One-way ANOVA (cont...)

What happens if my data fail these assumptions?

Firstly, don't panic! The first two of these assumptions are easily fixable, even if the last assumption is not. Lets go through the options as above:

1. The one-way ANOVA is considered a robust test against the normality assumption. This means that it tolerates violations to its normality assumption rather well. As regards the normality of group data, the one-way ANOVA can tolerate data that is non-normal (skewed or kurtotic distributions) with only a small effect on the Type I error rate. However, platykurtosis can have a profound effect when your group sizes are small. This leaves you with two options: (1) transform your data using various algorithms so that the shape of your distributions become normally distributed (see our normality guide here) or (2) choose the non-parametric Kruskal-Wallis H Test which does not require the assumption of normality (read our guide on this test here).
2. There are two tests that you can run that are applicable when the assumption of homogeneity of variances has been violated: (1) Welch or (2) Brown and Forsythe test. Alternatively, you could run a Kruskal-Wallis H Test. For most situations it has been shown that the Welsh test is best. Both the Welch and Brown and Forsythe tests are available in SPSS (see our One-way ANOVA using SPSS guide).
3. A lack of independence of cases has been stated as the most important assumptions to fail. Often, there is little you can do that offers a good solution to this problem. A full explanation of this problem and all assumptions mentioned here, including numerical explanations, are provided in Intermediate Statistics: A Modern Approach by Dr James Stevens.

How do I run a one-way ANOVA?

There are numerous ways to run a one-way ANOVA, however, we provide a comprehensive, step-by-step guide on how to do this using SPSS.

How do I report the results of a one-way ANOVA?

You will have calculated the following results or obtained them from SPSS:

Structure of results:

An example:

You will want to report this as follows:

There was a statistically significant difference between groups as determined by one-way ANOVA (F(2,27) = 4.467, P = .021). This is all you will need to write for the one-way ANOVA per se. However, in reality you will want probably also want to report means ± SD for your groups as well as follow-up a significant result with post-hoc tests. If you use SPSS then these descriptive statistics will be reported in the output along with the result from the one-way ANOVA. The general form of writing the result of a one-way ANOVA is as follows:

where df = degrees of freedom.

It is very important that you do not report the result as "significant difference" but that you report it as "statistically significant difference". This is because your decision as to whether the result is significant or not should not be based solely on your statistical test. Therefore, to indicate to readers that this "significance" is a statistical one, include this is your sentence.

Find out what else you have to do when you have a significant or a not-significant ANOVA result on the next page.