Q&A: One-way ANOVA

If I have data from three or more groups, but I am particularly interested in comparing certain groups with other groups. Is it OK to compare two groups at a time with a t test?

No. You should analyze all the groups at once with one-way ANOVA, and then follow up with multiple comparison post tests. The only exception is when some of the 'groups' are really controls to prove the assay worked, and are not really part of the experimental question you are asking.

I know the mean, SD (or SEM) and sample size for each group. Which tests can I run?

You can enter data as mean, SD (or SEM) and N, and Prism can compute one-way ANOVA. It is not possible to compute repeated measures ANOVA, or nonparametric ANOVA without access to the raw data.

I only know the group means, and don't have the raw data and don't know their SD or SEM. Can I run ANOVA?

No. ANOVA compares the difference among group means with the scatter within the groups, taking into account sample size. If you only know the means, there is no possible way to do any statistical comparison.

Can I use a normality test to make the choice of when to use a nonparametric test?

This is not a good idea. Choosing when to use a nonparametric test is not straightforward, and you can't really automate the process.

I want to compare three groups. The outcome has two possibilities, and I know the fraction of each possible outcome in each group. How can I compare the groups?

Not with ANOVA. Enter your data into a contingency table and analyze with a chi-square test.

What does 'one-way' mean?

One-way ANOVA, also called one-factor ANOVA, determines how a response is affected by one factor. For example, you might measure a response to three different drugs. In this example, drug treatment is the factor. Since there are three drugs, the factor is said to have three levels.

If you measure response to three different drugs, and two time points, then you have two factors: drug and time. One-way ANOVA would not be helpful. Use two-way ANOVA instead.

If you measure response to three different drugs at two time points with subjects from two age ranges, then you have three factors: drug, time and age. Prism does not perform three-way ANOVA, but other programs do.

If there are only two levels of one factor --say male vs. female, or control vs. treated --, then you should use a t test. One-way ANOVA is used when there are three or more groups (although the underlying math is the same for a t test and one-way ANOVA with two groups).

What does 'repeated measures' mean? How is it different than 'randomized block'?

The term repeated-measures strictly applies only when you give treatments repeatedly to each subject, and the term randomized block is used when you randomly assign treatments within each group (block) of matched subjects. The analyses are identical for repeated-measures and randomized block experiments, and Prism always uses the term repeated-measures.