Statistics for The Behavioral Sciences (MindTap Course List)
Statistics for The Behavioral Sciences (MindTap Course List)
10th Edition
ISBN: 9781305504912
Author: Frederick J Gravetter, Larry B. Wallnau
Publisher: Cengage Learning
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Textbook Question
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Chapter 13, Problem 9P

For the data in problem 8,

a. Compute S S total and S S between treatments .

b. Eliminate the mean difference between treatments by adding 2 points to each score in treatment I, adding 1 point to each score in treatment II, and subtracting 3 points from each score in treatment II. (All three treatments should end up with M = 3 and T = 15 .)

c. Calculate S S total for the modified scores. (Caution: You first must find the new value for X 2 .)

d. Because the treatment effects were eliminated in part b, you should find that S S total for the modified scores is smaller than S S total for the original scores. The difference between the two SS values should be exactly equal to the value of S S between treatments for the original scores.

Expert Solution & Answer
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To determine

For the data in problem 8,

  1. Compute S S total  and S S between treatments .
  2. Eliminate the mean differences between treatments by adding 2 points to each score in treatment I, adding 1 point to each score in treatment II and subtracting 3 points from each score in treatment III (All three treatments should end up with M=3 and T=15.)
  3. Calculate S S total for the modified scores. (Caution: You first must find the new value for X 2 )
  4. Because the treatment effects were eliminated in part b, you should find that S S total for the modified scores is smaller than S S total for the original scores. The difference between the two SS values should be exactly equal to the value of S S between treatments for the original scores.

Answer to Problem 9P

Solution:

  1. S S total =96 and S S between treatments =70 .
  2. To eliminate the mean differences between treatments we will add 2 points to each score in treatment I add 1 point to each score in treatment II and subtract 3 points from each score in treatment III. The resulting table is given below:
  3. Treatments
    Person I II III Person Totals
    A 3 2 1 P=6
    B 5 5 5 P=15 N=15
    C 2 3 4 P=9 G=45
    D 2 1 3 P=6 X 2 = 161
    E 3 4 2 P=9
    M=3 M=3 M=3
    T=15 T=15 T=15

    We clearly see that the Mean of all the three treatments = 3 and all the three treatments have T=15 .

  4. The modified S S total =26
  5. The original S S total =96 and modified S S total =26, therefore the modified S S total is smaller than original S S total .
  6. The difference between the original S S total and modified S S total is

    9626=70

    Also we know the original S S between treatments =70 . Therefore the difference the two SS values is exactly equal to the value of S S between treatments for the original scores..

Explanation of Solution

  1. We are given the below data in problem 8:
  2. Treatments
    Person I II III Person Totals
    A 1 1 4 P=6
    B 3 4 8 P=15 N=15
    C 0 2 7 P=9 G=45
    D 0 0 6 P=6 X 2 = 231
    E 1 3 5 P=9
    M=1 M=2 M=6
    T=5 T=10 T=30
    SS=6 SS=10 SS=10

    S S total = X 2 G 2 N =231 45 2 15 =231135=96

    S S Between Treatments = T 2 n G 2 N = 5 2 5 + 10 2 5 + 30 2 5 45 2 15 =5+20+180135=205135=70

  3. To eliminate the mean differences between treatments we will add 2 points to each score in treatment I add 1 point to each score in treatment II and subtract 3 points from each score in treatment III. The resulting table is given below:
  4. Treatments
    Person I II III Person Totals
    A 3 2 1 P=6
    B 5 5 5 P=15 N=15
    C 2 3 4 P=9 G=45
    D 2 1 3 P=6 X 2 = 161
    E 3 4 2 P=9
    M=3 M=3 M=3
    T=15 T=15 T=15

    We clearly see that the Mean of all the three treatments = 3 and all the three treatments have T=15 .

  5. Calculate S S total for the modified scores.
  6. To calculate the S S total for the modified scores, we have

    S S total = X 2 G 2 N =161 45 2 15 =161135=26

    Therefore the modified S S total =26

  7. The original S S total =96 and modified S S total =26, therefore the modified S S total is smaller than original S S total .
  8. The difference between the original S S total and modified S S total is

    9626=70

    Also we know the original S S between treatments =70 . Therefore the difference the two SS values is exactly equal to the value of S S between treatments for the original scores.

Conclusion:

  1. S S total =96 and S S between treatments =70 .
  2. To eliminate the mean differences between treatments we will add 2 points to each score in treatment I add 1 point to each score in treatment II and subtract 3 points from each score in treatment III. The resulting table is given below:
  3. Treatments
    Person I II III Person Totals
    A 3 2 1 P=6
    B 5 5 5 P=15 N=15
    C 2 3 4 P=9 G=45
    D 2 1 3 P=6 X 2 = 161
    E 3 4 2 P=9
    M=3 M=3 M=3
    T=15 T=15 T=15

    We clearly see that the Mean of all the three treatments = 3 and all the three treatments have T=15 .

  4. The modified S S total =26
  5. The original S S total =96 and modified S S total =26, therefore the modified S S total is smaller than original S S total .
  6. The difference between the original S S total and modified S S total is

    9626=70

    Also we know the original S S between treatments =70 . Therefore the difference the two SS values is exactly equal to the value of S S between treatments for the original scores..

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Chapter 13 Solutions

Statistics for The Behavioral Sciences (MindTap Course List)

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