1. A study of Frozen Salmon University faculty and their use of personal stress management counseling sessions (PSMCS) was conducted. The answers to two questions produced the following data. Calculate the marginals, row percents, and column percents for the following table:
| Count row% col% |
|
||||||
| Users | non-Users | Total | |||||
| Sex | m | 29 43.939% 72.500% |
37 56.061% 48.835% |
55.462% |
|||
| f | 11 20.755% 27.500% |
42 79.245% 53.165% |
53 44.538% |
||||
| Total | 40 33.613% |
79 66.387% |
|
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a. What would it mean to "percentage across, compare down" on this table?
It would mean that you compare the row percents in the Users column to one another; i.e. compare 43.939% to 20.755%.
b. Which is more appropriate for this table -- "percentage across, compare down"; or "percentage down, compare across"? Why?
% across, compare down is better because sex is the independent variable.
c. Interpret what this table tells you about the relation between sex and use of personal stress management counseling services.
43.939% of the male faculty used the service, compared to only 20.755% of the female faculty. The percentage of men who used it (43.939%) was more than than twice as large as the percentage of women who used it (20.755%).
2. Calculate the marginals, row percents, and column percents for the table shown below.
| Count row% col% |
|
||||
| Choc. | Vanil. | Strawb. | Total | ||
| Sex | m | 25 45.454% 41.667% |
15 27.273% 42.857% |
15 27.273% 60.000% |
55 45.83% |
| f | 35 53.846% 58.333% |
20 30.769% 57.143% |
10 15.384% 40.000% |
65 54.167% |
|
| Total | 60 50.0% |
35 29.167% |
25 20.833% |
120 | |
a. Do "percentage across, compare down" on this table.While more of the men (27.273%) and fewer of the women (15.384%) prefer Strawberry, more of the women (53.846%) and fewer of the men (45.454%) prefer chocolate, and slightly more of the women (30.769%) and fewer of the men (27.273%) prefer vaniilla.
b. Do "percentage down, compare across" on this table.
60.0% of those who prefer strawberry were males, compared to 41.667% and 42.857% of those who prefer chocolate or vanilla.
Alternatively, 60% of those who prefer strawberry were men, while almost equally large proportions of those who preferred chocolate or vanilla (58.333% and 57.143%) were women.
c. Which is more appropriate for this table -- "percentage across, compare down"; or "percentage down, compare across"? Why?
% across, compare down, because sex is the independent variable.
d. Interpret what this table tells you about the relation between sex and preferred ice cream flavor. Make sure your interpretation is in terms of the variables. ("Compared to women, men were more likely to ....." or "Compared to Chocolate and Vanilla, Strawberry was more likely to ...")
Sex is moderately related to flavor preference: men were more likely to prefer Strawberry and less likely to prefer chocolate or vanilla than women.
3. A large study was conducted in the Los Angeles area, where there are serious problems with STD's (sexually-transmitted diseases) and drug addiction.Compute the rest of the counts, the row and column percentages, and row and column marginal counts and percentages for the table below.
| Count row% col% |
|
|||
| yes | no | total | ||
|
carrier |
yes | 90 60.00% 47.37% |
60 40.00% 33.33% |
150 40.54% |
| no | 100 45.45% 52.63% |
120 54.55% 66.67% |
220 59.46% |
|
| total | 190 51.35% |
180 48.65% |
370 | |
4. Using the "percentage down compare across" strategy, explain what the table shows.
47.37% of drug users are STD carriers, compared to only 33.33% of those who don't use drugs. In other words, the proportion of drug users who have STDs (47.37%) is considerably higher than the proprtion of people who don't use drugs (33.33%).