In the two-way ANOVA, where a is the number of factor A levels, b is the number of factor B levels, and r is the number of replicates, which of the following expressions gives the formula for the number of degrees of freedom for error?
A) (a - 1)(b - 1)
B) abr - 1
C) (a - 1)(r - 1)
D) ab(r - 1)

Question

Quizplus · Accepted Answer

The formula for the number of degrees of freedom for error in a two-way ANOVA is df_error = ab(r-1). This represents the total number of observations (i.e., a*b*r) minus the number of parameters estimated in the model, which include the main effects of factor A and B, the interaction effect between factor A and B, and any covariates included in the model. Therefore, the correct answer is D, ab(r-1).

In the Two-Way ANOVA, Where a Is the Number of Factor