Explain what you have done and why to someone who is familiar with the t test for independent means but not with data transformation.

4. Carry out a chi–square test for independence for each of the following
contingency tables (use the .01 level). Also, figure the effect size for each.

5. A political analyst is interested in whether the community in which a person lives
is related to that person’s opinion on an upcoming water conservation ballot
initiative. The analyst surveys 90 people by phone. The results are shown in the
following table. Is opinion related to community at the .05 level?

(a) Carry out the five steps of hypothesis testing.

(b) Compute effect size and power.

(c) Explain your answers to (a) and (b) to a person who has never taken a course in statistics.
Community A Community B Community C
For 12 6 3
Against 18 3 15
No opinion 12 9 12

7. Figure the effect size for the following studies:
N Chi–Square Design
(a) 100 16 2×2
(b) 100 16 2×5
(c) 100 16 3×3
(d) 100 8 2×2
(e) 200 16 2×2

9. What is the power of the following planned studies using a chi–square test for
independence with p<.05?

(a) Small 2×2 25
(b) Medium 2×2 25
(c) Small 2×2 50
(d) Small 2×3 25
(e) Small 3×3 25
(f) Small 2×5 25

11. About how many participants do you need for 80% power in each of the following planned studies using a chi–square test for independence with p<.05?
Predicted Effect Size Design
(a) medium 2×2
(b) Large 2×2
(c) medium 2×5
(d) medium 3×3
(e) Large 2×3
12. 11.1–29 Full Alternative Text

13. Lydon, Pierce, and O’Regan (1997) conducted a study that compared long–
distance to local dating relationships. The researchers first administered
questionnaires to a group of students one month prior to their leaving home to
begin their first semester at McGill University (Time 1). Some of these students
had dating partners who lived in the McGill area (Montreal, Canada); others had
dating partners who lived a long way from McGill. The researchers contacted the
participants again late in the fall semester, asking them about the current status of
their original dating relationships (Time 2). Here is how they reported their
results:Of the 69 participants … 55 were involved in long–distance relationships, and 14 were in local relationships (dating partner living within 200 km of them).
Consistent with our predictions, 12 of the 14 local relationships were still intact at Time 2 (86%), whereas only 28 of the 55 long–distance relationships were still intact (51%), χ2(1, N=69)=5.55, p<.02. (p. 108)
a. Figure the chi–square yourself (your results should be the same,  within rounding error).

b. Figure the effect size.

c. Explain the results to parts (a) and (b) to a person who has never had a course in statistics.
9. For each of the following distributions, make a square–root transformation:
a. 16, 4, 9, 25, 36
b. 35, 14.3, 13, 12.9, 18

10. A researcher compares the typical family size in 10 cultures, 5 from Language Group A and 5 from Language Group B. The figures for the Group A cultures are 1.2, 2.5, 4.3, 3.8, and 7.2. The figures for the Group B cultures are 2.1, 9.2, 5.7, 6.7, and 4.8. Based on these 10 cultures, does typical family size differ in cultures with different language
groups? Use the .05 level.

(a) Carry out a t test for independent means using the actual scores.

(b) Carry out a square–root transformation (to keep things simple, round off the transformed scores to one decimal place).

(c) Carry out a t test for independent means using the transformed scores.

(d) Explain what you have done and why to someone who is familiar with the t test for independent means but not with data transformation.

11. A researcher randomly assigns participants to watch one of three kinds of films:
one that tends to make people sad, one that tends to make people angry, and one
that tends to make people exuberant. The participants are then asked to rate a
series of photos of individuals on how honest they appear. The ratings for the sad–
film group were 201, 523, and 614; the ratings for the angry–film group were 136,
340, and 301; and the ratings for the exuberant–film group were 838, 911, and
1,007.

(a) Carry out an analysis of variance using the actual scores (use p<.01).

(b) Carry out a square–root transformation of the scores (to keep things simple,
round off the transformed scores to one decimal place).

(c) Carry out an analysis of variance using the transformed scores.

(d) Explain what you have done and why to someone who is familiar with analysis of variance but not with data transformation.

12. Miller (1997) conducted a study of commitment to a romantic relationship and
how much attention a person pays to attractive alternatives. In this study,
participants were shown a set of slides of attractive individuals. At the start of the
Results section, Miller notes, “The self–reports on the Attentiveness to Alternative
Index and the time spent actually inspecting the attractive opposite–sex slides …
were positively skewed, so logarithmic transformations of the data were
performed” (p. 760).

Explain what is being described here (and why it is being done) to a person who understands ordinary parametric statistics but has never heard of data transformations.

13. Carry out a chi–square test for goodness of fit for each of the following (use the .01 level for each):
(a) Category Expected Observed
1 2% 5
2 14% 15
3 34% 90
4 34% 120
5 14% 50
6 2% 20

14. 11.1–30 Full Alternative Text
(b) Category Proportion Expected Observed
A 1/3 10
B 1/6 10
C 1/2 10

(c) Category Proportion Expected Observed
I 1/4 70
II 1/4 130
III 1/4 80
IV 1/4 120

16. Carry out a chi–square test for goodness of fit using your own clothes! Look in a closet or drawer and count up the number of items of clothing that you have of different colors.
To make it a little easier, consider counting only the four or five most common colors. So, you might have 15 black, 12 blue, 9 brown, and 6 gray items of clothing. Then, using this information, carry out the steps of hypothesis testing for a chi– square test for goodness of fit (assuming that you would expect an equal number of items of clothing for each color).

17. Carry out a chi–square test for independence for each of the following contingency tables (use the .05 level). Also, figure the effect size for each contingency table.
11.1–31 Full Alternative Text

18. The following results are from a survey of a sample of people buying ballet tickets, laid out according to the type of how regularly they attend. Is there a significant relation? (Use the .05 level.)

(a) Carry out the steps of hypothesis testing.

(b) Figure the effect size.

(c)Explain your answer to parts (a) and (b) to a person who has never taken a course in statistics.

19. Figure the effect size for the following studies:
N Chi–Square Design
(a) 40 10 2×2
(b) 400 10 2×2
(c) 40 10 4×4
(d) 400 10 4×4
(e) 40 20 2×2
20. 11.1–33 Full Alternative Text

21. What is the power of the following planned studies, using a chi–square test for independence with p<.05?

Predicted Effect Size Design N
(a) Medium 2×2 100
(b) Medium 2×3 100
(c) Large 2×2 100
(d) Medium 2×2 200
(e) Medium 2×3 50
(f) Small 3×3 25
22. 11.1–34 Full Alternative Text

Predicted Effect Size Design
(a) Small 2×2
(b) Medium 2×2
(c) Large 2×2
(d) Small 3×3
(e) Medium 3×3
(f) Large 3×3
24. 11.1–35 Full Alternative Text

25. Everett, Price, Bedell, and Telljohann (1997) mailed a survey to a random sample of physicians. Half were offered $1 if they would return the questionnaire (this was the experimental group); the other half served as a control group. The point of the study was to see if even a small incentive would increase the return rate for physician surveys. Everett et al. report their results as follows:
Of the 300 surveys mailed to the experimental group, 39 were undeliverable, 2 were returned uncompleted, and 164 were returned completed. Thus, the response rate for the experimental group was 63% [164/(300−39)=.63]. Of the 300 surveys mailed to the control group, 40 were undeliverable, and 118 were returned completed. Thus, the response rate for the control group was 45% [118/(300−40)=.45] A chi–square test comparing the response rates for the experimental and control groups found the $1 incentive had a statistically significantly improved response rate over the control group [χ2(1, N=521)=16.0, p<.001].

(a) Figure the chi–square yourself (your results should be the same, within rounding error).

(b) Figure the effect size.

(c)Explain the results to parts (a) and (b) to a person who has never had a course in statistics.

26. For each of the following distributions, make a square– root transformation:
a. 100, 1, 64, 81, 121
b. 45, 30, 17.4, 16.8, 47

27. A study compares performance on a novel task for university students who do the task either alone, in the presence of a stranger, or in the presence of a friend. The scores for the students in the alone condition are 1, 1, and 0; the scores of the participants in the stranger condition are 2, 6, and 1; and the scores for those in the friend condition are 3, 9, and 10.

(a) Carry out an analysis of variance using the actual scores (p<.05).

(b) Carry out a square–root transformation of the scores (to keep things simple, round off the transformed scores to one decimal place).

(c) Carry out using the transformed difference scores.

(d) Explain what you have done and why to someone who is familiar with analysis of variance but not with data transformation.

28. A researcher conducted an experiment organized around a major televised address by the U.S. president. Immediately after the address, three participants were
randomly assigned to listen to the commentaries provided by the television networks’ political commentators. The other three were assigned to spend the same time with the television off, reflecting quietly about the speech. Participants in both groups then completed a questionnaire that assessed how much of the content of the speech they remembered accurately. The group that heard the commentators had scores of 4, 0, and 1. The group that reflected quietly had scores of 9, 3, and 8. Did hearing the commentary affect memory? Use the .05 level, one–tailed, predicting higher scores for the reflected-quietly group.

(a) Carry out a t test for independent means using the actual scores.

(b) Carry out a square-root transformation (to keep things simple, round off the transformed scores to one decimal place).

(c) Carry out a t test for independent means using the transformed scores.

(d) Explain what you have done and why to someone who is familiar with the t test for independent means but not with data transformation.

13. As part of a larger study, Betsch, Plessner, Schwieren, and Gutig (2001)
manipulated the attention to information presented in TV ads and then gave
participants questions about the content of the ads as a check on the success of
their manipulation.

They reported:
Participants who were instructed to attend to the ads answered 51.5% … of
the questions correctly. In the other condition, only 41.1% of questions were
answered correctly. This difference is significant according to the Mann-
Whitney U test, U(84)=2317.0, p<.01. This shows that the attention
manipulation was effective. (p. 248)
Explain the general idea of what these researchers are doing (and why they didn’t
use an ordinary t test) to a person who is familiar with the t test but not with rank-
order tests.