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<span id="openzim-page-title" class="mw-page-title-main"><span class="mw-page-title-main">Randomization</span></span>

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<p><b>Randomization</b> is a statistical process in which a random mechanism is employed to select a sample from a population or assign subjects to different groups.<sup id="cite_ref-:0_1-0" class="reference"><a href="#cite_note-:0-1"><span class="cite-bracket">[</span>1<span class="cite-bracket">]</span></a></sup><sup id="cite_ref-:3_2-0" class="reference"><a href="#cite_note-:3-2"><span class="cite-bracket">[</span>2<span class="cite-bracket">]</span></a></sup><sup id="cite_ref-:6_3-0" class="reference"><a href="#cite_note-:6-3"><span class="cite-bracket">[</span>3<span class="cite-bracket">]</span></a></sup> The process is crucial in ensuring the random allocation of experimental units or treatment protocols, thereby minimizing <a href="Selection_bias" title="Selection bias">selection bias</a> and enhancing the <a href="Validity_(statistics)" title="Validity (statistics)">statistical validity</a>.<sup id="cite_ref-:4_4-0" class="reference"><a href="#cite_note-:4-4"><span class="cite-bracket">[</span>4<span class="cite-bracket">]</span></a></sup> It facilitates the objective comparison of treatment effects in <a href="Design_of_experiments" title="Design of experiments">experimental design</a>, as it equates groups statistically by balancing both known and unknown factors at the outset of the study. In statistical terms, it underpins the principle of probabilistic equivalence among groups, allowing for the unbiased estimation of treatment effects and the generalizability of conclusions drawn from sample data to the broader population.<sup id="cite_ref-5" class="reference"><a href="#cite_note-5"><span class="cite-bracket">[</span>5<span class="cite-bracket">]</span></a></sup><sup id="cite_ref-6" class="reference"><a href="#cite_note-6"><span class="cite-bracket">[</span>6<span class="cite-bracket">]</span></a></sup>

</p><p>Randomization is not haphazard; instead, a <a href="Stochastic_process" title="Stochastic process">random process</a> is a sequence of random variables describing a process whose outcomes do not follow a deterministic pattern but follow an evolution described by <a href="Probability_distribution" title="Probability distribution">probability distributions</a>. For example, a random sample of individuals from a population refers to a sample where every individual has a known probability of being sampled. This would be contrasted with <a href="Nonprobability_sampling" title="Nonprobability sampling">nonprobability sampling</a>, where <a href="Arbitrariness" title="Arbitrariness">arbitrary</a> individuals are selected. A <a href="Wald%E2%80%93Wolfowitz_runs_test" title="Wald–Wolfowitz runs test">runs test</a> can be used to determine whether the occurrence of a set of measured values is random.<sup id="cite_ref-7" class="reference"><a href="#cite_note-7"><span class="cite-bracket">[</span>7<span class="cite-bracket">]</span></a></sup> Randomization is widely applied in various fields, especially in scientific research, statistical analysis, and resource allocation, to ensure fairness and validity in the outcomes.<sup id="cite_ref-:5_8-0" class="reference"><a href="#cite_note-:5-8"><span class="cite-bracket">[</span>8<span class="cite-bracket">]</span></a></sup><sup id="cite_ref-9" class="reference"><a href="#cite_note-9"><span class="cite-bracket">[</span>9<span class="cite-bracket">]</span></a></sup><sup id="cite_ref-10" class="reference"><a href="#cite_note-10"><span class="cite-bracket">[</span>10<span class="cite-bracket">]</span></a></sup>

</p><p>In various contexts, randomization may involve

</p>

<ul><li><u>Generating Random Permutations</u>: This is essential in various situations, such as <a href="Shuffling" title="Shuffling">shuffling cards</a>. By randomly rearranging the sequence, it ensures fairness and unpredictability in games and experiments.</li>

<li><u>Selecting Random Samples from Populations</u>: In <a href="Sampling_(statistics)" title="Sampling (statistics)">statistical sampling</a>, this method is vital for obtaining representative samples. By randomly choosing a subset of individuals, biases are minimized, ensuring that the sample accurately reflects the larger population.</li>

<li><u>Random Allocation in Experimental Design</u>: Random assignment of experimental units to treatment or control conditions is fundamental in scientific studies. This approach ensures that each unit has an equal chance of receiving any treatment, thereby reducing <a href="Systematic_bias" class="mw-redirect" title="Systematic bias">systematic bias</a> and improving the reliability of experimental results.</li>

<li><u>Generating Random Numbers</u>: The process of <a href="Random_number_generation" title="Random number generation">random number generation</a> is central to simulations, <a href="Cryptography" title="Cryptography">cryptographic</a> applications, and statistical analysis. These numbers form the basis for simulations, model testing, and secure data encryption.</li>

<li><u>Data Stream Transformation</u>: In telecommunications, randomization is used to transform <a href="Data_stream" title="Data stream">data streams</a>. Techniques like <a href="Scrambler" title="Scrambler">scramblers</a> randomize the data to prevent predictable patterns, which is crucial for securing communication channels and enhancing transmission reliability."</li></ul>

<p>Randomization has many uses in <a href="Science" title="Science">gambling</a>, political use, statistical analysis, <a href="Art" title="Art">art</a>, <a href="Cryptography" title="Cryptography">cryptography</a>, <a href="Video_game" title="Video game">gaming</a> and other fields.

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<div class="mw-heading mw-heading2"><h2 id="In_gambling">In gambling</h2></div>

<p>In the world of <a href="Gambling" title="Gambling">gambling</a>, the integrity and fairness of games hinge significantly on effective randomization. This principle serves as a cornerstone in gambling, ensuring that each game outcome is unpredictable and not manipulable. The necessity for advanced randomization methods stems from the potential for skilled gamblers to exploit weaknesses in poorly randomized systems. High-quality randomization thwarts attempts at prediction or manipulation, maintaining the fairness of games. A quintessential example of randomization in gambling is the <a href="Shuffling_playing_cards" class="mw-redirect" title="Shuffling playing cards">shuffling of playing cards</a>. This process must be thoroughly random to prevent any predictability in the order of cards.<sup id="cite_ref-11" class="reference"><a href="#cite_note-11"><span class="cite-bracket">[</span>11<span class="cite-bracket">]</span></a></sup> Casinos often employ <a href="Shuffling_machine" title="Shuffling machine">automatic shuffling machines</a>, which enhance randomness beyond what manual shuffling can achieve.

</p><p>With the rise of online casinos, digital <a href="Random_number_generation" title="Random number generation">random number generators (RNGs)</a> have become crucial. These RNGs use complex algorithms to produce outcomes that are as unpredictable as their real-world counterparts.<sup id="cite_ref-12" class="reference"><a href="#cite_note-12"><span class="cite-bracket">[</span>12<span class="cite-bracket">]</span></a></sup> The gambling industry invests heavily in research to develop more effective randomization techniques. To ensure that gambling games are fair and random, regulatory bodies rigorously test and certify shuffling and random number generation methods. This oversight is vital in maintaining trust in the gambling industry, ensuring that players have equal chances of winning.

</p><p>The unpredictability inherent in randomization is also a key factor in the psychological appeal of gambling. The thrill and suspense created by the uncertainty of outcomes contribute significantly to the allure and excitement of gambling games.<sup id="cite_ref-13" class="reference"><a href="#cite_note-13"><span class="cite-bracket">[</span>13<span class="cite-bracket">]</span></a></sup>

</p><p>In summary, randomization in gambling is not just a technical necessity; it is a fundamental principle that upholds the fairness, integrity, and thrill of the games. As technology advances, so too do the methods to ensure that this randomization remains effective and beyond reproach

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<div class="mw-heading mw-heading2"><h2 id="In_politics">In politics</h2></div>

<p>The concept of randomization in political systems, specifically through the method of allotment or <a href="Sortition" title="Sortition">sortition</a>, has ancient roots and contemporary relevance, significantly impacting the evolution and practice of democracy.

</p><p>In the fifth century BC, <a href="Athenian_democracy" title="Athenian democracy">Athenian democracy</a> was pioneering in its approach to ensuring political equality, or <a href="Isonomia" title="Isonomia">isonomia</a>.<sup id="cite_ref-:1_14-0" class="reference"><a href="#cite_note-:1-14"><span class="cite-bracket">[</span>14<span class="cite-bracket">]</span></a></sup><sup id="cite_ref-:2_15-0" class="reference"><a href="#cite_note-:2-15"><span class="cite-bracket">[</span>15<span class="cite-bracket">]</span></a></sup> Central to this system was the principle of random selection, seen as a cornerstone for fair representation.<sup id="cite_ref-:1_14-1" class="reference"><a href="#cite_note-:1-14"><span class="cite-bracket">[</span>14<span class="cite-bracket">]</span></a></sup> The unique structure of Greek democracy, which translates to "rule by the people," was exemplified by administrative roles being rotated among citizens, selected randomly through lot. This method was perceived as more democratic than elections, which the Athenians argued could lead to inequalities. They believed that elections, which often favored candidates based on merit or popularity, contradicted the principle of equal rights for all citizens. Furthermore, the random allotment of positions like magistrates or jury members served as a deterrent to vote-buying and corruption, as it was impossible to predict who would be chosen for these roles.<sup id="cite_ref-:2_15-1" class="reference"><a href="#cite_note-:2-15"><span class="cite-bracket">[</span>15<span class="cite-bracket">]</span></a></sup>

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<p>In modern times, the concept of allotment, also known as <a href="Sortition" title="Sortition">sortition</a>, is primarily seen in the selection of <a href="Jury_selection" title="Jury selection">jurors</a> within Anglo-Saxon legal systems, such as those in the UK and the United States. However, its political implications extend further. There have been various proposals to integrate sortition into government structures. The idea is that sortition could introduce a new dimension of representation and fairness in political systems, countering issues associated with electoral politics.<sup id="cite_ref-16" class="reference"><a href="#cite_note-16"><span class="cite-bracket">[</span>16<span class="cite-bracket">]</span></a></sup> This concept has garnered academic interest, with scholars exploring the potential of random selection in enhancing the democratic process, both in political frameworks and organizational structures.<sup id="cite_ref-17" class="reference"><a href="#cite_note-17"><span class="cite-bracket">[</span>17<span class="cite-bracket">]</span></a></sup> The ongoing study and debate surrounding the use of sortition reflect its enduring relevance and potential as a tool for political innovation and integrity.

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<div class="mw-heading mw-heading2"><h2 id="Randomization_in_statistical_analysis">Randomization in statistical analysis</h2></div>

<p>Randomization is a core principle in <a href="Statistical_theory" title="Statistical theory">statistical theory</a>, whose importance was emphasized by <a href="Charles_Sanders_Peirce" title="Charles Sanders Peirce">Charles S. Peirce</a> in "<a href="Charles_Sanders_Peirce_bibliography#illus" title="Charles Sanders Peirce bibliography">Illustrations of the Logic of Science</a>" (1877–1878) and "<a href="Charles_Sanders_Peirce_bibliography#SIL" title="Charles Sanders Peirce bibliography">A Theory of Probable Inference</a>" (1883). Its application in statistical methodologies is multifaceted and includes critical processes such as <a href="Randomized_controlled_trial" title="Randomized controlled trial">randomized controlled experiments</a>, <a href="Survey_sampling" title="Survey sampling">survey sampling</a> and <a href="Simulation" title="Simulation">simulations</a>.

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<div class="mw-heading mw-heading3"><h3 id="Randomized_controlled_experiment">Randomized controlled experiment</h3></div>

<p>In the realm of scientific research, particularly within <a href="Clinical_study_design" title="Clinical study design">clinical study designs</a>, constraints such as limited manpower, material resources, financial backing, and time necessitate a selective approach to participant inclusion.<sup id="cite_ref-:3_2-1" class="reference"><a href="#cite_note-:3-2"><span class="cite-bracket">[</span>2<span class="cite-bracket">]</span></a></sup><sup id="cite_ref-:4_4-1" class="reference"><a href="#cite_note-:4-4"><span class="cite-bracket">[</span>4<span class="cite-bracket">]</span></a></sup> Despite the broad spectrum of potential participants who fulfill the inclusion criteria, it is impractical to incorporate every eligible individual in the target population due to these constraints. Therefore, a representative subset of <a href="Treatment_groups" class="mw-redirect" title="Treatment groups">treatment groups</a> is chosen based on the specific requirements of the research.<sup id="cite_ref-:5_8-1" class="reference"><a href="#cite_note-:5-8"><span class="cite-bracket">[</span>8<span class="cite-bracket">]</span></a></sup> A <a href="Random_sampling" class="mw-redirect" title="Random sampling">randomized sampling method</a> is employed to ensure the integrity and representativeness of the study. This method ensures that all qualified subjects within the target population have an equal opportunity to be selected. Such a strategy is pivotal in mirroring the overall characteristics of the target population and in mitigating the risk of selection bias.

</p><p>The selected samples (or continuous non-randomly sampled samples) are grouped using randomization methods so that all research subjects in the sample have an equal chance of entering the experimental group or the control group and receiving corresponding treatment. In particular, the random grouping after the research subjects are stratified can make the known or unknown influencing factors between the groups basically consistent, thereby enhancing the comparability between the groups.<sup id="cite_ref-:4_4-2" class="reference"><a href="#cite_note-:4-4"><span class="cite-bracket">[</span>4<span class="cite-bracket">]</span></a></sup>

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<div class="mw-heading mw-heading3"><h3 id="Survey_sampling">Survey sampling</h3></div>

<p><a href="Survey_sampling" title="Survey sampling">Survey sampling</a> uses randomization, following the criticisms of previous "representative methods" by <a href="Jerzy_Neyman" title="Jerzy Neyman">Jerzy Neyman</a> in his 1922 report to the <a href="International_Statistical_Institute" title="International Statistical Institute">International Statistical Institute</a>. It randomly displays the answer options to survey participants, which prevents order bias caused by the tendency of respondents to choose the first option when the same order is presented to different respondents.<sup id="cite_ref-18" class="reference"><a href="#cite_note-18"><span class="cite-bracket">[</span>18<span class="cite-bracket">]</span></a></sup> To overcome this, researchers can give the answer options in a random order so that the respondents allocate some time to read all the options and choose an honest answer. For example, consider an automobile dealer who wants to conduct a feedback survey and ask the respondents to select their preferred automobile brand. The user can create a study with randomized answers to display the different automobile brands so that the respondents do not see them in the same order.

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

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</style><div role="note" class="hatnote navigation-not-searchable">Main article: <a href="Resampling_(statistics)" title="Resampling (statistics)">Resampling (statistics)</a></div>

<p>Some important methods of statistical inference use <a href="Resampling_(statistics)" title="Resampling (statistics)">resampling</a> from the observed data. Multiple alternative versions of the data-set that "might have been observed" are created by randomization of the original data-set, the only one observed. The variation of statistics calculated for these alternative data-sets is a guide to the uncertainty of statistics estimated from the original data.

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

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

<p>In many scientific and engineering fields, computer simulations of real phenomena are commonly used. When the real phenomena are affected by unpredictable processes, such as radio noise or day-to-day weather, these processes can be simulated using random or pseudo-random numbers. One of the most prominent uses of randomization in simulations is in <a href="Monte_Carlo_method" title="Monte Carlo method">Monte Carlo methods</a>. These methods rely on repeated random sampling to obtain numerical results, typically to model probability distributions or to estimate uncertain quantities in a system.

</p><p>Randomization also allows for the testing of models or algorithms against unexpected inputs or scenarios. This is essential in fields like machine learning and artificial intelligence, where algorithms must be robust against a variety of inputs and conditions.<sup id="cite_ref-19" class="reference"><a href="#cite_note-19"><span class="cite-bracket">[</span>19<span class="cite-bracket">]</span></a></sup>

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<div class="mw-heading mw-heading2"><h2 id="In_cryptography">In cryptography</h2></div>

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

<p>Randomization plays a fascinating and often underappreciated role in literature, music, and art, where it introduces elements of unpredictability and spontaneity. Here is how it manifests in each of these creative fields:

</p>

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

<p>Pioneered by <a href="Surrealism" title="Surrealism">surrealists</a> and later popularized by writers like <a href="William_S._Burroughs" title="William S. Burroughs">William S. Burroughs</a>, automatic writing and <a href="Cut-up_technique" title="Cut-up technique">cut-up techniques</a> involve randomly rearranging text to create new literary forms. It disrupts linear narratives, fostering unexpected connections and meanings.<sup id="cite_ref-20" class="reference"><a href="#cite_note-20"><span class="cite-bracket">[</span>20<span class="cite-bracket">]</span></a></sup>

</p>

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

<p>In <a href="Aleatoric_music" title="Aleatoric music">aleatoric music</a>, elements of the composition are left to chance or the performer's discretion. Composers like <a href="John_Cage" title="John Cage">John Cage</a> used randomization to create music where certain elements are unforeseeable, resulting in each performance being uniquely different. Modern musicians sometimes employ computer algorithms that generate music based on random inputs. These compositions can range from electronic music to more classical forms, where randomness plays a key role in creating harmony, melody, or rhythm.

</p>

<div role="note" class="hatnote navigation-not-searchable">See also: <a href="Computer_music" title="Computer music">Computer music</a></div>

<p>Some artists in <a href="Abstract_expressionism" title="Abstract expressionism">abstract expressionism</a> movement, like <a href="Jackson_Pollock" title="Jackson Pollock">Jackson Pollock</a>, used random methods (like dripping or splattering paint) to create their artworks. This approach emphasizes the physical act of painting and the role of chance in the artistic process.Also, contemporary artists often use algorithms and computer-generated randomness to create visual art. This can result in intricate patterns and designs that would be difficult or impossible to predict or replicate manually.

</p>

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

<p>Although historically "manual" randomization techniques (such as shuffling cards, drawing pieces of paper from a bag, spinning a <a href="Roulette" title="Roulette">roulette</a> wheel) were common, nowadays automated techniques are mostly used. As both selecting <a href="Random_sample" class="mw-redirect" title="Random sample">random samples</a> and <a href="Random_permutation" title="Random permutation">random permutations</a> can be reduced to simply selecting random numbers, <a href="Random_number_generation" title="Random number generation">random number generation</a> methods are now most commonly used, both <a href="Hardware_random_number_generator" title="Hardware random number generator">hardware random number generators</a> and <a href="Pseudo-random_number_generator" class="mw-redirect" title="Pseudo-random number generator">pseudo-random number generators</a>.

</p>

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

<p>Randomization is used in optimization to alleviate the computational burden associated to robust control techniques: a sample of values of the uncertainty parameters is randomly drawn and robustness is enforced for these values only. This approach has gained popularity by the introduction of rigorous theories that permit one to have control on the probabilistic level of robustness, see <a href="Scenario_optimization" title="Scenario optimization">scenario optimization</a>.

</p><p>Common randomization methods including

</p>

<ul><li>Simple randomization (<a href="Coin_flipping" title="Coin flipping">coin flipping</a>, <a href="Drawing_lots_(decision_making)" title="Drawing lots (decision making)">drawing lots</a> and <a href="Random_number_generation" title="Random number generation">random number method</a>）<sup id="cite_ref-:6_3-1" class="reference"><a href="#cite_note-:6-3"><span class="cite-bracket">[</span>3<span class="cite-bracket">]</span></a></sup></li>

<li><a href="Stratified_randomization" title="Stratified randomization">Stratified randomization</a> (<a href="Stratified_sampling" title="Stratified sampling">stratified sampling</a> and stratified allocation)<sup id="cite_ref-:6_3-2" class="reference"><a href="#cite_note-:6-3"><span class="cite-bracket">[</span>3<span class="cite-bracket">]</span></a></sup></li>

<li>Block randomization<sup id="cite_ref-:6_3-3" class="reference"><a href="#cite_note-:6-3"><span class="cite-bracket">[</span>3<span class="cite-bracket">]</span></a></sup></li>

<li>Systematic randomization</li>

<li>Cluster randomization</li>

<li><a href="Multistage_sampling" title="Multistage sampling">Multistage sampling</a></li>

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

<li>Covariate Adaptive Randomization<sup id="cite_ref-:6_3-4" class="reference"><a href="#cite_note-:6-3"><span class="cite-bracket">[</span>3<span class="cite-bracket">]</span></a></sup></li></ul>

<ul><li><a href="Randomized_algorithm" title="Randomized algorithm">Randomized algorithm</a></li>

<li><a href="Random_number_generation" title="Random number generation">Random number generation</a></li></ul>

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

<li id="cite_note-:0-1"><span class="mw-cite-backlink"><b><a href="#cite_ref-:0_1-0">^</a></b></span> <span class="reference-text"><a href="Oxford_English_Dictionary" title="Oxford English Dictionary">Oxford English Dictionary</a> "randomization"</span>

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<div class="mw-heading mw-heading2"><h2 id="External_links">External links</h2></div>

<ul><li><a rel="nofollow" class="external text" href="http://jan.seifseit.de/programme/qube/qube.php">RQube</a> <a rel="nofollow" class="external text" href="https://web.archive.org/web/20190620002358/http://jan.seifseit.de/programme/qube/qube.php">Archived</a> 2019-06-20 at the <a href="Wayback_Machine" title="Wayback Machine">Wayback Machine</a> - Generate quasi-random stimulus sequences for experimental designs</li>

<li><a rel="nofollow" class="external text" href="http://www.randomisation.eu">RandList</a> - Randomization List Generator</li></ul>

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</style><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<br>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><b><a href="Optimal_design" class="mw-redirect" title="Optimal design">Optimal design</a></b>: <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="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><br> 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><b><a href="Glossary_of_experimental_design" title="Glossary of experimental design">Treatment</a></b></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><b><a href="Blocking_(statistics)" title="Blocking (statistics)">Blocking</a></b></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> <br> 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><b><a href="Random_effect" class="mw-redirect" title="Random effect">Random effect</a></b></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><b><a href="Analysis_of_variance" title="Analysis of variance">Analysis of variance (Anova)</a></b></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"><b>Manova</b> (<i>multivariate</i>)</a></li>

<li><a href="Analysis_of_covariance" title="Analysis of covariance"><b>Ancova</b> (<i>covariance</i>)</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> <br> <br><a href="Completely_randomized_design" title="Completely randomized design">Completely<br>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><b><a href="Factorial_experiment" title="Factorial experiment">Factorial</a></b></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><b><a href="Response_surface_methodology" title="Response surface methodology">Response surface methodology</a></b></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><b><a href="Randomized_block_design" class="mw-redirect" title="Randomized block design">Block</a></b></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> <br> <b><a href="Repeated_measures_design" title="Repeated measures design">Repeated measures design</a></b></li>

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

<ul><li><b><a href="Randomized_controlled_trial" title="Randomized controlled trial">Randomized controlled trial</a></b></li>

<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><span class="nowrap"><span class="skin-invert-image noviewer" typeof="mw:File"></span> </span><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 uncollapsed 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_controlled_trial" title="Randomized controlled trial">Randomized controlled trial</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">L<sup><i>p</i></sup> 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"><span style="font-size: 85%;">(monotone)</span></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"><i>Z</i>-test <span style="font-size: 85%;">(normal)</span></a></li>

<li><a href="Student's_t-test" title="Student's t-test">Student's <i>t</i>-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 <span style="font-size: 85%;">(Shapiro–Wilk)</span></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 <span style="font-size: 85%;">(Wilcoxon)</span></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 <span style="font-size: 85%;">(Mann–Whitney)</span></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 <span style="font-size: 85%;">(Kruskal–Wallis)</span></a></li>

<li><a href="Friedman_test" title="Friedman test">2-way <span style="font-size: 85%;">(Friedman)</span></a></li>

<li><a href="Jonckheere's_trend_test" title="Jonckheere's trend test">Ordered alternative <span style="font-size: 85%;">(Jonckheere–Terpstra)</span></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 <span style="font-size: 85%;">(Bernoulli)</span></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 <span style="font-size: 85%;">(Ljung–Box)</span></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 <span style="font-size: 85%;">(Box–Jenkins)</span></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 mw-collapsed 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><span class="noviewer" typeof="mw:File"><span title="Category"></span></span><b>Category</b></li>

<li><b><span class="nowrap"><span class="skin-invert-image noviewer" typeof="mw:File"></span> </span><a href="Portal%3AMathematics" title="Portal:Mathematics">Mathematics portal</a></b></li>

<li><span class="noviewer" typeof="mw:File"><span title="Commons page"></span></span><b><a href="https://commons.wikimedia.org/wiki/Category:Statistics" class="extiw external" title="commons:Category:Statistics">Commons</a></b></li>

<li><span class="noviewer" typeof="mw:File"><span title="WikiProject"></span></span> <b>WikiProject</b></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=Randomization&oldid=1304365750">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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