Question

Group A has three scores, 15, 34, 16. Group B has three scores, 21, 16, 38. Group C has three scores, 35, 13, 10. Calculate SS effect. Round to one digit. 1 points

QUESTION 8 Group A has three scores, 32, 23, 16. Group B has three scores, 23, 35, 11. Group C has three scores, 49, 37, 42. Calculate the F-value. Round to one digit.

Answer 1

Q7) For the given data, the summary stats are as below

	A	B	C
Total	65	75	58
n	3	3	3
Mean	21.67	25.000	19.33
SS	228.67	266	372.67

SS Effect = SS error = SUM (Sum of squares) = 228.67 + 266 + 372.67 = 867.3

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8) From the given data, the summary statistics are as below

	A	B	C
Total	71	69	128
n	3	3	3
Mean	23.67	23.000	42.67
SS	128.67	288	72.67

K = number of rows = 3 and N = Total Observations = 9

DF 1 = DF between = k - 1 = 3 - 1 = 2

DF 2 = DF Error = N - k = 9 - 3 = 6

Overall Mean = (71 + 69 + 128) / 9 = 29.78

SS between = SUM [ n * ( - Overall Mean)²] = 3 * (23.67 - 29.78)² + 3 * (23 - 29.78)² + 3 * (42.67 - 29.78)² = 748.24

MS Between = SS between / DF 1 = 748.24 / 2 = 374.12

SS error = SUM(SS) = 128.67 + 288 + 72.67 = 489.34

MS Error = SS error / DF2 = 489.34/6 = 81.56

F = SS between / MS between = 374.12 / 81.56 = 4.6

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SS for Question (7)

SS = (X - )².

For Group A

	Sample 1	Mean 1	SS1
1	15	21.667	44.448889
2	34	21.667	152.102889
3	16	21.667	32.114889
Total	65		228.67

For Group B

	Sample 2	Mean2	SS2
1	21	25	16
2	16	25	81
3	38	25	169
4	75		266

For Group C

	Sample 3	Mean3	SS3
1	35	19.333	245.4549
2	13	19.333	40.10689
3	10	19.333	87.10489
Total	58		372.67

Therefore Sum of Squares = 228.67 + 266 + 372.67 = 867.33

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SS In Question 8

SS = (X - )².

For Group A

	Sample 1	Mean 1	(X - )2.
1	32	23.667	69.438889
2	23	23.667	0.444889
3	16	23.667	58.782889
Total	71		128.67

For Group B

	Sample 2	Mean 2	(X - )2.
1	23	23	0
2	35	23	144
3	11	23	144
Total	69		288

For Group C

	Sample 3	Mean3	(X - )2.
1	49	42.667	40.10689
2	37	42.667	32.11489
3	42	42.667	0.444889
Total	128		72.67

SS = 128.67 + 288 + 72.67 = 489.33