A sleep researcher conducts an experiment to determine whether a hypnotic drug c
ID: 3170859 • Letter: A
Question
A sleep researcher conducts an experiment to determine whether a hypnotic drug called Drowson, which is advertised as a remedy for insomnia, actually does promote sleep. In addition, the researcher is interested in whether a tolerance to the drug develops with chronic use. The design of the experiment is a 2 × 2 factorial independent groups design. One of the variables is the concentration of Drowson. There are two levels: (1) zero concentration (placebo) and (2) the manufacturer's minimum recommended dosage. The other variable concerns the previous use of Drowson. Again there are two levels: (1) subjects with no previous use and (2) chronic users. Sixteen individuals with sleep-onset insomnia (difficulty in falling asleep) who have had no previous use of Drowson are randomly assigned to the two concentration conditions such that there are eight subjects in each condition. Sixteen chronic users of Drowson are also assigned randomly to the two conditions, eight subjects per condition. All subjects take their prescribed "medication" for 3 consecutive nights, and the time to fall asleep is recorded. The scores shown in the following table are the mean times in minutes to fall asleep for each subject, averaged over the 3 days:
(g) What is the value of Fcrit for previous use of Drowson?
(h) What is the value of Fcrit for concentration of Drowson?
(i) What is the value of Fcrit for the interaction between previous use of Drowson and concentration of Drowson in their effects on insomnia?
Concentration of Drowson Previous Use Placebo Minimumrecommended
dosage No previous use 45 53 30 47 48 58 33 35 62 55 40 31 70 64 50 39 Chronic users 47 68 52 46 52 64 60 49 55 58 58 50 62 59 68 55
Explanation / Answer
Result:
At 0.05 level of significance,
(g) What is the value of Fcrit for previous use of Drowson? F( 1,28) = 4.196
(h) What is the value of Fcrit for concentration of Drowson? : F( 1,28) = 4.196
(i) What is the value of Fcrit for the interaction between previous use of Drowson and concentration of Drowson in their effects on insomnia?: F( 1,28) = 4.196
ANOVA
Source of Variation
SS
df
MS
F
P-value
F crit
Sample
639.0313
1
639.0313
11.6329
0.0020
4.1960
Columns
979.0313
1
979.0313
17.8223
0.0002
4.1960
Interaction
472.7813
1
472.7813
8.6065
0.0066
4.1960
Within
1538.1250
28
54.9330
Total
3628.9688
31
Level of significance
0.05
ANOVA
Source of Variation
SS
df
MS
F
P-value
F crit
Sample
639.0313
1
639.0313
11.6329
0.0020
4.1960
Columns
979.0313
1
979.0313
17.8223
0.0002
4.1960
Interaction
472.7813
1
472.7813
8.6065
0.0066
4.1960
Within
1538.1250
28
54.9330
Total
3628.9688
31
Level of significance
0.05