Concept explainers
The following data are from a repeated-measures study comparing three treatment conditions.
- a. Use a repealed-measures ANOVA with α – 05 to determine whether there are significant differences among the treatments and compute η’ to measure the size of the treatment effect.
- b. Double the number of scores in each treatment by simply repeating the original scores in each treatment a second time. For example, the n = 8 scores in Treatment I become 1.4, 2.1, 1.4, 2.1. Note that this will not change the treatment means but it will double SSbetween treatments, SSbetween subjects, and the SS value for each treatment. For the new data, use u repeated-measures ANOVA with α - 05 to determine whether there are significant differences among the treatments and compute η’ to measure the Size of treatment effect.
- c. Describe how doubling the
sample size affected the value of the F-radio and the value of η’.
a.
To compute: The value of
Answer to Problem 11P
There are significant differences between the treatments. The value of
Explanation of Solution
Given info:
Following data are from a repeated-measure study comparing three treatments conditions.
Treatments | |||||
Person | I | II | III | Person totals | |
A | 1 | 4 | 7 |
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B | 4 | 8 | 6 |
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C | 2 | 7 | 9 |
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D | 1 | 5 | 6 |
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Calculation:
The hypotheses are given below:
Null Hypothesis: There are no differences among treatments.
Alternate Hypothesis: There are significant differences among the treatments.
Let k and n represents the total numbers of treatments and participants. Then,
Let, N represents total numbers of observations. Then,
Degrees of freedom corresponding to
Degrees of freedoms corresponding to
F-ratio is given as:
From the table
Since, F-ratio is greater than the critical value; therefore, reject the null hypothesis and conclude that there are significant differences between the treatments.
Conclusion:
There are significant differences between the treatments. The value of
b.
To compute: The value of
Answer to Problem 11P
There are significant differences between the treatments. The value of
Explanation of Solution
Calculation:
The new data is obtained by doubling the number of scores in each treatment by simply repeating the original scores in each treatment a second time.
The hypotheses are given below:
Null Hypothesis: There are no differences among treatments.
Alternate Hypothesis: There are significant differences among the treatments.
Let k1 and n1 represents the total numbers of treatments and participants of the new data. Then,
Let, N1 represents total numbers of observations of new data. Then,
Degrees of freedom corresponding to
Degrees of freedoms corresponding to
F-ratio is given as:
From the table
Since, F-ratio is greater than the critical value; therefore, reject the null hypothesis and conclude that there are significant differences between the treatments for the new data.
Conclusion:
There are significant differences between the treatments. The value of
c.
Answer to Problem 11P
The F-ratio got increased and there is no effect on
Explanation of Solution
Given info:
Sample size has been doubled.
Calculation:
From part a. the F-ratio is
After doubling the sample size, from part b. the F-ratio is
But value of
Conclusion:
The F-ratio got increased and there is no effect on
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Chapter 13 Solutions
ESS. OF STATIS F/BEHAV.SCENCES+ACCESS>B
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