Question

In: Statistics and Probability

Group A has three scores, 32, 23, 16. Group B has three scores, 23, 35, 11....

  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.

Solutions

Expert Solution

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

_________________________________________________

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

___________________________________________________

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

_________________________________________________________

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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