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Student's t-test

Index Student's t-test

The t-test is any statistical hypothesis test in which the test statistic follows a Student's ''t''-distribution under the null hypothesis. [1]

102 relations: Analysis of variance, Arithmetic mean, Average, Šidák correction for t-test, Bartlett's test, Behrens–Fisher problem, Bias of an estimator, Biochemistry, Biometrika, Blocking (statistics), Brewery, Brown–Forsythe test, Cambridge University Press, Central limit theorem, Chi-squared distribution, Conditional change model, Confounding, CRC Press, DAP (software), Data, Degrees of freedom (statistics), Dublin, Expected value, F-test, F-test of equality of variances, Google Docs, Sheets, and Slides, Gretl, Guinness, Hotelling's T-squared distribution, Independence (probability theory), Independent and identically distributed random variables, Ireland, Java (programming language), Julia (programming language), Karl Pearson, Kolmogorov–Smirnov test, Levene's test, LibreOffice, LibreOffice Calc, Linear regression, Location test, Location testing for Gaussian scale mixture distributions, Mann–Whitney U test, Mark Thoma, MATLAB, Mean, Microsoft Excel, Minitab, Minnesota Multiphasic Personality Inventory, Nonparametric statistics, ..., Normal distribution, Normality test, Null hypothesis, Observational study, One- and two-tailed tests, Outlier, P-value, Paired difference test, Pearson correlation coefficient, Pediatrics (journal), Pen name, Pooled variance, Power (statistics), PSPP, Python (programming language), Q–Q plot, QtiPlot, R (programming language), Sample mean and covariance, Sampling (statistics), SAS (software), Scale parameter, Shapiro–Wilk test, Skewness, Slutsky's theorem, Spreadsheet, SPSS, Standard deviation, Standard error, Stata, Statistical hypothesis testing, Statistical population, Statistical Science, Statistical significance, Statistical unit, Statistics, Stout, Student, Student's t-distribution, T-statistic, Test statistic, Type I and type II errors, University College London, University of Cambridge, University of Oxford, Variance, Welch's t-test, Welch–Satterthwaite equation, Wilcoxon signed-rank test, William Sealy Gosset, Wolfram Mathematica, Z-test. Expand index (52 more) »

Analysis of variance

Analysis of variance (ANOVA) is a collection of statistical models and their associated estimation procedures (such as the "variation" among and between groups) used to analyze the differences among group means in a sample.

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Arithmetic mean

In mathematics and statistics, the arithmetic mean (stress on third syllable of "arithmetic"), or simply the mean or average when the context is clear, is the sum of a collection of numbers divided by the number of numbers in the collection.

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In colloquial language, an average is a middle or typical number of a list of numbers.

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Šidák correction for t-test

One of the application of Student's t-test is to test the location of one sequence of independent and identically distributed random variables.

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Bartlett's test

In statistics, Bartlett's test (see Snedecor and Cochran, 1989) is used to test if k samples are from populations with equal variances.

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Behrens–Fisher problem

In statistics, the Behrens–Fisher problem, named after Walter Behrens and Ronald Fisher, is the problem of interval estimation and hypothesis testing concerning the difference between the means of two normally distributed populations when the variances of the two populations are not assumed to be equal, based on two independent samples.

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Bias of an estimator

In statistics, the bias (or bias function) of an estimator is the difference between this estimator's expected value and the true value of the parameter being estimated.

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Biochemistry, sometimes called biological chemistry, is the study of chemical processes within and relating to living organisms.

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Biometrika is a peer-reviewed scientific journal published by Oxford University Press for the Biometrika Trust.

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Blocking (statistics)

In the statistical theory of the design of experiments, blocking is the arranging of experimental units in groups (blocks) that are similar to one another.

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A brewery or brewing company is a business that makes and sells beer.

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Brown–Forsythe test

The Brown–Forsythe test is a statistical test for the equality of group variances based on performing an ANOVA on a transformation of the response variable.

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Cambridge University Press

Cambridge University Press (CUP) is the publishing business of the University of Cambridge.

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Central limit theorem

In probability theory, the central limit theorem (CLT) establishes that, in some situations, when independent random variables are added, their properly normalized sum tends toward a normal distribution (informally a "bell curve") even if the original variables themselves are not normally distributed.

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Chi-squared distribution

No description.

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Conditional change model

The conditional change model in statistics is the analytic procedure in which change scores are regressed on baseline values, together with the explanatory variables of interest (often including indicators of treatment groups).

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In statistics, a confounder (also confounding variable, confounding factor or lurking variable) is a variable that influences both the dependent variable and independent variable causing a spurious association.

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CRC Press

The CRC Press, LLC is a publishing group based in the United States that specializes in producing technical books.

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DAP (software)

Dap is a statistics and graphics program based on the C programming language that performs data management, analysis, and C-style graphical visualization tasks without requiring complex syntax.

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Data is a set of values of qualitative or quantitative variables.

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Degrees of freedom (statistics)

In statistics, the number of degrees of freedom is the number of values in the final calculation of a statistic that are free to vary.

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Dublin is the capital of and largest city in Ireland.

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Expected value

In probability theory, the expected value of a random variable, intuitively, is the long-run average value of repetitions of the experiment it represents.

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An F-test is any statistical test in which the test statistic has an ''F''-distribution under the null hypothesis.

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F-test of equality of variances

In statistics, an F-test of equality of variances is a test for the null hypothesis that two normal populations have the same variance.

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Google Docs, Sheets, and Slides

Google Docs, Google Sheets, and Google Slides are a word processor, a spreadsheet and a presentation program respectively, all part of a free, web-based software office suite offered by Google within its Google Drive service.

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gretl is an open-source statistical package, mainly for econometrics.

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Guinness is an Irish dry stout that originated in the brewery of Arthur Guinness (1725–1803) at St. James's Gate brewery in the capital city of Dublin, Ireland.

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Hotelling's T-squared distribution

In statistics Hotelling's T-squared distribution (T2) is a multivariate distribution proportional to the ''F''-distribution and arises importantly as the distribution of a set of statistics which are natural generalizations of the statistics underlying Student's ''t''-distribution.

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Independence (probability theory)

In probability theory, two events are independent, statistically independent, or stochastically independent if the occurrence of one does not affect the probability of occurrence of the other.

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Independent and identically distributed random variables

In probability theory and statistics, a sequence or other collection of random variables is independent and identically distributed (i.i.d. or iid or IID) if each random variable has the same probability distribution as the others and all are mutually independent.

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Ireland (Éire; Ulster-Scots: Airlann) is an island in the North Atlantic.

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Java (programming language)

Java is a general-purpose computer-programming language that is concurrent, class-based, object-oriented, and specifically designed to have as few implementation dependencies as possible.

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Julia (programming language)

Julia is a high-level dynamic programming language designed to address the needs of high-performance numerical analysis and computational science, without the typical need of separate compilation to be fast, while also being effective for general-purpose programming, web use or as a specification language.

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Karl Pearson

Karl Pearson HFRSE LLD (originally named Carl; 27 March 1857 – 27 April 1936) was an English mathematician and biostatistician. He has been credited with establishing the discipline of mathematical statistics. He founded the world's first university statistics department at University College London in 1911, and contributed significantly to the field of biometrics, meteorology, theories of social Darwinism and eugenics. Pearson was also a protégé and biographer of Sir Francis Galton.

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Kolmogorov–Smirnov test

In statistics, the Kolmogorov–Smirnov test (K–S test or KS test) is a nonparametric test of the equality of continuous, one-dimensional probability distributions that can be used to compare a sample with a reference probability distribution (one-sample K–S test), or to compare two samples (two-sample K–S test).

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Levene's test

In statistics, Levene's test is an inferential statistic used to assess the equality of variances for a variable calculated for two or more groups.

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LibreOffice is a free and open source office suite, a project of The Document Foundation.

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LibreOffice Calc

LibreOffice Calc is the spreadsheet component of the LibreOffice software package.

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Linear regression

In statistics, linear regression is a linear approach to modelling the relationship between a scalar response (or dependent variable) and one or more explanatory variables (or independent variables).

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Location test

A location test is a statistical hypothesis test that compares the location parameter of a statistical population to a given constant, or that compares the location parameters of two statistical populations to each other.

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Location testing for Gaussian scale mixture distributions

In statistics, the topic of location testing for Gaussian scale mixture distributions arises in some particular types of situations where the more standard Student's t-test is inapplicable.

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Mann–Whitney U test

In statistics, the Mann–Whitney U test (also called the Mann–Whitney–Wilcoxon (MWW), Wilcoxon rank-sum test, or Wilcoxon–Mann–Whitney test) is a nonparametric test of the null hypothesis that it is equally likely that a randomly selected value from one sample will be less than or greater than a randomly selected value from a second sample.

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Mark Thoma

Mark Allen Thoma (born December 15, 1956) is a macroeconomist and econometrician and a Professor of Economics at the Department of Economics of the University of Oregon.

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MATLAB (matrix laboratory) is a multi-paradigm numerical computing environment and proprietary programming language developed by MathWorks.

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In mathematics, mean has several different definitions depending on the context.

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Microsoft Excel

Microsoft Excel is a spreadsheet developed by Microsoft for Windows, macOS, Android and iOS.

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Minitab is a statistics package developed at the Pennsylvania State University by researchers Barbara F. Ryan, Thomas A. Ryan, Jr., and Brian L. Joiner in 1972.

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Minnesota Multiphasic Personality Inventory

The Minnesota Multiphasic Personality Inventory (MMPI) is a standardized psychometric test of adult personality and psychopathology.

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Nonparametric statistics

Nonparametric statistics is the branch of statistics that is not based solely on parameterized families of probability distributions (common examples of parameters are the mean and variance).

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Normal distribution

In probability theory, the normal (or Gaussian or Gauss or Laplace–Gauss) distribution is a very common continuous probability distribution.

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Normality test

In statistics, normality tests are used to determine if a data set is well-modeled by a normal distribution and to compute how likely it is for a random variable underlying the data set to be normally distributed.

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Null hypothesis

In inferential statistics, the term "null hypothesis" is a general statement or default position that there is no relationship between two measured phenomena, or no association among groups.

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Observational study

In fields such as epidemiology, social sciences, psychology and statistics, an observational study draws inferences from a sample to a population where the independent variable is not under the control of the researcher because of ethical concerns or logistical constraints.

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One- and two-tailed tests

In statistical significance testing, a one-tailed test and a two-tailed test are alternative ways of computing the statistical significance of a parameter inferred from a data set, in terms of a test statistic.

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In statistics, an outlier is an observation point that is distant from other observations.

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In statistical hypothesis testing, the p-value or probability value or asymptotic significance is the probability for a given statistical model that, when the null hypothesis is true, the statistical summary (such as the sample mean difference between two compared groups) would be the same as or of greater magnitude than the actual observed results.

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Paired difference test

In statistics, a paired difference test is a type of location test that is used when comparing two sets of measurements to assess whether their population means differ.

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Pearson correlation coefficient

In statistics, the Pearson correlation coefficient (PCC, pronounced), also referred to as Pearson's r, the Pearson product-moment correlation coefficient (PPMCC) or the bivariate correlation, is a measure of the linear correlation between two variables X and Y. It has a value between +1 and −1, where 1 is total positive linear correlation, 0 is no linear correlation, and −1 is total negative linear correlation.

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Pediatrics (journal)

Pediatrics is a peer-reviewed medical journal published by the American Academy of Pediatrics.

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Pen name

A pen name (nom de plume, or literary double) is a pseudonym (or, in some cases, a variant form of a real name) adopted by an author and printed on the title page or by-line of their works in place of their "real" name.

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Pooled variance

In statistics, pooled variance (also known as combined, composite, or overall variance) is a method for estimating variance of several different populations when the mean of each population may be different, but one may assume that the variance of each population is the same.

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Power (statistics)

The power of a binary hypothesis test is the probability that the test correctly rejects the null hypothesis (H0) when a specific alternative hypothesis (H1) is true.

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PSPP is a free software application for analysis of sampled data, intended as a free alternative for IBM SPSS Statistics.

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Python (programming language)

Python is an interpreted high-level programming language for general-purpose programming.

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Q–Q plot

In statistics, a Q–Q (quantile-quantile) plot is a probability plot, which is a graphical method for comparing two probability distributions by plotting their quantiles against each other.

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QtiPlot is a cross-platform computer program for interactive scientific graphing and data analysis.

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R (programming language)

R is a programming language and free software environment for statistical computing and graphics that is supported by the R Foundation for Statistical Computing.

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Sample mean and covariance

The sample mean or empirical mean and the sample covariance are statistics computed from a collection (the sample) of data on one or more random variables.

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Sampling (statistics)

In statistics, quality assurance, and survey methodology, sampling is the selection of a subset (a statistical sample) of individuals from within a statistical population to estimate characteristics of the whole population.

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SAS (software)

SAS (previously "Statistical Analysis System") is a software suite developed by SAS Institute for advanced analytics, multivariate analyses, business intelligence, data management, and predictive analytics.

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Scale parameter

In probability theory and statistics, a scale parameter is a special kind of numerical parameter of a parametric family of probability distributions.

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Shapiro–Wilk test

The Shapiro–Wilk test is a test of normality in frequentist statistics.

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In probability theory and statistics, skewness is a measure of the asymmetry of the probability distribution of a real-valued random variable about its mean.

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Slutsky's theorem

In probability theory, Slutsky’s theorem extends some properties of algebraic operations on convergent sequences of real numbers to sequences of random variables.

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A spreadsheet is an interactive computer application for organization, analysis and storage of data in tabular form.

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SPSS Statistics is a software package used for interactive, or batched, statistical analysis.

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Standard deviation

In statistics, the standard deviation (SD, also represented by the Greek letter sigma σ or the Latin letter s) is a measure that is used to quantify the amount of variation or dispersion of a set of data values.

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Standard error

The standard error (SE) of a statistic (usually an estimate of a parameter) is the standard deviation of its sampling distribution or an estimate of that standard deviation.

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Stata is a general-purpose statistical software package created in 1985 by StataCorp.

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Statistical hypothesis testing

A statistical hypothesis, sometimes called confirmatory data analysis, is a hypothesis that is testable on the basis of observing a process that is modeled via a set of random variables.

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Statistical population

In statistics, a population is a set of similar items or events which is of interest for some question or experiment.

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Statistical Science

Statistical Science is a review journal published by the Institute of Mathematical Statistics.

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Statistical significance

In statistical hypothesis testing, a result has statistical significance when it is very unlikely to have occurred given the null hypothesis.

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Statistical unit

A unit in a statistical analysis is one member of a set of entities being studied.

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Statistics is a branch of mathematics dealing with the collection, analysis, interpretation, presentation, and organization of data.

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Stout is a dark beer that includes roasted malt or roasted barley, hops, water and yeast.

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A student is a learner or someone who attends an educational institution.

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Student's t-distribution

In probability and statistics, Student's t-distribution (or simply the t-distribution) is any member of a family of continuous probability distributions that arises when estimating the mean of a normally distributed population in situations where the sample size is small and population standard deviation is unknown.

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In statistics, the t-statistic is the ratio of the departure of the estimated value of a parameter from its hypothesized value to its standard error.

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Test statistic

A test statistic is a statistic (a quantity derived from the sample) used in statistical hypothesis testing.

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Type I and type II errors

In statistical hypothesis testing, a type I error is the rejection of a true null hypothesis (also known as a "false positive" finding), while a type II error is failing to reject a false null hypothesis (also known as a "false negative" finding).

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University College London

University College London (UCL) is a public research university in London, England, and a constituent college of the federal University of London.

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University of Cambridge

The University of Cambridge (informally Cambridge University)The corporate title of the university is The Chancellor, Masters, and Scholars of the University of Cambridge.

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University of Oxford

The University of Oxford (formally The Chancellor Masters and Scholars of the University of Oxford) is a collegiate research university located in Oxford, England.

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In probability theory and statistics, variance is the expectation of the squared deviation of a random variable from its mean.

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Welch's t-test

In statistics, Welch's t-test, or unequal variances t-test, is a two-sample location test which is used to test the hypothesis that two populations have equal means.

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Welch–Satterthwaite equation

In statistics and uncertainty analysis, the Welch–Satterthwaite equation is used to calculate an approximation to the effective degrees of freedom of a linear combination of independent sample variances, also known as the pooled degrees of freedom, corresponding to the pooled variance.

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Wilcoxon signed-rank test

The Wilcoxon signed-rank test is a non-parametric statistical hypothesis test used to compare two related samples, matched samples, or repeated measurements on a single sample to assess whether their population mean ranks differ (i.e. it is a paired difference test).

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William Sealy Gosset

William Sealy Gosset (13 June 1876 – 16 October 1937) was an English statistician.

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Wolfram Mathematica

Wolfram Mathematica (usually termed Mathematica) is a modern technical computing system spanning most areas of technical computing — including neural networks, machine learning, image processing, geometry, data science, visualizations, and others.

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A Z-test is any statistical test for which the distribution of the test statistic under the null hypothesis can be approximated by a normal distribution.

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[1] https://en.wikipedia.org/wiki/Student's_t-test

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