Chapter 11, Problem 19P

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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

**Calculation:**

The pooled variance,

Substitute 34 for

**b.**

To determine

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

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