One of the major advantages of a repeated-measures design is that it removes individual differences from the variance and, therefore, reduces the standard error. The following two sets of data demonstrate this fact. The first set of data represents the original results from a repeated-measures study. To create the second set of data we started with the original scores but increased the individual differences by adding 10 points to each score for subject B, adding 20 points to each score for subject C, and adding 30 points to each score for subject D. Note that this change produces a huge increase in the differences from one subject to another and a huge increase in the variability of the scores within each treatment condition. Set 1 Set 2 Subject I II Subject I II A 12 14 A 12 14 B 7 17 B 17 27 C 11 13 C 31 33 D 10 12 D 40 42 M = 10 M = 14 M = 25 M = 29 SS = 14 SS = 14 SS = 494 SS = 414 A. Find the difference scores for each set of data and compute the mean and variance for each sample of difference scores. Set 1 MD = _________________________ Set 1 SS = _________________________ Set 1 s² = __________________________ Set 2 MD = _________________________ Set 2 SS = _________________________ Set 2 s² = _________________________ B. You should find that both sets of data produce the same mean difference and the same variance for the difference scores. Explain what happened to the huge individual differences that were added to the second set of data.
One of the major advantages of a repeated-measures design is that it removes individual differences from the variance and, therefore, reduces the standard error. The following two sets of data demonstrate this fact. The first set of data represents the original results from a repeated-measures study. To create the second set of data we started with the original scores but increased the individual differences by adding 10 points to each score for subject B, adding 20 points to each score for subject C, and adding 30 points to each score for subject D. Note that this change produces a huge increase in the differences from one subject to another and a huge increase in the variability of the scores within each treatment condition.
Set 1 Set 2
Subject I II Subject I II
A 12 14 A 12 14
B 7 17 B 17 27
C 11 13 C 31 33
D 10 12 D 40 42
M = 10 M = 14 M = 25 M = 29
SS = 14 SS = 14 SS = 494 SS = 414
A. Find the difference scores for each set of data and compute the mean and variance for each sample of difference scores.
Set 1 MD = _________________________
Set 1 SS = _________________________
Set 1 s² = __________________________
Set 2 MD = _________________________
Set 2 SS = _________________________
Set 2 s² = _________________________
B. You should find that both sets of data produce the same mean difference and the same variance for the difference scores. Explain what happened to the huge individual differences that were added to the second set of data.
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