If the degrees of freedom in a two-way ANOVA for MS_A, MS_B, MS_AB, and MS_W are 4, 7, 28, and 200, respectively, how many treatments exist in factor A and factor B, and how many subjects are in each cell of the design? A) 3, 6, 12 (Factor A, Factor B, Subjects/cell, respectively) B) 4, 7, 5 (Factor A, Factor B, Subjects/cell, respectively) C) 5, 8, 6 (Factor A, Factor B, Subjects/cell, respectively) D) 5, 8, 4(Factor A, Factor B, Subjects/cell, respectively)

Question

Quizplus · Accepted Answer

The degrees of freedom for factor A (dfA) is 4, indicating 5 levels (dfA + 1). The degrees of freedom for factor B (dfB) is 7, indicating 8 levels (dfB + 1). The degrees of freedom for the interaction (dfAB) is 28, which is (5-1)(8-1). The degrees of freedom for within (dfW) is 200, which is the product of the number of levels of A, B, and the number of subjects per cell minus 1, i.e., 5*8*(n-1) = 200, solving gives n = 6.

If the Degrees of Freedom in a Two-Way ANOVA for MSA

If the Degrees of Freedom in a Two-Way ANOVA for MS_A