Definition

A family of comparisons is a set of comparisons grouped together for the purpose of error rate control. All multiple comparison correction methods, whether they control the familywise error rate (FWER) using methods such as Bonferroni, Tukey, and Holm, or control the false discovery rate (FDR), operate at the level of the family rather than at the level of individual comparisons.

The significance threshold alpha and the FDR threshold both apply to the family as a whole. For FWER methods, the correction is designed so that, assuming all null hypotheses in the family are true, the probability of obtaining even one spuriously significant result across the entire family stays at or below alpha. For FDR methods, the correction limits the expected proportion of false positives among all comparisons declared significant within the family. In both cases, the family defines the scope over which error rates are controlled.

The number of comparisons in a family determines the strength of the correction

More comparisons per family means a stricter correction and less power to detect true differences. Fewer comparisons per family means a less strict correction and more power, at the cost of higher false positive risk within each individual family.

In some analyses, Prism lets you choose how families are defined. For example, in two-way ANOVA with simple effects comparisons, you can define one family per row, which keeps each family small and comparisons powerful. Alternatively, you can pool all comparisons across rows into a single large family for a more conservative analysis. The right choice depends on your experimental design and scientific question.

Why no correction method is available when a family has only one comparison

When a family contains exactly one comparison, Prism does not offer a correction method. This is not a limitation of the software; it is the statistically correct behavior.

The problem that correction methods solve is the inflation of false positive risk that comes from testing multiple comparisons simultaneously within a family. When there is only one comparison in a family, no such inflation exists. The per-comparison error rate equals the familywise error rate by definition, because there is only one comparison in the family to consider. Applying a correction would leave the P value unchanged, so the uncorrected P value is both the per-comparison and the familywise result.

For this reason, when Prism detects that a family contains only one comparison, it reports "No correction" as the only option and reports unadjusted P values directly. This is not a weaker analysis; it is the appropriate result for that family structure.

What to do if you encounter this in Prism

If Prism is not offering correction methods, it has detected that one or more of your families contains only one comparison. This most commonly happens when the number of defined families equals or exceeds the total number of comparisons, leaving each family with at most one comparison to correct.

Check the "How many families?" setting in the Multiple Comparisons tab. Consider whether defining fewer, larger families better reflects your experimental design. Grouping comparisons into fewer families increases the number of comparisons per family, at which point correction methods become available.

If you have intentionally defined families that contain only one comparison each, no action is needed. The unadjusted P values are the correct and complete result for that analysis.

Learn more

To learn about the three general approaches to dealing with multiple comparisons, see Three approaches to dealing with multiple comparisons. For how families are defined specifically within two-way ANOVA, see Multiple comparisons tab: Two-way ANOVA.