Question

A study of depression and exercise was conducted. A total of 5 groups were used: each group differs by the extent to which group members exercise. A depression rating (scale: 1-100, a continuous variable) was given to all 1410 participants in the sample. An incompleted ANOVA table is provided below. What is the obtained F (i.e., value in Cell [8])?

	Sum of Squares	df	Mean Square	F
Between-Group	[1]	[2]	[5]	[8]
Within-Group	185	[3]	[6]	[9]
Total	222	[4]	[7]	[10]

0.84

70.08

None provided.

58.54

0.2

Answer 1

Answer:

Number of groups = c = 5

No of participants = n = 1410

Sum of Squares    df       Mean Square       F

Between-Group               [1]                [2]                [5]                [8]

Within-Group                   185              [3]                [6]                [9]

Total                                222              [4]                [7]                [10]

Sum of Squares between group + Sum of squares within group = Sum of squares Total

[1] + 185 = 222

[1] = 222-185 = 37

SSA [1] = 37

df between groups [2] = c-1 = 5-1 = 4

df within group [3] = n-c = 1410 – 5 = 1405

df total [4] = n-1 = 1410-1 = 1409

You compute the mean squares by dividing the sum of squares by the corresponding degree of freedom

MSA (Between group) [5] = SSA [1] / c-1 = 37/4 = 9.25

MSW (Within group) [6] = 185/n-c = 185/1405 = 0.132

MST (Total) = 222/n-1 [7] = 222/1409 = 0.158

F stat = [8] = MSA/MSW = 9.25/0.132 = 70.07