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Hypothesis Tests

t-test, F-test, chi-square goodness-of-fit test, and more

Statistics and Machine Learning Toolbox™ provides parametric and nonparametric hypothesis tests to help you determine if your sample data comes from a population with particular characteristics.

Distribution tests , such as Anderson-Darling and one-sample Kolmogorov-Smirnov, test whether sample data comes from a population with a particular distribution. Test whether two sets of sample data have the same distribution using tests such as two-sample Kolmogorov-Smirnov.

Location tests, such as z-test and one-sample t-test, test whether sample data comes from a population with a particular mean or median. Test two or more sets of sample data for the same location value using a two-sample t-test or multiple comparison test.

Dispersion tests, such as Chi-square variance, test whether sample data comes from a population with a particular variance. Compare the variances of two or more sample data sets using a two-sample F-test or multiple-sample test.

Determine additional features of sample data by cross-tabulating, conducting a run test for randomness, and determine the sample size and power for a hypothesis test.


adtestAnderson-Darling test
chi2gofChi-square goodness-of-fit test
dwtestDurbin-Watson test
fishertestFisher’s exact test
jbtestJarque-Bera test
kstestOne-sample Kolmogorov-Smirnov test
kstest2Two-sample Kolmogorov-Smirnov test
lillietestLilliefors test
runstestRun test for randomness
friedmanFriedman’s test
kruskalwallisKruskal-Wallis test
multcompareMultiple comparison test
ranksumWilcoxon rank sum test
sampsizepwrSample size and power of test
signrankWilcoxon signed rank test
signtestSign test
ttestOne-sample and paired-sample t-test
ttest2Two-sample t-test
ansaribradleyAnsari-Bradley test
barttestBartlett’s test
sampsizepwrSample size and power of test
vartestChi-square variance test
vartest2Two-sample F-test for equal variances
vartestn Multiple-sample tests for equal variances

Examples and How To

Hypothesis Testing

Use hypothesis testing to analyze gas prices measured across the state of Massachusetts during two separate months.


Introduction to Hypothesis Tests

Hypothesis testing is a common method of drawing inferences about a population based on statistical evidence from a sample.

Hypothesis Test Terminology

All hypothesis tests share the same basic terminology and structure.

Hypothesis Test Assumptions

Different hypothesis tests make different assumptions about the distribution of the random variable being sampled in the data.

Available Hypothesis Tests

Tests of distributions and statistics

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