Question

A team of cognitive psychologists studying the effects of sleep deprivation on short-term memory decay had four participants stay in a sleep lab for two days. The participants completed a short-term memory task for a baseline score. That night they were not permitted to sleep. The next day, at the same time of day as the day before, the participants completed another short-term memory task. The results are presented in the table below. Using the .05 significance level, did sleep deprivation reduce short-term memory?

Mean Number of Letters Remembered

Baseline Scores Sleep Deprived Scores Diff Diff-M (Diff-M)²

9 7

8 8

11 7

9 8

What is the Md and the SSd ?

Answer 1

Baseline Scores	Sleep Deprived Scores	Diff	Diff-M	(Diff-M)2
9	7	2	0.25	0.0625
8	8	0	-1.75	3.0625
11	7	4	2.25	5.0625
9	8	1	-0.75	0.5625

Mean Diff, Md = (2 + 0 + 4 + 1) / 4 = 1.75

Sum of squares of differences, SSd = 0.0625 + 3.0625 + 5.0625 + 0.5625 = 8.75

Standard deviation of differences, Sd = = 1.707825

Standard error of mean difference, SE = Sd / = 1.707825 / =  0.8539125

Test statistic , t = (Md - 0) / SE = 1.75 / 0.8539125 = 2.05

Degree of freedom = n-1 = 4-1 = 3

Critical value of t at .05 significance level and df = 3 is 2.35

Since the observed t (2.05) is less than the critical value, we conclude that there is no strong evidence that sleep deprivation reduce short-term memory.