One-way ANOVA (cont...)

When might you need to use this test? (cont...)

A second study design is to recruit a group of individuals and then split them into groups based on some independent variable. Again, each individual will be assigned to one group only. This independent variable is sometimes called an attribute independent variable because you are splitting the group based on some attribute that they possess, e.g. their level of education; every individual has a level of education, even if it is "none". Each group is then measured on the same dependent variable having undergone the same task or condition (or none at all). For example, a researcher is interested in determining whether there are differences in leg strength between amateur, semi-professional and professional rugby players. The force/strength measured on an isokinetic machine is the dependent variable. This type of study design is illustrated schematically in the Figure below:

Why not compare groups with multiple t-tests?

Every time you conduct a t-test there is a chance that you will make a Type 1 error. This error is usually 5%. Therefore, by running two t-tests on the same data you will have increased your chance of "making a mistake" to 10%. Three t-tests would be 15% and so on. These are unacceptable errors. An ANOVA controls for these errors so that the Type 1 error remains at 5% and you can be more confident that any significant result you find is not just down to chance. See our guide on hypothesis testing for more information on Type I errors.

What assumptions does the test make?

There are three main assumptions, listed here:

1. The dependent variable is normally distributed in each group that is being compared in the one-way ANOVA. So, for example, if we were comparing three groups; amateur, semi-professional and professional rugby players; on their leg strength, then their leg strength values (dependent variable) would have to be normally distributed for the amateur group of players, normally distributed for the semi-professionals and normally distributed for the professional players. You can test for normality in SPSS (see our guide here).
2. There is homogeneity of variances. This means that the population variances in each group are equal. If you use SPSS, Levene's Test for Homogeneity of Variances is included in the output when you run a one-way ANOVA in SPSS (see our One-way ANOVA using SPSS guide).
3. This is a study design issue that you will so you will need to examine your study design to determine whether this could have occurred.

What to do when the assumptions are not met is dealt with on the next page.