7.Below are data showing the results of six subjects on a memory test. The three

Question

7.Below are data showing the results of six subjects on a memory test. The three scores per subject are their scores on three trials (a, b, and c) of a memory task. Are the subjects getting better each trial? Test the linear effect of trial for the data.

a

b

c

4

6

7

3

7

8

2

8

5

1

4

7

4

6

9

2

4

2

a. Compute L for each subject using the contrast weights -1, 0, and 1. That is, compute (-1)(a) + (0)(b) + (1)(c) for each subject.

b. Compute a one-sample t-test on this column (with the L values for each subject) you created.

a

b

c

4

6

7

3

7

8

2

8

5

1

4

7

4

6

9

2

4

2

Explanation / Answer

(A) HEre i have computed L for each subject using the contraast weights

(b) Now the L column

Sample mean Lbar =  3.6667

sample standard deviation s = 2.16

standard error of standard deviation = s/ sqrt(n) = 2.16/sqrt(6) =0.882

Test statistic

t = (3.6667 - 0)/0.882 = 4.157

so, here for dF = 7 -1 = 6 and alpha = 0.05

tcritical = 2.447

so here t > tcritical so we shall reject the null hypothesis and can conclude that subjects are getting better each trial

a b c L 4 6 7 3 3 7 8 5 2 8 5 3 1 4 7 6 4 6 9 5 2 4 2 0

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