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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

Significance of the Difference Between Two Sample Means

Problems

For each of the following, compute <a onClick="window.open('/olcweb/cgi/pluginpop.cgi?it=gif:: ::/sites/dl/free/0072832517/55319/c10_s2.gif','popWin', 'width=NaN,height=NaN,resizable,scrollbars');" href="#"><img valign="absmiddle" height="16" width="16" border="0" src="/olcweb/styles/shared/linkicons/image.gif"> (0.0K)</a> using both the raw-score and the defining formulas. Assume that the samples are independent.
1. N₁ = N₂ = 12, s₁ = 3.6, s₂ = 4.3
2. N₁ = 22, ∑X₁ = 112.2, ∑X₁² = 643.5; N₂ = 22, ∑X₂ = 138.6, ∑X₂² = 1,010.68
3. N₁ = N₂ = 25, s₁² = 2.25, s₂² = 1.96

In a military training program, the complex reaction-time ability of pilots and navigators is compared. Determine whether there is a significant difference between the groups in the number of errors made (failure to respond) in 100 stimulus presentations.

Pilots	Navigators

N = 15	N = 20
= 23.5	= 41.3
s = 10.5	s = 12.7

Experimental evidence indicates that persons with a family history of alcoholism are more likely to become alcoholic than persons with no such history. A large group of adults with and without family histories of alcoholism is selected, and from this large group, eight pairs of participants are matched in terms of race, age, marital status, and drinking history. Each participant is given a drink of alcohol; 30 minutes later, a blood sample is taken, and a metabolite of alcohol is measured. The results are shown here.
Pair
Number
Family History
(µg/ml)
No Family History
(µg/ml)
1 3.1 2.5
2 3.5 2.1
3 3.2 1.8
4 2.8 2.3
5 2.6 2.2
6 3.0 1.9
7 1.9 2.3
8 2.7 2.5
Compare the groups with and without a family history of alcoholism.
Thirty-two students are randomly selected from a large introductory class and are randomly and evenly assigned to one of two groups. Each participant is given four 15-second exposures to a list of 15 nouns. After 30 minutes, each participant in one group is given a free recall test, whereas each participant in the other group is given a recognition test. The results in terms of the number of words correctly retained are shown here. Compare the groups.
Recall Test Recognition Test
X f X f
4 1 15 6
2 5 14 1
1 7 13 4
0 3 12 2
10 1
8 1
6 1
In an attempted replication of the Rosenthal effect (experimenter bias can influence the outcome of an experiment), two groups of 15 randomly selected students each are given some rats to train. One group is told that the rats are retarded, whereas the other group is told that the rats are intelligent. Errors are recorded during training, and the data for each group are shown here.
Group "Stupid" Group "Intelligent"
∑X = 379.5 ∑X = 252
∑X² = 9,853.5 ∑X² = 4,450.2
N = 15 N = 15
1. Before you analyze the data, determine whether there is a rationale for using the one-tailed test of significance. If so, what is it?
2. Compare the groups using the appropriate statistical test.
Ten politically active individuals are selected, all of whom label themselves as liberal. Each is attached to a physiograph, and heart rate is recorded while a sequence of 20 slides is projected on a screen at which the participant is looking. Half of the slides are pictures of famous individuals without any expressed political philosophy; the other half are known conservatives. The arrangement of the slides is random. Each participant receives two scores: The first is the average heart rate during exposure to the neutral slides, and the second is the average heart rate during exposure to the conservative slides. The data are shown here. Does reaction to the slides differ?
Participant Neutral Conservative
1 65.3 71.8
2 75.7 73.5
3 85.6 99.3
4 73.7 81.7
5 69.5 75.7
6 68.2 73.5
7 70.1 79.8
8 72.5 70.3
9 71.0 85.3
10 83.5 107.1

An experiment is performed to compare the performance of students taught statistics by a traditional lecture approach with students taught by group discussion sessions. Fifty students are randomly and equally assigned to one of the two treatment conditions. In each case, the same instructor is present; he lectures to one group and leads the discussion in the other. The final class averages based on scores on standardized, machine-scored tests are presented here. Is there a significant difference between the groups?

Lecture	Discussion

N = 25	N = 25
= 81.7	= 74.1
s = 8.3	s = 10.1

The average ACT score for 937 freshmen at State University is 21.4, with a variance of 24.1. For Private University in the same city, the average ACT score for 421 freshmen is 22.1, with a variance of 14.5. Is there a significant difference between the schools in average freshman ACT scores? If so, how can you account for it in terms of factors affecting the power of a test?
Ten students are tested for accuracy of distance estimation using either one or both eyes. The test object is 24 inches from the viewer. Is there a significant difference in the amount of error (in inches) between the two conditions?
Student One Eye Two Eyes
A 3 2
B 11 8
C 5 7
D 4 2
E 6 4
F 3 1
G 15 10
H 4 5
I 8 7
J 9 7

A study is done to see whether children are more likely to have psychic powers than young adults. Thirteen randomly selected 8-year-old children each make one run through a standard PSI deck trying to guess the identity of each target card by "reading" the mind of the tester. There are four different targets, and each child receives a score indicating proportion of "hits." The same procedure is used on 15 randomly selected college students. Compare the groups.

Children	Young Adults

N = 13	N = 15
= .28	= .24
s = .067	s = .073

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