A psychologist employs a two-factor experiment to study the combined effect of s
ID: 3298343 • Letter: A
Question
A psychologist employs a two-factor experiment to study the combined
effect of sleep deprivation and alcohol consumption on the performance of
automobile drivers. Before the driving test, the subjects go without sleep
for various time periods and then drink a glass of orange juice laced with
controlled amounts of vodka. Their performance is measured by the number
of errors made on a driving simulator. Two subjects are randomly
assigned to each cell, that is, each possible combination of sleep deprivation
(either 0, 24, 48, or 72 hours) and alcohol consumption (either 0, 1,
2, or 3 ounces), yielding the following results:
(a) Summarize the results with an ANOVA table.
(b) If appropriate, conduct additional F tests, estimate effect sizes, and use
Tukey’s HSD test.
NUMBER OF DRIVING ERRORS ALCOHOLSLEEP DEPRIVATION CONSUMPTION HOURS) (OUNCES) 024 48 72 0 2 55 29 841 136 536 1296 3 3 78 53 2809 5 5 11 12 4 410 9 6 7 1315 68 4624 ase 25 30 64 67 uT 625 900 4096 4489 = 1466 G= 186 G"-34596Explanation / Answer
Answer:
A psychologist employs a two-factor experiment to study the combined effect of sleep deprivation and alcohol consumption on the performance of automobile drivers. Before the driving test, the subjects go without sleep for various time periods and then drink a glass of orange juice laced with controlled amounts of vodka. Their performance is measured by the number of errors made on a driving simulator. Two subjects are randomly assigned to each cell, that is, each possible combination of sleep deprivation (either 0, 24, 48, or 72 hours) and alcohol consumption (either 0, 1, 2, or 3 ounces), yielding the following results:
(a) Summarize the results with an ANOVA table.
Two factor ANOVA
Factor 2
Means:
0hour
24hour
48hour
72hour
0ounce
1.5
3.0
4.5
5.5
3.6
Factor 1
1ounce
2.0
3.0
6.5
6.5
4.5
2ounce
4.0
3.5
9.5
9.5
6.6
3ounce
5.0
5.5
11.5
12.0
8.5
3.1
3.8
8.0
8.4
5.8
2
replications per cell
ANOVA table
Source
SS
df
MS
F
p-value
Alcohol
115.13
3
38.375
9.16
.0009
Time
182.63
3
60.875
14.54
.0001
Interaction
20.13
9
2.236
0.53
.8292
Error
67.00
16
4.188
Total
384.88
31
Alcohol is significantly significant, F=9.16, P=0.0009 which is < 0.05 level.
Time is significantly significant, F=14.54, P=0.0001 which is < 0.05 level.
Interaction is not significant, F=0.53, P=0.8292 which is > 0.05 level.
(b) If appropriate, conduct additional F tests, estimate effect sizes, and use
Tukey’s HSD test.
Tukey simultaneous comparison t-values (d.f. = 16)
0ounce
1ounce
2ounce
3ounce
3.6
4.5
6.6
8.5
0ounce
3.6
1ounce
4.5
0.86
2ounce
6.6
2.93
2.08
3ounce
8.5
4.76
3.91
1.83
critical values for experimentwise error rate:
0.05
2.86
0.01
3.67
Post hoc analysis
Tukey simultaneous comparison t-values (d.f. = 16)
0hour
24hour
48hour
72hour
3.1
3.8
8.0
8.4
0hour
3.1
24hour
3.8
0.61
48hour
8.0
4.76
4.15
72hour
8.4
5.13
4.52
0.37
critical values for experimentwise error rate:
0.05
2.86
0.01
3.67
Post hoc test shows that 0 ounce is significant from 2 and 3 ounces. 1 ounce is significant from 2 ounce.
0 hour is significant from 48 and 72 hours. 24 ounce is significant from 48 and 72 hours.
Effect size for Alcohol, 115.13/384.88 =0.2991.
Effect size for Time, 182.63 /384.88 =0.4745.
Two factor ANOVA
Factor 2
Means:
0hour
24hour
48hour
72hour
0ounce
1.5
3.0
4.5
5.5
3.6
Factor 1
1ounce
2.0
3.0
6.5
6.5
4.5
2ounce
4.0
3.5
9.5
9.5
6.6
3ounce
5.0
5.5
11.5
12.0
8.5
3.1
3.8
8.0
8.4
5.8
2
replications per cell
ANOVA table
Source
SS
df
MS
F
p-value
Alcohol
115.13
3
38.375
9.16
.0009
Time
182.63
3
60.875
14.54
.0001
Interaction
20.13
9
2.236
0.53
.8292
Error
67.00
16
4.188
Total
384.88
31
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