis testing">Testing hypotheses</a></th><td class="navbox-list-with-group navbox-list navbox-even" style="width:100%;padding:0"><div style="padding:0 0.25em">

<ul><li><a href="One-_and_two-tailed_tests" title="One- and two-tailed tests">1- & 2-tails</a></li>

<li><a href="Power_(statistics)" title="Power (statistics)">Power</a>

<ul><li><a href="Uniformly_most_powerful_test" title="Uniformly most powerful test">Uniformly most powerful test</a></li></ul></li>

<li><a href="Permutation_test" title="Permutation test">Permutation test</a>

<ul><li><a href="Randomization_test" class="mw-redirect" title="Randomization test">Randomization test</a></li></ul></li>

<li><a href="Multiple_comparisons" class="mw-redirect" title="Multiple comparisons">Multiple comparisons</a></li></ul>

</div></td></tr><tr><th scope="row" class="navbox-group" style="width:1%;font-weight:normal;"><a href="Parametric_statistics" title="Parametric statistics">Parametric tests</a></th><td class="navbox-list-with-group navbox-list navbox-odd" style="width:100%;padding:0"><div style="padding:0 0.25em">

<ul><li><a href="Likelihood-ratio_test" title="Likelihood-ratio test">Likelihood-ratio</a></li>

<li><a href="Score_test" title="Score test">Score/Lagrange multiplier</a></li>

</div></td></tr></tbody></table><div></div></td></tr><tr><th scope="row" class="navbox-group" style="width:12.5em"><a href="List_of_statistical_tests" title="List of statistical tests">Specific tests</a></th><td class="navbox-list-with-group navbox-list navbox-odd" style="padding:0"><div style="padding:0 0.25em"></div><table class="nowraplinks navbox-subgroup" style="border-spacing:0"><tbody><tr><td colspan="2" class="navbox-list navbox-even" style="width:100%;padding:0"><div style="padding:0 0.25em">

<ul><li><a href="Z-test" title="Z-test">Z-test (normal)</a></li>

<li><a href="Student's_t-test" title="Student's t-test">Student's t-test</a></li>

</div></td></tr><tr><th scope="row" class="navbox-group" style="width:1%;font-weight:normal;"><a href="Goodness_of_fit" title="Goodness of fit">Goodness of fit</a></th><td class="navbox-list-with-group navbox-list navbox-odd" style="width:100%;padding:0"><div style="padding:0 0.25em">

<ul><li><a href="Chi-squared_test" title="Chi-squared test">Chi-squared</a></li>

<li><a href="Kolmogorov%E2%80%93Smirnov_test" title="Kolmogorov–Smirnov test">Kolmogorov–Smirnov</a></li>

<li><a href="Anderson%E2%80%93Darling_test" title="Anderson–Darling test">Anderson–Darling</a></li>

<li><a href="Lilliefors_test" title="Lilliefors test">Lilliefors</a></li>

<li><a href="Jarque%E2%80%93Bera_test" title="Jarque–Bera test">Jarque–Bera</a></li>

<li><a href="Shapiro%E2%80%93Wilk_test" title="Shapiro–Wilk test">Normality (Shapiro–Wilk)</a></li>

<li><a href="Likelihood-ratio_test" title="Likelihood-ratio test">Likelihood-ratio test</a></li>

<li><a href="Model_selection" title="Model selection">Model selection</a>

<ul><li><a href="Cross-validation_(statistics)" title="Cross-validation (statistics)">Cross validation</a></li>

</div></td></tr><tr><th scope="row" class="navbox-group" style="width:1%;font-weight:normal;"><a href="Rank_statistics" class="mw-redirect" title="Rank statistics">Rank statistics</a></th><td class="navbox-list-with-group navbox-list navbox-even" style="width:100%;padding:0"><div style="padding:0 0.25em">

<ul><li><a href="Sample_median" class="mw-redirect" title="Sample median">Sample median</a></li></ul></li>

<li><a href="Wilcoxon_signed-rank_test" title="Wilcoxon signed-rank test">Signed rank (Wilcoxon)</a>

<ul><li><a href="Hodges%E2%80%93Lehmann_estimator" title="Hodges–Lehmann estimator">Hodges–Lehmann estimator</a></li></ul></li>

<li><a href="Mann%E2%80%93Whitney_U_test" title="Mann–Whitney U test">Rank sum (Mann–Whitney)</a></li>

<li><a href="Nonparametric_statistics" title="Nonparametric statistics">Nonparametric</a> <a href="Analysis_of_variance" title="Analysis of variance">anova</a>

<ul><li><a href="Kruskal%E2%80%93Wallis_test" title="Kruskal–Wallis test">1-way (Kruskal–Wallis)</a></li>

<li><a href="Friedman_test" title="Friedman test">2-way (Friedman)</a></li>

<li><a href="Jonckheere's_trend_test" title="Jonckheere's trend test">Ordered alternative (Jonckheere–Terpstra)</a></li></ul></li>

<li><a href="Van_der_Waerden_test" title="Van der Waerden test">Van der Waerden test</a></li></ul>

</div></td></tr></tbody></table><div></div></td></tr><tr><th scope="row" class="navbox-group" style="width:12.5em"><a href="Bayesian_inference" title="Bayesian inference">Bayesian inference</a></th><td class="navbox-list-with-group navbox-list navbox-odd" style="padding:0"><div style="padding:0 0.25em">

<ul><li><a href="Bayesian_probability" title="Bayesian probability">Bayesian probability</a>

<ul><li><a href="Prior_probability" title="Prior probability">prior</a></li>

<li><a href="Posterior_probability" title="Posterior probability">posterior</a></li></ul></li>

<li><a href="Credible_interval" title="Credible interval">Credible interval</a></li>

<li><a href="Bayes_factor" title="Bayes factor">Bayes factor</a></li>

<li><a href="Bayes_estimator" title="Bayes estimator">Bayesian estimator</a>

<ul><li><a href="Maximum_a_posteriori_estimation" title="Maximum a posteriori estimation">Maximum posterior estimator</a></li></ul></li></ul>

</div></td></tr></tbody></table><div></div></td></tr></tbody></table><div></div></td></tr><tr><td colspan="2" class="navbox-list navbox-odd" style="width:100%;padding:0"><div style="padding:0 0.25em"></div><table class="nowraplinks mw-collapsible mw-collapsed navbox-subgroup" style="border-spacing:0"><tbody><tr><th scope="col" class="navbox-title" colspan="2"><div id="CorrelationRegression_analysis654" style="font-size:114%;margin:0 4em"><div class="hlist"><ul><li><a href="Correlation_and_dependence" class="mw-redirect" title="Correlation and dependence">Correlation</a></li><li><a href="Regression_analysis" title="Regression analysis">Regression analysis</a></li></ul></div></div></th></tr><tr><td colspan="2" class="navbox-list navbox-odd" style="width:100%;padding:0"><div style="padding:0 0.25em"></div><table class="nowraplinks navbox-subgroup" style="border-spacing:0"><tbody><tr><th scope="row" class="navbox-group" style="width:12.5em"><a href="Correlation_and_dependence" class="mw-redirect" title="Correlation and dependence">Correlation</a></th><td class="navbox-list-with-group navbox-list navbox-odd" style="padding:0"><div style="padding:0 0.25em">

<ul><li><a href="Pearson_product-moment_correlation_coefficient" class="mw-redirect" title="Pearson product-moment correlation coefficient">Pearson product-moment</a></li>

<li><a href="Partial_correlation" title="Partial correlation">Partial correlation</a></li>

<li><a href="Confounding" title="Confounding">Confounding variable</a></li>

<li><a href="Coefficient_of_determination" title="Coefficient of determination">Coefficient of determination</a></li></ul>

</div></td></tr><tr><th scope="row" class="navbox-group" style="width:12.5em"><a href="Regression_analysis" title="Regression analysis">Regression analysis</a></th><td class="navbox-list-with-group navbox-list navbox-even" style="padding:0"><div style="padding:0 0.25em">

<ul><li><a href="Errors_and_residuals" title="Errors and residuals">Errors and residuals</a></li>

<li><a href="Regression_validation" title="Regression validation">Regression validation</a></li>

<li><a href="Mixed_model" title="Mixed model">Mixed effects models</a></li>

<li><a href="Simultaneous_equations_model" title="Simultaneous equations model">Simultaneous equations models</a></li>

<li><a href="Multivariate_adaptive_regression_splines" class="mw-redirect" title="Multivariate adaptive regression splines">Multivariate adaptive regression splines (MARS)</a></li></ul>

</div></td></tr><tr><th scope="row" class="navbox-group" style="width:12.5em"><a href="Linear_regression" title="Linear regression">Linear regression</a></th><td class="navbox-list-with-group navbox-list navbox-odd" style="padding:0"><div style="padding:0 0.25em">

<ul><li><a href="Simple_linear_regression" title="Simple linear regression">Simple linear regression</a></li>

<li><a href="Ordinary_least_squares" title="Ordinary least squares">Ordinary least squares</a></li>

<li><a href="General_linear_model" title="General linear model">General linear model</a></li>

<li><a href="Bayesian_linear_regression" title="Bayesian linear regression">Bayesian regression</a></li></ul>

</div></td></tr><tr><th scope="row" class="navbox-group" style="width:12.5em">Non-standard predictors</th><td class="navbox-list-with-group navbox-list navbox-even" style="padding:0"><div style="padding:0 0.25em">

<ul><li><a href="Nonlinear_regression" title="Nonlinear regression">Nonlinear regression</a></li>

<li><a href="Nonparametric_regression" title="Nonparametric regression">Nonparametric</a></li>

<li><a href="Semiparametric_regression" title="Semiparametric regression">Semiparametric</a></li>

<li><a href="Isotonic_regression" title="Isotonic regression">Isotonic</a></li>

<li><a href="Robust_regression" title="Robust regression">Robust</a></li>

<li><a href="Homoscedasticity_and_heteroscedasticity" title="Homoscedasticity and heteroscedasticity">Homoscedasticity and Heteroscedasticity</a></li></ul>

</div></td></tr><tr><th scope="row" class="navbox-group" style="width:12.5em"><a href="Generalized_linear_model" title="Generalized linear model">Generalized linear model</a></th><td class="navbox-list-with-group navbox-list navbox-odd" style="padding:0"><div style="padding:0 0.25em">

<ul><li><a href="Exponential_family" title="Exponential family">Exponential families</a></li>

<li><a href="Logistic_regression" title="Logistic regression">Logistic (Bernoulli)</a> / <a href="Binomial_regression" title="Binomial regression">Binomial</a> / <a href="Poisson_regression" title="Poisson regression">Poisson regressions</a></li></ul>

</div></td></tr><tr><th scope="row" class="navbox-group" style="width:12.5em"><a href="Partition_of_sums_of_squares" title="Partition of sums of squares">Partition of variance</a></th><td class="navbox-list-with-group navbox-list navbox-even" style="padding:0"><div style="padding:0 0.25em">

<ul><li><a href="Analysis_of_variance" title="Analysis of variance">Analysis of variance (ANOVA, anova)</a></li>

<li><a href="Analysis_of_covariance" title="Analysis of covariance">Analysis of covariance</a></li>

<li><a href="Multivariate_analysis_of_variance" title="Multivariate analysis of variance">Multivariate ANOVA</a></li>

<li><a href="Degrees_of_freedom_(statistics)" title="Degrees of freedom (statistics)">Degrees of freedom</a></li></ul>

</div></td></tr></tbody></table><div></div></td></tr></tbody></table><div></div></td></tr><tr><td colspan="2" class="navbox-list navbox-odd" style="width:100%;padding:0"><div style="padding:0 0.25em"></div><table class="nowraplinks mw-collapsible mw-collapsed navbox-subgroup" style="border-spacing:0"><tbody><tr><th scope="col" class="navbox-title" colspan="2"><div id="Categorical_/_multivariate_/_time-series_/_survival_analysis654" style="font-size:114%;margin:0 4em"><a href="Categorical_variable" title="Categorical variable">Categorical</a> / <a href="Multivariate_statistics" title="Multivariate statistics">multivariate</a> / <a href="Time_series" title="Time series">time-series</a> / <a href="Survival_analysis" title="Survival analysis">survival analysis</a></div></th></tr><tr><td colspan="2" class="navbox-list navbox-odd" style="width:100%;padding:0"><div style="padding:0 0.25em"></div><table class="nowraplinks navbox-subgroup" style="border-spacing:0"><tbody><tr><th scope="row" class="navbox-group" style="width:12.5em"><a href="Categorical_variable" title="Categorical variable">Categorical</a></th><td class="navbox-list-with-group navbox-list navbox-odd" style="padding:0"><div style="padding:0 0.25em">

<ul><li><a href="Cohen's_kappa" title="Cohen's kappa">Cohen's kappa</a></li>

<li><a href="Contingency_table" title="Contingency table">Contingency table</a></li>

<li><a href="Graphical_model" title="Graphical model">Graphical model</a></li>

<li><a href="Poisson_regression" title="Poisson regression">Log-linear model</a></li>

<li><a href="McNemar's_test" title="McNemar's test">McNemar's test</a></li>

<li><a href="Cochran%E2%80%93Mantel%E2%80%93Haenszel_statistics" title="Cochran–Mantel–Haenszel statistics">Cochran–Mantel–Haenszel statistics</a></li></ul>

</div></td></tr><tr><th scope="row" class="navbox-group" style="width:12.5em"><a href="Multivariate_statistics" title="Multivariate statistics">Multivariate</a></th><td class="navbox-list-with-group navbox-list navbox-even" style="padding:0"><div style="padding:0 0.25em">

<ul><li><a href="General_linear_model" title="General linear model">Regression</a></li>

<li><a href="Multivariate_analysis_of_variance" title="Multivariate analysis of variance">Manova</a></li>

<li><a href="Principal_component_analysis" title="Principal component analysis">Principal components</a></li>

<li><a href="Canonical_correlation" title="Canonical correlation">Canonical correlation</a></li>

<li><a href="Linear_discriminant_analysis" title="Linear discriminant analysis">Discriminant analysis</a></li>

<li><a href="Cluster_analysis" title="Cluster analysis">Cluster analysis</a></li>

<li><a href="Statistical_classification" title="Statistical classification">Classification</a></li>

<li><a href="Structural_equation_modeling" title="Structural equation modeling">Structural equation model</a>

<ul><li><a href="Factor_analysis" title="Factor analysis">Factor analysis</a></li></ul></li>

<li><a href="Multivariate_distribution" class="mw-redirect" title="Multivariate distribution">Multivariate distributions</a>

<ul><li><a href="Elliptical_distribution" title="Elliptical distribution">Elliptical distributions</a>

<ul><li><a href="Multivariate_normal_distribution" title="Multivariate normal distribution">Normal</a></li></ul></li></ul></li></ul>

</div></td></tr><tr><th scope="row" class="navbox-group" style="width:12.5em"><a href="Time_series" title="Time series">Time-series</a></th><td class="navbox-list-with-group navbox-list navbox-odd" style="padding:0"><div style="padding:0 0.25em"></div><table class="nowraplinks navbox-subgroup" style="border-spacing:0"><tbody><tr><th scope="row" class="navbox-group" style="width:1%;font-weight:normal;">General</th><td class="navbox-list-with-group navbox-list navbox-odd" style="width:100%;padding:0"><div style="padding:0 0.25em">

<ul><li><a href="Decomposition_of_time_series" title="Decomposition of time series">Decomposition</a></li>

<li><a href="Trend_estimation" class="mw-redirect" title="Trend estimation">Trend</a></li>

<li><a href="Stationary_process" title="Stationary process">Stationarity</a></li>

<li><a href="Seasonal_adjustment" title="Seasonal adjustment">Seasonal adjustment</a></li>

<li><a href="Exponential_smoothing" title="Exponential smoothing">Exponential smoothing</a></li>

<li><a href="Cointegration" title="Cointegration">Cointegration</a></li>

<li><a href="Structural_break" title="Structural break">Structural break</a></li>

<li><a href="Granger_causality" title="Granger causality">Granger causality</a></li></ul>

</div></td></tr><tr><th scope="row" class="navbox-group" style="width:1%;font-weight:normal;">Specific tests</th><td class="navbox-list-with-group navbox-list navbox-even" style="width:100%;padding:0"><div style="padding:0 0.25em">

<ul><li><a href="Dickey%E2%80%93Fuller_test" title="Dickey–Fuller test">Dickey–Fuller</a></li>

<li><a href="Johansen_test" title="Johansen test">Johansen</a></li>

<li><a href="Ljung%E2%80%93Box_test" title="Ljung–Box test">Q-statistic (Ljung–Box)</a></li>

<li><a href="Durbin%E2%80%93Watson_statistic" title="Durbin–Watson statistic">Durbin–Watson</a></li>

<li><a href="Breusch%E2%80%93Godfrey_test" title="Breusch–Godfrey test">Breusch–Godfrey</a></li></ul>

</div></td></tr><tr><th scope="row" class="navbox-group" style="width:1%;font-weight:normal;"><a href="Time_domain" title="Time domain">Time domain</a></th><td class="navbox-list-with-group navbox-list navbox-odd" style="width:100%;padding:0"><div style="padding:0 0.25em">

<ul><li><a href="Autocorrelation" title="Autocorrelation">Autocorrelation (ACF)</a>

<ul><li><a href="Partial_autocorrelation_function" title="Partial autocorrelation function">partial (PACF)</a></li></ul></li>

<li><a href="Cross-correlation" title="Cross-correlation">Cross-correlation (XCF)</a></li>

<li><a href="Autoregressive%E2%80%93moving-average_model" class="mw-redirect" title="Autoregressive–moving-average model">ARMA model</a></li>

<li><a href="Box%E2%80%93Jenkins_method" title="Box–Jenkins method">ARIMA model (Box–Jenkins)</a></li>

<li><a href="Autoregressive_conditional_heteroskedasticity" title="Autoregressive conditional heteroskedasticity">Autoregressive conditional heteroskedasticity (ARCH)</a></li>

<li><a href="Vector_autoregression" title="Vector autoregression">Vector autoregression (VAR)</a></li></ul>

</div></td></tr><tr><th scope="row" class="navbox-group" style="width:1%;font-weight:normal;"><a href="Frequency_domain" title="Frequency domain">Frequency domain</a></th><td class="navbox-list-with-group navbox-list navbox-even" style="width:100%;padding:0"><div style="padding:0 0.25em">

<ul><li><a href="Spectral_density_estimation" title="Spectral density estimation">Spectral density estimation</a></li>

<li><a href="Fourier_analysis" title="Fourier analysis">Fourier analysis</a></li>

<li><a href="Least-squares_spectral_analysis" title="Least-squares spectral analysis">Least-squares spectral analysis</a></li>

<li><a href="Wavelet" title="Wavelet">Wavelet</a></li>

<li><a href="Whittle_likelihood" title="Whittle likelihood">Whittle likelihood</a></li></ul>

</div></td></tr></tbody></table><div></div></td></tr><tr><th scope="row" class="navbox-group" style="width:12.5em"><a href="Survival_analysis" title="Survival analysis">Survival</a></th><td class="navbox-list-with-group navbox-list navbox-odd" style="padding:0"><div style="padding:0 0.25em"></div><table class="nowraplinks navbox-subgroup" style="border-spacing:0"><tbody><tr><th scope="row" class="navbox-group" style="width:1%;font-weight:normal;"><a href="Survival_function" title="Survival function">Survival function</a></th><td class="navbox-list-with-group navbox-list navbox-odd" style="width:100%;padding:0"><div style="padding:0 0.25em">

<ul><li><a href="Kaplan%E2%80%93Meier_estimator" title="Kaplan–Meier estimator">Kaplan–Meier estimator (product limit)</a></li>

<li><a href="Proportional_hazards_model" title="Proportional hazards model">Proportional hazards models</a></li>

<li><a href="Accelerated_failure_time_model" title="Accelerated failure time model">Accelerated failure time (AFT) model</a></li>

<li><a href="First-hitting-time_model" title="First-hitting-time model">First hitting time</a></li></ul>

</div></td></tr><tr><th scope="row" class="navbox-group" style="width:1%;font-weight:normal;"><a href="Failure_rate" title="Failure rate">Hazard function</a></th><td class="navbox-list-with-group navbox-list navbox-even" style="width:100%;padding:0"><div style="padding:0 0.25em">

<ul><li><a href="Nelson%E2%80%93Aalen_estimator" title="Nelson–Aalen estimator">Nelson–Aalen estimator</a></li></ul>

</div></td></tr><tr><th scope="row" class="navbox-group" style="width:1%;font-weight:normal;">Test</th><td class="navbox-list-with-group navbox-list navbox-odd" style="width:100%;padding:0"><div style="padding:0 0.25em">

</div></td></tr></tbody></table><div></div></td></tr></tbody></table><div></div></td></tr></tbody></table><div></div></td></tr><tr><td colspan="2" class="navbox-list navbox-odd" style="width:100%;padding:0"><div style="padding:0 0.25em"></div><table class="nowraplinks mw-collapsible uncollapsed navbox-subgroup" style="border-spacing:0"><tbody><tr><th scope="col" class="navbox-title" colspan="2"><div id="Applications654" style="font-size:114%;margin:0 4em"><a href="List_of_fields_of_application_of_statistics" title="List of fields of application of statistics">Applications</a></div></th></tr><tr><td colspan="2" class="navbox-list navbox-odd" style="width:100%;padding:0"><div style="padding:0 0.25em"></div><table class="nowraplinks navbox-subgroup" style="border-spacing:0"><tbody><tr><th scope="row" class="navbox-group" style="width:12.5em"><a href="Biostatistics" title="Biostatistics">Biostatistics</a></th><td class="navbox-list-with-group navbox-list navbox-odd" style="padding:0"><div style="padding:0 0.25em">

<ul><li><a href="Bioinformatics" title="Bioinformatics">Bioinformatics</a></li>

<li><a href="Clinical_trial" title="Clinical trial">Clinical trials</a> / <a href="Clinical_study_design" title="Clinical study design">studies</a></li>

<li><a href="Epidemiology" title="Epidemiology">Epidemiology</a></li>

<li><a href="Medical_statistics" title="Medical statistics">Medical statistics</a></li></ul>

</div></td></tr><tr><th scope="row" class="navbox-group" style="width:12.5em"><a href="Engineering_statistics" title="Engineering statistics">Engineering statistics</a></th><td class="navbox-list-with-group navbox-list navbox-even" style="padding:0"><div style="padding:0 0.25em">

<ul><li><a href="Chemometrics" title="Chemometrics">Chemometrics</a></li>

<li><a href="Methods_engineering" title="Methods engineering">Methods engineering</a></li>

<li><a href="Probabilistic_design" title="Probabilistic design">Probabilistic design</a></li>

<li><a href="Statistical_process_control" title="Statistical process control">Process</a> / <a href="Quality_control" title="Quality control">quality control</a></li>

<li><a href="Reliability_engineering" title="Reliability engineering">Reliability</a></li>

<li><a href="System_identification" title="System identification">System identification</a></li></ul>

</div></td></tr><tr><th scope="row" class="navbox-group" style="width:12.5em"><a href="Social_statistics" title="Social statistics">Social statistics</a></th><td class="navbox-list-with-group navbox-list navbox-odd" style="padding:0"><div style="padding:0 0.25em">

<ul><li><a href="Actuarial_science" title="Actuarial science">Actuarial science</a></li>

<li><a href="Census" title="Census">Census</a></li>

<li><a href="Crime_statistics" title="Crime statistics">Crime statistics</a></li>

<li><a href="Demographic_statistics" title="Demographic statistics">Demography</a></li>

<li><a href="Econometrics" title="Econometrics">Econometrics</a></li>

<li><a href="Jurimetrics" title="Jurimetrics">Jurimetrics</a></li>

<li><a href="National_accounts" title="National accounts">National accounts</a></li>

<li><a href="Official_statistics" title="Official statistics">Official statistics</a></li>

<li><a href="Population_statistics" class="mw-redirect" title="Population statistics">Population statistics</a></li>

<li><a href="Psychometrics" title="Psychometrics">Psychometrics</a></li></ul>

</div></td></tr><tr><th scope="row" class="navbox-group" style="width:12.5em"><a href="Spatial_analysis" title="Spatial analysis">Spatial statistics</a></th><td class="navbox-list-with-group navbox-list navbox-even" style="padding:0"><div style="padding:0 0.25em">

<ul><li><a href="Cartography" title="Cartography">Cartography</a></li>

<li><a href="Environmental_statistics" title="Environmental statistics">Environmental statistics</a></li>

<li><a href="Geographic_information_system" title="Geographic information system">Geographic information system</a></li>

<li><a href="Geostatistics" title="Geostatistics">Geostatistics</a></li>

<li><a href="Kriging" title="Kriging">Kriging</a></li></ul>

</div></td></tr></tbody></table><div></div></td></tr></tbody></table><div></div></td></tr><tr><td class="navbox-abovebelow" colspan="2"><div>

<ul><li>Category</li>

<li> <a href="Portal%3AMathematics" title="Portal:Mathematics">Mathematics portal</a></li>

<li><a href="https://commons.wikimedia.org/wiki/Category:Statistics" class="extiw external" title="commons:Category:Statistics">Commons</a></li>

<li> WikiProject</li></ul>

</div></td></tr></tbody></table></div>

<div class="navbox-styles"></div><div role="navigation" class="navbox" aria-labelledby="Public_health650" style="padding:3px"><table class="nowraplinks hlist mw-collapsible autocollapse navbox-inner" style="border-spacing:0;background:transparent;color:inherit"><tbody><tr><th scope="col" class="navbox-title" colspan="2"><div id="Public_health650" style="font-size:114%;margin:0 4em"><a href="Public_health" title="Public health">Public health</a></div></th></tr><tr><th scope="row" class="navbox-group" style="width:1%">General</th><td class="navbox-list-with-group navbox-list navbox-odd wraplinks" style="width:100%;padding:0"><div style="padding:0 0.25em">

<ul><li><a href="Auxology" title="Auxology">Auxology</a></li>

<li><a href="Biological_hazard" title="Biological hazard">Biological hazard</a></li>

<li><a href="Chief_medical_officer" title="Chief medical officer">Chief medical officer</a></li>

<li><a href="Cultural_competence_in_health_care" class="mw-redirect" title="Cultural competence in health care">Cultural competence</a></li>

<li><a href="Deviance_(sociology)" title="Deviance (sociology)">Deviance</a></li>

<li><a href="Environmental_health" title="Environmental health">Environmental health</a></li>

<li><a href="Eugenics" title="Eugenics">Eugenics</a>

<ul><li><a href="History_of_eugenics" title="History of eugenics">History of</a></li>

<li><a href="New_eugenics" title="New eugenics">Liberal</a></li></ul></li>

<li><a href="Euthenics" title="Euthenics">Euthenics</a></li>

<li><a href="Public_health_genomics" title="Public health genomics">Genomics</a></li>

<li><a href="Globalization_and_disease" title="Globalization and disease">Globalization and disease</a></li>

<li><a href="Harm_reduction" title="Harm reduction">Harm reduction</a></li>

<li><a href="Health_economics" title="Health economics">Health economics</a></li>

<li><a href="Health_literacy" title="Health literacy">Health literacy</a></li>

<li><a href="Health_policy" title="Health policy">Health policy</a>

<ul><li><a href="Health_system" title="Health system">Health system</a></li>

<li><a href="Health_care_reform" title="Health care reform">Health care reform</a></li></ul></li>

<li><a href="Housing_First" title="Housing First">Housing First</a></li>

<li><a href="Human_right_to_water_and_sanitation" title="Human right to water and sanitation">Human right to water and sanitation</a></li>

<li><a href="Management_of_depression" title="Management of depression">Management of depression</a>

<ul><li><a href="Public_health_law" title="Public health law">Public health law</a></li>

<li><a href="National_public_health_institutes" class="mw-redirect" title="National public health institutes">National public health institute</a></li></ul></li>

<li><a href="Health_politics" title="Health politics">Health politics</a></li>

<li><a href="Labor_rights" title="Labor rights">Labor rights</a></li>

<li><a href="Maternal_health" title="Maternal health">Maternal health</a></li>

<li><a href="Medical_anthropology" title="Medical anthropology">Medical anthropology</a></li>

<li><a href="Medical_sociology" title="Medical sociology">Medical sociology</a></li>

<li><a href="Mental_health" title="Mental health">Mental health</a> (<a href="Minister_of_Mental_Health" title="Minister of Mental Health">Ministers</a>)</li>

<li><a href="Occupational_safety_and_health" title="Occupational safety and health">Occupational safety and health</a></li>

<li><a href="Pharmaceutical_policy" title="Pharmaceutical policy">Pharmaceutical policy</a></li>

<li><a href="Pollution" title="Pollution">Pollution</a>

<li><a href="Water_pollution" title="Water pollution">Water</a></li>

<li><a href="Radioactive_contamination" title="Radioactive contamination">Radiation</a></li>

<li><a href="Light_pollution" title="Light pollution">Light</a></li></ul></li>

<li><a href="Prisoners'_rights" title="Prisoners' rights">Prisoners' rights</a></li>

<li><a href="Public_health_intervention" title="Public health intervention">Public health intervention</a></li>

<li><a href="Public_health_laboratory" title="Public health laboratory">Public health laboratory</a></li>

<li><a href="Right_to_food" title="Right to food">Right to food</a></li>

<li><a href="Right_to_health" title="Right to health">Right to health</a></li>

<li><a href="Right_to_a_healthy_environment" title="Right to a healthy environment">Right to a healthy environment</a></li>

<li><a href="Right_to_housing" title="Right to housing">Right to housing</a></li>

<li><a href="Right_to_rest_and_leisure" title="Right to rest and leisure">Right to rest and leisure</a></li>

<li><a href="Right_to_sit" title="Right to sit">Right to sit</a></li>

<li><a href="Security_of_person" title="Security of person">Security of person</a></li>

<li><a href="Sexual_and_reproductive_health" title="Sexual and reproductive health">Sexual and reproductive health</a></li>

<li><a href="Social_psychology" title="Social psychology">Social psychology</a></li>

<li><a href="Sociology_of_health_and_illness" title="Sociology of health and illness">Sociology of health and illness</a></li>

<li><a href="Unisex_changing_rooms" title="Unisex changing rooms">Unisex changing rooms</a></li>

<li><a href="Unisex_public_toilets" class="mw-redirect" title="Unisex public toilets">Unisex public toilets</a></li>

<li><a href="Workers'_right_to_access_the_toilet" title="Workers' right to access the toilet">Workers' right to access the toilet</a></li></ul>

</div></td></tr><tr><th scope="row" class="navbox-group" style="width:1%"><a href="Preventive_healthcare" title="Preventive healthcare">Preventive healthcare</a></th><td class="navbox-list-with-group navbox-list navbox-even wraplinks" style="width:100%;padding:0"><div style="padding:0 0.25em">

<ul><li><a href="Behavior_change_(public_health)" title="Behavior change (public health)">Behavior change</a>

<ul><li><a href="Behavioural_change_theories" title="Behavioural change theories">Theories</a></li></ul></li>

<li><a href="Drug_checking" title="Drug checking">Drug checking</a></li>

<li><a href="Family_planning" title="Family planning">Family planning</a></li>

<li><a href="Harm_reduction" title="Harm reduction">Harm reduction</a></li>

<li><a href="Health_promotion" title="Health promotion">Health promotion</a></li>

<li><a href="Human_nutrition" title="Human nutrition">Human nutrition</a>

<ul><li><a href="Healthy_diet" title="Healthy diet">Healthy diet</a></li>

<li><a href="Preventive_nutrition" title="Preventive nutrition">Preventive nutrition</a></li></ul></li>

<li><a href="Hygiene" title="Hygiene">Hygiene</a>

<ul><li><a href="Food_safety" title="Food safety">Food safety</a></li>

<li><a href="Hand_washing" title="Hand washing">Hand washing</a></li>

<li><a href="Infection_control" class="mw-redirect" title="Infection control">Infection control</a></li>

<li><a href="Oral_hygiene" title="Oral hygiene">Oral hygiene</a></li></ul></li>

<li><a href="Needle_and_syringe_programmes" title="Needle and syringe programmes">Needle and syringe programmes</a></li>

<li><a href="Occupational_safety_and_health" title="Occupational safety and health">Occupational safety and health</a>

<ul><li><a href="Human_factors_and_ergonomics" class="mw-redirect" title="Human factors and ergonomics">Human factors and ergonomics</a></li>

<li><a href="Occupational_hygiene" title="Occupational hygiene">Hygiene</a></li>

<li><a href="Drug_policy" title="Drug policy">Controlled Drugs</a></li>

<li><a href="Injury_prevention" title="Injury prevention">Injury prevention</a></li>

<li><a href="Occupational_medicine" title="Occupational medicine">Medicine</a></li>

<li><a href="Occupational_health_nursing" title="Occupational health nursing">Nursing</a></li></ul></li>

<li><a href="Patient_safety" title="Patient safety">Patient safety</a>

<ul><li><a href="Patient_safety_organization" title="Patient safety organization">Organization</a></li></ul></li>

<li><a href="Pharmacovigilance" title="Pharmacovigilance">Pharmacovigilance</a></li>

<li><a href="Reagent_testing" title="Reagent testing">Reagent testing</a></li>

<li><a href="Sanitation" title="Sanitation">Sanitation</a>

<ul><li><a href="Emergency_sanitation" title="Emergency sanitation">Emergency</a></li>

<li><a href="Fecal%E2%80%93oral_route" title="Fecal–oral route">Fecal–oral transmission</a></li>

<li><a href="Open_defecation" title="Open defecation">Open defecation</a></li>

<li><a href="Sanitary_sewer" title="Sanitary sewer">Sanitary sewer</a></li>

<li><a href="Waterborne_diseases" class="mw-redirect" title="Waterborne diseases">Waterborne diseases</a></li>

<li><a href="Sanitation_worker" title="Sanitation worker">Worker</a></li></ul></li>

<li><a href="School_hygiene" title="School hygiene">School hygiene</a></li>

<li><a href="Smoking_cessation" title="Smoking cessation">Smoking cessation</a></li>

<li><a href="Supervised_injection_site" title="Supervised injection site">Supervised injection site</a></li>

<li><a href="Vaccination" title="Vaccination">Vaccination</a></li>

<li><a href="Vector_control" title="Vector control">Vector control</a></li></ul>

</div></td></tr><tr><th scope="row" class="navbox-group" style="width:1%"><a href="Population_health" title="Population health">Population health</a></th><td class="navbox-list-with-group navbox-list navbox-odd wraplinks" style="width:100%;padding:0"><div style="padding:0 0.25em">

<ul><li><a href="Biostatistics" title="Biostatistics">Biostatistics</a></li>

<li><a href="Child_mortality" title="Child mortality">Child mortality</a></li>

<li><a href="Community_health" title="Community health">Community health</a></li>

<li><a href="Epidemiology" title="Epidemiology">Epidemiology</a></li>

<li><a href="Global_health" title="Global health">Global health</a></li>

<li><a href="Health_impact_assessment" title="Health impact assessment">Health impact assessment</a></li>

<li><a href="Health_system" title="Health system">Health system</a></li>

<li><a href="Infant_mortality" title="Infant mortality">Infant mortality</a></li>

<li><a href="List_of_open-source_health_software" title="List of open-source health software">Open-source healthcare software</a></li>

<li><a href="Multimorbidity" title="Multimorbidity">Multimorbidity</a></li>

<li><a href="Public_health_informatics" title="Public health informatics">Public health informatics</a></li>

<li><a href="Social_determinants_of_health" title="Social determinants of health">Social determinants of health</a>

<ul><li><a href="Commercial_determinants_of_health" title="Commercial determinants of health">Commercial determinants of health</a></li>

<li><a href="Health_equity" title="Health equity">Health equity</a></li>

<li><a href="Race_and_health" title="Race and health">Race and health</a></li></ul></li>

<li><a href="Social_medicine" title="Social medicine">Social medicine</a></li></ul>

</div></td></tr><tr><th scope="row" class="navbox-group" style="width:1%">Biological and epidemiological statistics</th><td class="navbox-list-with-group navbox-list navbox-even wraplinks" style="width:100%;padding:0"><div style="padding:0 0.25em">

<ul><li><a href="Case%E2%80%93control_study" title="Case–control study">Case–control study</a></li>

<li><a href="Relative_risk" title="Relative risk">Relative risk</a></li>

<li><a href="Statistical_hypothesis_testing" class="mw-redirect" title="Statistical hypothesis testing">Statistical hypothesis testing</a>

<ul><li><a href="Analysis_of_variance" title="Analysis of variance">Analysis of variance (ANOVA)</a></li>

<li><a href="Regression_analysis" title="Regression analysis">Regression analysis</a></li>

<li><a href="ROC_curve" class="mw-redirect" title="ROC curve">ROC curve</a></li>

<li><a href="Student's_t-test" title="Student's t-test">Student's t-test</a></li>

<li><a href="List_of_statistical_packages" class="mw-redirect" title="List of statistical packages">Statistical software</a></li></ul>

</div></td></tr><tr><th scope="row" class="navbox-group" style="width:1%">Infectious and epidemic disease prevention</th><td class="navbox-list-with-group navbox-list navbox-odd wraplinks" style="width:100%;padding:0"><div style="padding:0 0.25em">

<ul><li><a href="Asymptomatic_carrier" title="Asymptomatic carrier">Asymptomatic carrier</a></li>

<li><a href="Epidemic" title="Epidemic">Epidemics</a>

<li><a href="Notifiable_disease" title="Notifiable disease">Notifiable diseases</a>

<li><a href="Public_health_surveillance" title="Public health surveillance">Public health surveillance</a>

<ul><li><a href="Disease_surveillance" title="Disease surveillance">Disease surveillance</a></li></ul></li>

<li><a href="Quarantine" title="Quarantine">Quarantine</a></li>

<li><a href="Sexually_transmitted_infection" title="Sexually transmitted infection">Sexually transmitted infection</a></li>

<li><a href="Social_distancing" title="Social distancing">Social distancing</a></li>

<li><a href="Tropical_disease" title="Tropical disease">Tropical disease</a></li>

<li><a href="Vaccine_trial" title="Vaccine trial">Vaccine trial</a></li>

</div></td></tr><tr><th scope="row" class="navbox-group" style="width:1%">Food hygiene and safety management</th><td class="navbox-list-with-group navbox-list navbox-even wraplinks" style="width:100%;padding:0"><div style="padding:0 0.25em">

<ul><li>Food

<ul><li><a href="Food_additive" title="Food additive">Additive</a></li>

<li><a href="Food_chemistry" title="Food chemistry">Chemistry</a></li>

<li><a href="Food_engineering" title="Food engineering">Engineering</a></li>

<li><a href="Food_microbiology" title="Food microbiology">Microbiology</a></li>

<li><a href="Food_processing" title="Food processing">Processing</a></li>

<li><a href="Food_safety" title="Food safety">Safety</a></li>

<li>Safety scandals</li></ul></li>

<li><a href="Good_agricultural_practice" title="Good agricultural practice">Good agricultural practice</a></li>

<li><a href="Good_manufacturing_practice" title="Good manufacturing practice">Good manufacturing practice</a>

<ul><li><a href="HACCP" class="mw-redirect" title="HACCP">HACCP</a></li>

</div></td></tr><tr><th scope="row" class="navbox-group" style="width:1%">Health behavioral sciences</th><td class="navbox-list-with-group navbox-list navbox-odd wraplinks" style="width:100%;padding:0"><div style="padding:0 0.25em">

<ul><li><a href="Diffusion_of_innovations" title="Diffusion of innovations">Diffusion of innovations</a></li>

<li><a href="Health_belief_model" title="Health belief model">Health belief model</a></li>

<li><a href="Health_communication" title="Health communication">Health communication</a></li>

<li><a href="Health_psychology" title="Health psychology">Health psychology</a></li>

<li><a href="Positive_deviance" title="Positive deviance">Positive deviance</a></li>

<li><a href="PRECEDE%E2%80%93PROCEED_model" title="PRECEDE–PROCEED model">PRECEDE–PROCEED model</a></li>

<li><a href="Social_cognitive_theory" title="Social cognitive theory">Social cognitive theory</a></li>

<li><a href="Social_norms_approach" title="Social norms approach">Social norms approach</a></li>

<li><a href="Theory_of_planned_behavior" title="Theory of planned behavior">Theory of planned behavior</a></li>

<li><a href="Transtheoretical_model" title="Transtheoretical model">Transtheoretical model</a></li></ul>

</div></td></tr><tr><th scope="row" class="navbox-group" style="width:1%">Organizations, education and history</th><td class="navbox-list-with-group navbox-list navbox-odd wraplinks" style="width:100%;padding:0"><div style="padding:0 0.25em"></div><table class="nowraplinks navbox-subgroup" style="border-spacing:0"><tbody><tr><th scope="row" class="navbox-group" style="width:1%">Organizations</th><td class="navbox-list-with-group navbox-list navbox-even" style="width:100%;padding:0"><div style="padding:0 0.25em">

<ul><li>Caribbean

<ul><li><a href="Caribbean_Public_Health_Agency" title="Caribbean Public Health Agency">Caribbean Public Health Agency</a></li></ul></li>

<li>China

<ul><li><a href="Chinese_Center_for_Disease_Control_and_Prevention" title="Chinese Center for Disease Control and Prevention">Center for Disease Control and Prevention</a></li></ul></li>

<li>Europe

<ul><li><a href="European_Centre_for_Disease_Prevention_and_Control" title="European Centre for Disease Prevention and Control">Centre for Disease Prevention and Control</a></li>

<li><a href="European_Parliament_Committee_on_the_Environment%2C_Public_Health_and_Food_Safety" title="European Parliament Committee on the Environment, Public Health and Food Safety">Committee on the Environment, Public Health and Food Safety</a></li></ul></li>

<li>Russia

<ul><li><a href="Rospotrebnadzor" title="Rospotrebnadzor">Rospotrebnadzor</a></li></ul></li>

<li>India

<ul><li><a href="Ministry_of_Health_and_Family_Welfare" title="Ministry of Health and Family Welfare">Ministry of Health and Family Welfare</a></li></ul></li>

<li>Canada

<ul><li><a href="Health_Canada" title="Health Canada">Health Canada</a></li>

<li><a href="Public_Health_Agency_of_Canada" title="Public Health Agency of Canada">Public Health Agency</a></li></ul></li>

<li>U.S.

<ul><li><a href="Centers_for_Disease_Control_and_Prevention" title="Centers for Disease Control and Prevention">Centers for Disease Control and Prevention</a></li>

<li><a href="Health_departments_in_the_United_States" title="Health departments in the United States">Health departments in the United States</a></li>

<li><a href="Council_on_Education_for_Public_Health" title="Council on Education for Public Health">Council on Education for Public Health</a></li>

<li><a href="United_States_Public_Health_Service" title="United States Public Health Service">Public Health Service</a></li></ul></li>

<li><a href="World_Health_Organization" title="World Health Organization">World Health Organization</a></li>

<li><a href="World_Toilet_Organization" title="World Toilet Organization">World Toilet Organization</a></li>

</div></td></tr><tr><th scope="row" class="navbox-group" style="width:1%">Education</th><td class="navbox-list-with-group navbox-list navbox-odd" style="width:100%;padding:0"><div style="padding:0 0.25em">

<ul><li><a href="Health_education" title="Health education">Health education</a></li>

<li>Higher education

<ul><li><a href="Bachelor_of_Science_in_Public_Health" title="Bachelor of Science in Public Health">Bachelor of Science in Public Health</a></li>

<li><a href="Doctor_of_Public_Health" title="Doctor of Public Health">Doctor of Public Health</a></li>

<li><a href="Professional_degrees_of_public_health" title="Professional degrees of public health">Professional degrees of public health</a></li>

<li>Schools of public health</li></ul></li></ul>

</div></td></tr><tr><th scope="row" class="navbox-group" style="width:1%">History</th><td class="navbox-list-with-group navbox-list navbox-even" style="width:100%;padding:0"><div style="padding:0 0.25em">

<ul><li><a href="History_of_public_health_in_the_United_Kingdom" title="History of public health in the United Kingdom">History of public health in the United Kingdom</a></li>

<li><a href="History_of_public_health_in_the_United_States" title="History of public health in the United States">History of public health in the United States</a></li>

<li><a href="History_of_public_health_in_Australia" title="History of public health in Australia">History of public health in Australia</a></li>

<li><a href="Sara_Josephine_Baker" title="Sara Josephine Baker">Sara Josephine Baker</a></li>

<li><a href="Samuel_Jay_Crumbine" title="Samuel Jay Crumbine">Samuel Jay Crumbine</a></li>

<li><a href="Carl_Rogers_Darnall" title="Carl Rogers Darnall">Carl Rogers Darnall</a></li>

<li><a href="Joseph_Lister" title="Joseph Lister">Joseph Lister</a></li>

<li><a href="Margaret_Sanger" title="Margaret Sanger">Margaret Sanger</a></li>

<li><a href="Mary_Mallon" title="Mary Mallon">Typhoid Mary</a></li>

<li><a href="Radium_Girls" title="Radium Girls">Radium Girls</a></li>

<li><a href="Germ_theory_of_disease" title="Germ theory of disease">Germ theory of disease</a></li>

<li><a href="Social_hygiene_movement" title="Social hygiene movement">Social hygiene movement</a></li></ul>

</div></td></tr></tbody></table><div></div></td></tr><tr><td class="navbox-abovebelow" colspan="2"><div>

<ul><li> Category</li>

<li> <a href="https://commons.wikimedia.org/wiki/Category:Public_health" class="extiw external" title="commons:Category:Public health">Commons</a></li>

<li> WikiProject</li></ul>

</div></td></tr></tbody></table></div></div><div><div class="zim-footer">

This article is issued from <a class="external text" title="Last edited on 2025-08-05" href="https://en.wikipedia.org/wiki/?title=Randomized_controlled_trial&oldid=1304366012">Wikipedia</a>. The text is available under <a class="external text" href="https://creativecommons.org/licenses/by-sa/4.0/deed.en">Creative Commons Attribution-Share Alike 4.0</a> unless otherwise noted. Additional terms may apply for the media files.

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