# Tests for equality of means/medians (independent samples)

Tests for the equality of means/medians of independent samples and their properties and assumptions.

Test | Purpose |
---|---|

Z | Test if the difference between means is equal to a hypothesized value when the population standard deviation is known. |

Student's t | Test if the difference between means is equal to a hypothesized value. Assumes the populations are normally distributed. Due to the central limit theorem, the test may still be useful when this assumption is not true if the sample sizes are equal, moderate size, and the distributions have a similar shape. However, in this situation the Wilcoxon-Mann-Whitney test may be more powerful. Assumes the population variances are equal. This assumption can be tested using the Levene test. The test may still be useful when this assumption is not true if the sample sizes are equal. However, in this situation, the Welch t-test may be preferred. |

Welch t | Test if the difference between means is equal to a hypothesized value. Assumes the populations are normally distributed. Due to the central limit theorem, the test may still be useful when this assumption is not true if the sample sizes are equal, moderate size, and the distributions have a similar shape. However, in this situation the Wilcoxon-Mann-Whitney test may be more powerful. Does not assume the population variances are equal. |

ANOVA | Test if two or means are equal. Assumes the populations are normally distributed. Due to the central limit theorem, the test may still be useful when this assumption is not true if the sample sizes are equal and moderate size. However, in this situation the Kruskal-Wallis test is may be more powerful. Assumes the population variances are equal. This assumption can be tested using the Levene test. The test may still be useful when this assumption is not true if the sample sizes are equal. However, in this situation, the Welch ANOVA may be preferred. |

Welch ANOVA | Test if two or more means are equal. Assumes the populations are normally distributed. Due to the central limit theorem, the test may still be useful when this assumption is not true when the sample sizes are equal and moderate size. The Kruskal-Wallis test may be preferable as it is more powerful than Welch's ANOVA. Does not assume the population variances are equal. |

Wilcoxon-Mann-Whitney | Test if there is a shift in location. When the population distributions are identically shaped, except for a possible shift in central location, the hypotheses can be stated in terms of a difference between means/medians. When the population distributions are not identically shaped, the hypotheses can be stated as a test of whether the samples come from populations such that the probability is 0.5 that a random observation from one group is greater than a random observation from another group. |

Kruskal-Wallis | Test if two or more medians are equal. Assumes the population distributions are identically shaped, except for a possible shift in central location. |

**Related concepts**

- What is Analyse-it?
- 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
- Tests for equality of means/medians
- Testing equality of means/medians
- 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
- Measurement systems analysis (MSA)
- Reference interval
- Diagnostic performance
- Control charts
- Process capability
- Pareto analysis
- Bibliography

Published 8-Jan-2017

Version 4.90