Chapter 11, Problem 19P

### Essentials of Statistics for the B...

8th Edition
Frederick J Gravetter + 1 other
ISBN: 9781133956570

Chapter
Section

### Essentials of Statistics for the B...

8th Edition
Frederick J Gravetter + 1 other
ISBN: 9781133956570
Textbook Problem

# Problem 18 shows that removing individual differences can substantially reduce variance and lower the standard error. However, this benefit only occurs if the individual differences are consistent across treatment conditions. In problem 18, for example, the first two participants (top two rows) consistently had the highest scores in both treatment conditions. Similarly, the last two participants consistently had the lowest scores in both treatments. To construct the following data, we started with the scores in problem 18 and scrambled the scores in treatment 1 to eliminate the consistency of the individual differences. a. Assume that the data are from an independent-measures study using two separate samples, each with n = 6 participants. Compute the pooled variance and the estimated standard error for the mean difference. b. Now assume that the data are from a repeated measures study using the same sample of n = 6 participants in both treatment conditions. Compute the variance for the sample of difference scores and the estimated standard error for the mean difference. (This time you should find that removing the individual differences does not reduce the variance or the standard error.)

a.

To determine

To find: The value of pooled variance and standard error.

Explanation

Given info:

The independent-measures study with scores of n=6 participants is used and samples means of the two treatments are 8 and 10 while SS values are 34 and 30 respectively. Also, the means for Â difference is 2 while SS value is 64

Calculation:

The pooled variance, sp2, is calculated using formula:

sp2=SS1+SS2df1+df2

Substitute 34 for SS1, 30 for SS2 and 5 for both df1 and df2 in the above formula

sp2=34+305+5=6

b.

To determine

To find: The value of variance for the mean difference and standard error for the mean difference.

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