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# Unequal variance ANOVA

### Background

Although conventional parametric (and non-parametric) ANOVA require the assumption of equal variances, Welch (1951) developed an unequal variance one-way analysis of variance. This test has been little used to date, although its provision in R (as oneway.test) probably means it will be more heavily used in future.

Subsequent multiple comparison of means should be done using pairwise.t.test with a non-pooled standard deviation. This calculates pairwise comparisons between group levels with Bonferroni-type corrections for multiple testing.

### How to do it

#### Worked example

We will analyse the data from Johnston et al. (2001) using R:

### One-way unequal variance ANOVA

Gives something like this:

```One-way analysis of means (not assuming equal variances)

data:  con and trt
F = 5.9763, num df = 2.000, denom df = 42.893, p-value = 0.005134

Pairwise comparisons using t tests with non-pooled SD

data:  con and trt

A      B
B 0.0596 -
C 0.0044 0.1280 