What are individual and family error rates?

The type I error rates associated with the multiple comparisons are often used to identify significant differences between specific factor levels in an ANOVA. The individual and simultaneous confidence level = 1 - the error rate.

What is the individual error rate?

The individual error rate is the maximum probability that one or more comparisons will incorrectly conclude that the observed difference is significantly different from the null hypothesis.

What is the family error rate?

The family error rate is the maximum probability that a procedure consisting of more than one comparison will incorrectly conclude that at least one of the observed differences is significantly different from the null hypothesis. The family error rate is based on both the individual error rate and the number of comparisons. For a single comparison, the family error rate is equal to the individual error rate which is the alpha value. However, each additional comparison causes the family error rate to increase in a cumulative manner.

It is important to consider the family error rate when making multiple comparisons because your chances of committing a type I error for a series of comparisons is greater than the error rate for any one comparison alone. Tukey's method, Fisher's least significant difference (LSD), Hsu's multiple comparisons with the best (MCB), and Bonferroni confidence intervals are methods for calculating and controlling the individual and family error rates for multiple comparisons.

Are the individual error rates and family error rates exact?

Individual error rates are exact in all cases. Family error rates are exact for equal group sizes. If group sizes are unequal, the true family error rate for Tukey, Fisher, and MCB will be slightly smaller than stated, resulting in conservative confidence intervals. The Dunnett family error rates are exact for unequal sample sizes.