Lognormal one-way ANOVA compares the means of three or more unmatched groups. This checklist is specific for performing a one-way ANOVA with no repeated measures. There is a separate checklist for a repeated measures one-way ANOVA. Read elsewhere to learn about choosing a test, interpreting the results, and a long article about lognormal ANOVA and lognormal distributions in general.
Are the populations distributed according to a lognormal distribution?
Lognormal one-way ANOVA assumes that you have sampled your data from populations that follow a lognormal distribution.
Do the populations have the same geometric standard deviation?
Lognormal one-way ANOVA assumes that all the populations have the same geometric standard deviation (GeoSD). This assumption is not very important when all the groups have the same (or almost the same) sample size, but is very important when sample sizes differ.
Prism tests for equality of GeoSDs with two tests: The Brown-Forsythe test and Bartlett's test. The P value from these tests answer this question: If the populations really have the same GeoSDs, what is the chance that you'd randomly select samples whose GeoSDs are as different from one another as those observed in your experiment. A small P value suggests that the GeoSDs are different.
Don't base your conclusion solely on these tests. Also think about data from other similar experiments. If you have plenty of previous data that convinces you that the variances are really equal, ignore these tests (unless the P value is really tiny) and interpret the ANOVA results as usual. Some statisticians recommend ignoring tests for equal variance altogether if the sample sizes are equal (or nearly so).
Prism offers the choice of performing Brown-Forsythe lognormal ANOVA and Bartlett's lognormal ANOVA, which don’t assume equal GeoSDs.
In some experimental contexts, finding different GeoSDs may be as important as finding different geometric means. If the GeoSDs are different, then the populations are different -- regardless of what ANOVA concludes about differences between the geometric means.
Are you testing the right hypothesis?
The null hypothesis for this test is that the geometric means of all groups are equal. If the corresponding P value is small, you may reject this null hypothesis. In many cases, this overall null hypothesis is of little interest, and it makes sense to focus on the results of multiple comparison testing.
Are the data unmatched?
If the data are matched or paired, then you should choose repeated-measures ANOVA instead. If the matching is effective in controlling for experimental variability, repeated-measures ANOVA will be more powerful than an ordinary (or regular) ANOVA.
Are the “errors” independent?
The term “error” refers to the difference between each value and the group geometric mean. The results of one-way ANOVA only make sense when the scatter is random – that whatever factor caused a value to be too high or too low affects only that one value. Prism cannot test this assumption. You must think about the experimental design. For example, the errors are not independent if you have six values in each group, but these were obtained from two animals in each group (in triplicate). In this case, some factor may cause all triplicates from one animal to be high or low.
Do you really want to compare geometric means?
One-way ANOVA compares the geometric means of three or more groups. It is possible to have a tiny P value – clear evidence that the population geometric means are different – even if the distributions overlap considerably. In some situations – for example, assessing the usefulness of a diagnostic test – you may be more interested in the overlap of the distributions than in differences between geometric means.
Is there only one factor?
One-way ANOVA compares three or more groups defined by one factor. For example, you might compare a control group, with a drug treatment group and a group treated with drug plus antagonist. Or you might compare a control group with five other groups that each receive a different drug treatment.
Some experiments involve more than one factor. For example, you might compare three different drugs in men and women. There are two factors in that experiment: drug treatment and gender. These data need to be analyzed by two-way ANOVA, also called two-factor ANOVA.
Is the factor “fixed” rather than “random”?
When calculating an ordinary one-way ANOVA, Prism performs a fixed-effect one-way ANOVA. This tests for differences among the means of the particular groups you have collected data from. Another type of test known as random-effect one-way ANOVA assumes that you have randomly selected groups from an infinite (or at least large) number of possible groups, and that you want to reach conclusions about differences among ALL the groups, even the ones you didn't include in this experiment. This random-effect one-way ANOVA is rarely used, and Prism does not perform it.
Do the different columns represent different levels of a grouping variable?
One-way ANOVA asks whether the value of a single variable differs significantly among three or more groups. In Prism, you enter each group in its own column. If the different columns represent different variables, rather than different groups, then one-way ANOVA is not an appropriate analysis. For example, one-way lognormal ANOVA would not be helpful if column A was glucose concentration, column B was insulin concentration, and column C was the concentration of glycosylated hemoglobin.
