Question

1. 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.

1 points   

QUESTION 9

1. Group A has three scores, 11, 26, 22. Group B has three scores, 16, 28, 33. Group C has three scores, 21, 36, 25. Calculate the grand mean (round to two digits).

1 points   

QUESTION 10

1. Group A has three scores, 24, 36, 29. Group B has three scores, 45, 50, 12. Group C has three scores, 18, 27, 10. Calculate MS effect (Mean squared error for the Effect). Round to one digit.

Answer 1

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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Q9) Grand Mean = Sum of all scores / Number of scores = (11 + 26 + 22 + 16 + 28 + 33 + 21 + 36 + 25) / 9 = 218/9 = 24.22

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Q10) The Summary Statistics from the given data are as below

	A	B	C
Total	89	107	55
n	3	3	3
Mean	29.667	35.667	18.333
SS	72.67	852.67	144.67

k = 3 and N = 9. DF Error = N - k = 9 - 3 = 6

SS error = SUM (Sum of Squares) = 72.67 + 852.67 + 144.67 = 1070 (Calculations shown below)

MS error = SS error / DF error = 1070 / 6 = 178.3

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SS In Question 8

SS = (X - )².

For Group A

	Sample 1 Mean1 (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 Mean2 (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

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SS In Question (10)

SS = (X - )².

For Group A

	Sample 1	Mean 1	(X - )2
1	24	29.667	32.114889
2	36	29.667	40.106889
3	29	29.667	0.444889
Total	89		72.67

For Group B

	Sample 2	Mean2	(X - )2
1	45	35.667	87.104889
2	50	35.667	205.434889
3	12	35.667	560.126889
Total	107		852.67

For Group C

	Sample 3	Mean3	(X - )2
1	18	18.333	0.110889
2	27	18.333	75.11689
3	10	18.333	69.43889
Total	55		144.67

Therefore the SS = 72.67 + 852.67 + 144.67 = 1070

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