# Equality of means/medians hypothesis test (independent samples)

An equality hypothesis test formally tests if two or more population means/medians are different.

The hypotheses to test depends on the number of samples:

- For two samples, the null hypothesis states that the difference between the mean/medians of the populations is equal to a hypothesized value (0 indicating no difference), against the alternative hypothesis that it is not equal to (or less than, or greater than) the hypothesized value.
- For more than two samples, the null hypothesis states that the means/medians of the populations are equal, against the alternative hypothesis that at least one population mean/median is different.

When the test p-value is small, you can reject the null hypothesis and conclude that the populations differ in means/medians.

Tests for more than two samples are omnibus tests and do not tell you which groups differ from each other. You should use multiple comparisons to make these inferences.

**Available in Analyse-it Editions**

Standard edition

Method Validation edition

Quality Control & Improvement edition

Ultimate edition

- What is Analyse-it?
- What's new?
- Administrator's Guide
- User's Guide
- Statistical Reference Guide
- Distribution
- Compare groups
- Calculating univariate descriptive statistics, by group
- Side-by-side univariate plots
- Creating side-by-side univariate plots
- Equality of means/medians hypothesis test
- Equivalence of means hypothesis test
- Tests for means/medians
- Testing equality of means/medians
- Testing equivalence of means
- Difference between means/medians effect size
- Estimators for the difference in means/medians
- Estimating the difference between means/medians
- Multiple comparisons
- Mean-Mean scatter plot
- Multiple comparison procedures
- Comparing multiple means/medians
- Homogeneity of variance hypothesis test
- Tests for homogeneity of variance
- Testing homogeneity of variance
- Study design
- Compare pairs
- Contingency tables
- Correlation and association
- Principal component analysis (PCA)
- Factor analysis (FA)
- Item reliability
- Fit model
- Method comparison / Agreement
- Measurement systems analysis (MSA)
- Reference interval
- Diagnostic performance
- Survival/Reliability
- Control charts
- Process capability
- Pareto analysis
- Study Designs
- Bibliography

Version 6.15

Published 18-Apr-2023