Question

Dr. Lewis investigated the effects of caffeine consumption and sleep deprivation on mental alertness. He recruited 30 college students to participate in his study. He had each student stay in the lab overnight. One-third of the sample was allowed a full night’s sleep (no sleep deprivation), one-third was woken up two hours earlier than usual (2 hours sleep deprivation), and the other one-third was woken up four hours earlier than usual (4 hours sleep deprivation). Within 30 minutes of waking up, half of the participants were given 150 mg of caffeine (the same as a standard cup of coffee) and the other half were given nothing. One hour after waking up, all participants took a mental alertness task. Dr. Lewis began to copy his ANOVA source table from his computer output, but had to leave the office before it was completed. His lab manager needs the results ASAP and asks you to finish the incomplete table.

Source	SS	df	MS	F
Caffeine	228
Sleep Deprivation			710
Caffeine x Sleep Deprivation
Within		24	45	--
Total	4,538		--	--

Complete the source table for the lab manager. Using the source table, what do you conclude about the effects by looking at the F values using α = .05?

Answer 1

The calculations with the formulas are given in the table below:

Source	SS	df	MS	F
Caffeine	228	p - 1 = 2 - 1 = 1	228/1 = 228	MS(Caffeine)/MS(Within) = 228/45 = 5.07
Sleep Deprivation	710*2 = 1420	k - 1 = 3 - 1 = 2	710	710/45 = 15.78
Caffeine x Sleep Deprivation	4538-1420-1080-228 = 1820	(p-1)*(k-1)=1*2 = 2		905/45=20.11
Within	24*45 = 1080	24	45	--
Total	4,538		--	--

The final table is:

Source	SS	df	MS	F	p-value
Caffeine	228	1	228	5.07	0.0338218
Sleep Deprivation	1420	2	710	15.78	0.0000422
Caffeine x Sleep Deprivation	1,810	2	905	20.11	0.0000074
Within	1080	24	45	--
Total	4,538	29	--	--

The p-values are calculated for each F-statistic. The numerator degrees of freedom are the corresponding df in the row and denominator degrees of freedom are the within degrees of freedom which is 45.

Results: 1. As the p-value < 0.05, there is a significant effect of caffeine on mental alertness

2. As the p-value < 0.05, there is a significant effect of sleep deprivation on mental alertness

3. As the p-value < 0.05, there is a significant interaction effect of caffeine and sleep deprivation on mental alertness.