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Statistics for the Behavioral Sciences, 4/e

Michael Thorne, Mississippi State University -- Mississippi State
Martin Giesen, Mississippi State University -- Mississippi State

One-Way Analysis of Variance With Post Hoc Comparisons

Problems

From a large introductory psychology class, 32 snake-phobic students were selected and randomly assigned to one of four experimental groups. Group 1 received five sessions of relaxation training; Group 2 received five sessions of imagery training (they were required to imagine each of several feared situations); Group 3 received relaxation training combined with the imagery training; Group 4 participants were told that there would be a few weeks' delay in the beginning of therapy. Three weeks from the beginning of the experiment, each participant was given a behavioral avoidance test to determine how closely he or she would approach a live snake in an aquarium. The response measure is the distance from the snake in feet.
Compute the following:
∑X₁ = ∑X₂ = ∑X₃ = ∑X₄ = ∑X =
∑X²₁ = ∑X²₂ = ∑X²₃ = ∑X²₄ = ∑X =
N₁ = N₂ = N₃ = N₄ = N =
Find the sums of squares:
SS_tot =
SS_w =
Find SSb by subtraction:
SS_b = SS_tot - SS_w =
Compute SS_b:
SS_b =
Complete the ANOVA summary table:

The computed value of F is_________________. The df for the numerator is_________________, and the df for the denominator is_________________. The table values required for rejection of H₀ are _________________ at the 5% level and ________________ at the 1% level. What is your decision, and what does it mean in the context of the problem?
Use the Fisher LSD test to analyze the data in Problem 1 further.
Three different commercial sleeping aids and a placebo are given to four groups of randomly selected young adults. After a suitable period of time for the drugs to take effect, each participant is placed in a room with a bed, and his or her EEG is monitored. The response measured is the length of time before onset of sleep as determined by the EEG. The results are as follows: Group Placebo, N = 9, ∑X = 29.7, ∑X ² = 105.49; Group Potion 1, N = 8, ∑X = 30.4, ∑X ² = 120.22; Group Potion 2, N = 9, ∑X = 32, ∑X ² = 121.26; Group Potion 3, N = 8, ∑X = 30.1, ∑X ² = 131.51.
Compute the sums of squares and fill in the summary table.
SS_tot =
SS_w =
SS_b =

Is the F ratio significant, and what does your conclusion mean in the context of the problem?
During WWII, the RAF noticed that a large number of fighter pilots were being killed because they were not dark-adapted during night air raids. An experiment was performed to determine whether different levels of preflight illumination might result in significant differences in time to dark adaptation. Twenty-four pilots were randomly and equally assigned to one of three treatment groups. Group A spent 30 minutes in a brightly lighted room; Group B spent 30 minutes in a dimly lighted room; Group C spent 30 minutes in a brightly lighted room wearing red-tinted goggles. The length of time in minutes for complete dark adaptation was recorded for each pilot. Determine whether the groups differed significantly.
Group A Group B Group C
N = 8 N = 8 N = 8
∑X = 260 ∑X = 78 ∑X = 36
∑X ² = 8,492 ∑X ² = 788 ∑X ² = 196
Using the Fisher LSD, do all pairwise comparisons of the groups in Problem 4.
We hypothesize that the experience of taking a statistics course will reduce mathematics anxiety. To test this hypothesis, we select nine statistics students and assess their mathematics anxiety on four occasions: on the first day of class, after 3 weeks of class, after 6 weeks of class, and after 9 weeks of class. Perform the appropriate overall test of significance.
Student First Day 3 Weeks 6 Weeks 9 Weeks
A 14 12 9 8
B 8 7 5 3
C 6 7 4 2
D 9 10 8 7
E 15 12 10 9
F 12 10 8 9
G 9 8 7 6
H 7 6 5 3
I 10 9 7 7
Use the Fisher LSD test to perform all pairwise comparisons for the data in Problem 6.
A manufacturing company is concerned about the effect of fatigue on the speed with which its workers can assemble pocket calculators. For 10 workers, the average time (in seconds) it takes to assemble a pocket calculator is measured at the beginning, in the middle, and at the end of the shift. Does performance change across periods of the workers' shift?
Worker Beginning Middle End
A 20 21 23
B 28 30 31
C 22 23 24
D 19 19 22
E 24 26 28
F 26 27 29
G 19 18 19
H 24 25 27
I 20 21 22
J 19 21 22
Use the Tukey HSD to make all pairwise comparisons for the data in Problem 8.
In a study of dark adaptation, eight participants seated in an almost totally dark room were asked to determine visually the presence or absence of an object. All participants were given 10 trials after 1 minute of adaptation, after 15 minutes, and after 30 minutes. At each testing, the number of correct detections out of 10 trials was recorded. Perform an overall significance test, and tell what your conclusion means in the context of the problem.
Participant 1 Minute 15 Minutes 30 Minutes
A 2 6 6
B 0 2 4
C 4 7 9
D 3 5 6
E 6 8 10
F 0 2 4
G 2 5 1
H 3 5 8
Use the Fisher LSD test to make all pairwise comparisons and summarize your results.
A study was done to see whether the source of dietary fat affects visual discrimination. Rats were placed on one of four diets for 2 months: Diet 1 had 5% corn oil; Diet 2 was the same as Diet 1 with the addition of 20% safflower oil; Diet 3 was Diet 1 with 20% added coconut oil; Diet 4 was Diet 1 with 20% added olive oil. All the rats were trained on a simple visual discrimination task, and their errors before achieving a certain criterion were recorded. Test the data to see whether the different diets affected learning of the task.
Diet 1 Diet 2 Diet 3 Diet 4
13 10 7 14
20 20 17 19
31 34 11 27
18 27 23 31
11 7 14 15
11 27 13 21
11 10 26 14
12 12 23
12 32 4
12 11

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