# Chapter 11: Analysing Other Forms of Data: Chi-square and Distribution-free Tests

1. A team of researchers conducts a large study looking at factors that predict poor health in the workplace. They find that more men than women have heart attacks at work. They plan to analyse their data using a binomial test, but are aware of the need to take into account relevant base-rate information. Which of the following constitutes relevant base-rate information for this purpose? [TY11.1]

1. The proportion of people in the workplace who are men.
2. The proportion of people in the workplace who have heart attacks.
3. The proportion of men in the workplace who have heart attacks.
4. The proportion of women in the workplace who have heart attacks.
5. None of the above, as base-rate information is irrelevant here.

2. A researcher is interested in seeing whether families who go to a particular coastal town for their holiday are more likely to come from some towns than from others. In his research he looks at the visitors’ books of three hotels and finds that together they have been visited by 1204 families over the past year. Of these, 261 are from Town A, 403 are from Town B, 312 are from Town C and 228 are from Town D. Which of these towns makes the greatest contribution to χ2? [TY11.2]

1. Town A.
2. Town B.
3. Town C.
4. Town D.
5. All make an equal contribution.

3. The statistical odds of an event occurring are .25. Which of the following statements is true? [TY11.3]

1. The probability of the event occurring is .25.
2. In four independent tests the expected frequency of the event is 1.
3. The probability of the event occurring is .2.
4. We cannot make a statement about probability or expected frequency, because odds are only ever calculated by bookmakers who are trying to make a profit.
5. None of the above.

4. Which of the following statements is true? [TY11.4]

1. Distribution-free tests do not involve distributions.
2. Non-parametric tests do not involve distributions.
3. Non-parametric tests are very different from distribution-free tests.
4. Distribution-free tests are free of assumptions about the parameters of the distribution from which a sample is drawn.
5. None of the above.

5. The Mann-Whitney test is the distribution-free analogue of which of the following tests? [TY11.5]

1. The between-subjects t-test.
2. The within-subjects t-test.
3. One-way ANOVA.
4. Two-way ANOVA.
5. Pearson’s r.

6. An organizational psychologist conducts a piece of research in which he tests the hypothesis that companies that have a pension plan retain more employees than companies that do not have a plan. To test this hypothesis he collects data from 60 companies recording (a) whether or not they have a pension plan and (b) what percentage of their employees are still working for the company after a year. However, on inspecting his data, the researcher finds that most companies retain a very high proportion of their employees and that scores on this measure are therefore very highly skewed. Which of the following tests would be most appropriate for comparing central tendencies? [TY11.6]

1. ANOVA.
2. The χ2 test of independence.
3. The χ2 test of goodness of fit.
4. The Mann–Whitney test.
5. The between-subjects t-test.

7. Which of the following statements is false? [TY11.7]

1. Distribution-free tests can be useful when the assumptions of other tests are violated.
2. Distribution-free tests are useful when handling categorical data.
3. Non-parametric tests are useful when handling categorical data.
4. Non-parametric tests have very few uses.
5. Non-parametric tests and distribution-free tests both make relaxed assumptions about the parameters of population distributions.

8. Which of the following is the main limitation of tests with relaxed assumptions? [TY11.8]

1. Their assumptions are generally too relaxed.
2. They are usually very difficult to conduct.
3. They can only be used effectively in applied settings.
4. They provide information about odds rather than probabilities.
5. They generally have less power than parametric tests.

9. Which of the folliwing statements is true?

1. Sometimes we need to use distribution-free tests because we do not know enough about the population from which data are drawn.
2. Sometimes we need to use distribution-free tests because we are unable to make assumptions about the population from which data are drawn.
3. Sometimes we need to use distribution-free tests because we are unwilling to make assumptions about the population from which data are drawn.
4. Both (a) and (b).
5. All of the above.

10. The sign test involves analysing what form of data?

1. Data in which one variable has two levels.
2. Data in which one variable has two or more levels.
3. Data in which two variables have two levels.
4. Data in which two variables have many levels.
5. None of the above.

11. “The incidence of a particular phenomenon among a population of interest. Information about these is required in order to establish the significance of the incidence of the phenomenon within a subset of that population (e.g. people who have been subjected to a particular treatment).” What is this a glossary definition of?

1. Population rates
2. Backgrount rates
3. Incidence rates
4. Base rate.
5. General rate.

12. “Statements of the likelihood of one event occurring given that another has occurred. These are obtained from the data in specific rows or columns of contingency tables, and are expressed in terms of the frequency with which the event occurs in a given row or column divided by the frequency with which it does not occur in the same row or column.” What is this a glossary definition of?

1. Conditional odds.
2. Betting odds.
3. Likelihood ratios.
4. Relative odds.
5. Likelihood odds.

13. “Statements of the likelihood of a given event occurring expressed in terms of the expected frequency of it occurring divided by the expected frequency of it not occurring. Note that this is not the same as the probability of the event occurring.” What is this a glossary definition of?

1. Likelihood ratio.
2. Odds ratio.
3. General probability.
4. Frequency odds.
5. Statistical odds.

14. “A distribution-free test that is usually used to compare the central tendency of two independent groups. In this regard it is the distribution-free analogue of a between-subjects t-test.” Which statistical test is this a glossary definition of?

1. Kruskal-Wallis test
2. Wilcoxon matched-pairs signed-ranks test
3. Chi-square test
4. Mann-Whitney test
5. McNemar test.