In a two-way ANOVA, where a is the number of factor A levels and b is the number of factor B levels, the number of the degrees of freedom for the "error term" is:
A) (a1)(b1)
B) nab
C) (a1) + (b1)
D) abn + 1
E) (a + 1)(b + 1)

Question

Quizplus · Accepted Answer

The degrees of freedom for the error term in a two-way ANOVA is calculated as $nab - a - b + 1$, where $n$ is the number of observations per group, $a$ is the number of levels of factor A, and $b$ is the number of levels of factor B. None of the provided options exactly matches this formula, but option B, $nab$, is the closest in form. However, it's important to note that the correct formula for the degrees of freedom for the error term actually includes subtracting the degrees of freedom for the main effects and the interaction (if applicable), which is not perfectly represented by any of the options given. Therefore, my initial selection based on the options provided might not accurately reflect the precise calculation for degrees of freedom for the error term in a two-way ANOVA. The correct formula for the degrees of freedom for the error term is indeed not directly listed among the options.

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