﻿ Interpreting results: Repeated measures two-way ANOVA

# Interpreting results: Repeated measures two-way ANOVA

## Are you sure that ANOVA is the best analysis?

Before interpreting the ANOVA results, first do a reality check. If one of the factors is a quantitative factor like time or dose, consider alternatives to ANOVA.

## Interpreting P values from repeated measures two-way ANOVA

When interpreting the results of two-way ANOVA, most of the considerations are the same whether or not you have repeated measures. So read the general page on interpreting two-way ANOVA results first. Also read the general page on the assumption of sphericity, and assessing violations of that assumption with epsilon.

Repeated measures ANOVA has one additional row in the ANOVA table, "Subjects (matching)". This row quantifies how much of all the variation among the values is due to differences between subjects. The corresponding P value tests the null hypothesis that the subjects are all the same. If the P value is small, this shows you have justification for choosing repeated measures ANOVA. If the P value is high, then you may question the decision to use repeated measures ANOVA in future experiments like this one.

## How the repeated measures ANOVA is calculated

Prism computes repeated-measures two-way ANOVA calculations using the standard method explained especially well in Glantz and Slinker (1).

If you have data with repeated measures in both factors, Prism uses methods from Chapter 12 of

## Multiple comparisons tests

Multiple comparisons testing is one of the most confusing topics in statistics. Since Prism offers nearly the same multiple comparisons tests for one-way ANOVA and two-way ANOVA, we have consolidated the information on multiple comparisons.

## Reference

1. SA Glantz and BK Slinker, Primer of Applied Regression and Analysis of Variance, McGraw-Hill, second edition, 2000.

2. SE Maxwell and HD Delaney. Designing Experiments and Analyzing Data, second edition. Laurence Erlbaum, 2004.