Choosing multiple comparisons for two-way ANOVA is not straightforward. Make this choice carefully, and after learning about two-way ANOVA. Consider getting help.

Which kind of comparison?

This is the most important decision. You need to pick a multiple comparison scheme that matches your scientific goal. The pictures, shown below and on the dialog, are probably more helpful than the explanations

The choices of comparisons (in the drop down) depend on the number of rows and columns in your data set.

This was the only choice in early versions of Prism, and is probably the most useful kind of multiple comparisons. This choice is available only if there are exactly two columns. For each row, therefore, there are two cell means, and Prism compares these.

This choice is only available if you have three or more columns of data. Within each row, Prism does multiple comparisons between cell means.

For each row, compare the mean of side-by-side replicates of one column with another. This only makes sense, so the choice is only available, only when there are three or more columns. You must decide whether each row becomes its own family of comparisons, or whether all the comparisons are defined to be one family.

Within each column, compare the mean of side by side replicates of one row with the mean of other rows. This choice is only available when you have three or more rows. You must decide whether each column becomes its own family of comparisons, or whether all the comparisons are defined to be one family.

Testing for main column effects involves computing the mean of each data set column, and comparing those means. This makes sense (so the choice is available) only if there are data in three or more data set columns. If your data table has only two data set columns, then the main ANOVA computations give a P value for the effect of the variable that defines the columns, and no multiple comparison testing for column effects makes sense.

Testing for main row effects involves computing the mean value for each row, and then comparing those means. It only makes sense, so the choice is only available, when there are three or more rows. If your data table has only two rows, then the main ANOVA computations give a P value for the effect of the variable that defines the rows, and no multiple comparison testing for row effects makes sense.

Compare each cell means with every other cell mean, paying no attention to which row and column each cell mean is part of. This choice is not available when one factor is repeated measures, but is available when both factors are repeated measures.

How many comparisons?

Do you want to compare each mean (in the set) with each other mean? Or only compare each mean to the first, control, mean? The latter approach makes fewer comparisons, so has more power. The choice should be based on experimental design and the scientific questions you are asking.

How many families? (Applies to simple effects only.)

Multiple comparisons take into account the number of comparisons in the family of comparisons. The significance level (alpha) applies to the entire family of comparisons. Similarly, the confidence level (usually 95%) applies to the entire family of intervals, and the multiplicity adjusted P values adjust each P value based on the number of comparisons in a family.

If you choose to look at Simple effects (defined above), the definition of family is not obvious, and Prism offers two choices:

•One family for all comparisons. With this choice, there is always one family of comparisons for all rows (or all columns).This approach has less power, because it applies a stricter correction for multiple comparisons. This makes sense because there are more comparisons in the family.

•One family per column (or per row). Define the comparisons for each column (or each row) to be its own family of comparisons. With this choice, there are fewer comparisons per family (but more families), so comparisons have more power. We recommend this choice unless you have strong reason to consider all the comparisons to be one family.

The results page will repeat your choices, so it is clear how to interpret the results.

Prism 5.04 and 5.0d use the first definition of family (and do not offer you a choice of the other definition). If you wish to compare results with Prism 5, note this bug in releases of Prism 5 prior to 5.04 (Windows) and 5.0d (Mac).