STATISTICAL TESTS

On this page you can find links to detailed descriptions of a wide variety of statistical tests.

The links are organized by purpose and there's an alphabetical list at the bottom of the page.

If you're not sure which test to use, check out our Choosing a Statistical Test page.

Each link will take you to a series of test pages which have the following:

A brief description of the purpose of the test and what the results represent.
Step-by-step instructions showing how to perform the test.

TESTS COMPARING AVERAGE VALUES (I.E., MEANS OR MEDIANS)

Unpaired heteroscedastic t test

Compare the means of two normally distributed groups using the unpaired heteroscedastic t test.

Unpaired homoscedastic t test

Compare the means of two normally distributed groups, which have equal variances, using the unpaired homoscedastic t test.

Paired t test

Compare the means of two normally distributed groups, which have paired data values, using the paired t test.

Mann-Whitney test

Compare the average values of two groups using the Mann-Whitney test.

One-factor ANOVA

Compare the means of more than two normally distributed groups, which have equal variances, using the one-factor ANOVA.

Kruskal Wallis test

Compare the average values of more than two groups using the Kruskal-wallis test.

TESTS COMPARING VARIANCES

Barlett's test

Compare two variances using the Barlett's test.

Brown-Forsythe test

Compare two variances using the Brown-Forsythe test.

F ratio test

Compare two variances using the F ratio variance test described here.

Levene's test

Compare two variances using the Levene's test.

F_max test

Compare more than two variances using the F_max variance test described here.

TESTS COMPARING PROPORTIONS (I.E., OBSERVED TO EXPECTED VALUES)

Chi-squared test of independence

Compare observed and predicted frequencies for observations in categories defined by two sets of labels using the chi-squared (X²) test described here.

Chi-squared goodness-of-fit (GOF) test

Compare observed and predicted frequencies for observations in categories defined by two sets of labels using the chi-squared (X²) test described here.

Odds ratio (2x2 X² tests)

Compare observed and predicted frequencies for observations in categories defined by two sets of labels using the chi-squared (X²) test described here.

TESTS IDENTIFYING ASSOCIATIONS AND RELATIONSHIPS

Two-factor ANOVA

Look for associations between two different factors and the means of groups that vary for those factors here.

Correlation

Look for a linear relationship between two variables when you don't know whether other factors have been controlled for.

Regression

Look for a linear relationship between two variables when you know that all other factors have been controlled for.

ALPHABETICAL LIST OF STATISTICAL TESTS