28: Chi square

Question 1

Chi-square is used to look at:
a. The difference between group means.
b. The proportions of individuals in different categories.
c. The variance in categories.
d. The difference between frequencies in more than two groups.

Answer 1

B
Rationale: Chi-square is a test of proportions.

Question 2

A researcher uses chi-square to examine the association between gender and the presence of migraine headaches. The null hypothesis for this study would be:
a. There is no difference between the number of men and women with migraine
headaches.
b. There is no difference between the number of individuals with and without
migraine headaches.
c. The proportion of men or women with or without migraines will not be different
from what would be expected by chance.
d. There is an association between gender and the presence of migraine headaches.

Answer 2

C
Rationale: The chi-square test focuses on how actual and expected chance frequencies are different.

Question 3

The degrees of freedom for chi-square associated with a 2  3 contingency table will be:
a. 6
b. 4
c. 3
d. 2

Answer 3

D
Rationale: The degrees of freedom will be determined by (Rows –1)(Columns –1) = (2-1)(3-1) = 2.

Question 4

What type of data are applied to a chi-square test?
a. Categorical c. Ratio
b. Ordinal d. Continuous

Answer 4

A
Rationale: Chi-square looks at frequencies within categories. Categories may be nominal or ordinal. Ordinal would only a correct choice if it was categorical.

Question 5

What is the purpose of a goodness-of-fit test?
a. To identify differences between categorical variables.
b. To determine if there is a significant difference between a pattern of observed
frequencies and the pattern that would be expected by chance.
c. To determine which categorical variables have the highest frequencies.
d. To determine if sample frequencies differ from population frequencies.

Answer 5

B
Rationale: The goodness-of-fit test considers the fit of observed data to an expected chance pattern.

Question 6

BWhich of the following statistics is not used as an effect size index for chi-square? a. w c. ?1?
b. 2 d. Odds ratio

Answer 6

B
B
Rationale: The phi coefficient (?1?) is the typical effect size, which is the same as w. The odds ratio can also be used as an effect size. 2 is not its own effect size.

Question 7

A test for goodness of fit is used to look at the distribution of handedness in children in a particular school. Assume that the distribution in the population is 80% right handed, 15% left handed, and 5% ambidextrous. In a class of 200 students, the distribution is 140 right handed, 45 left handed, and 15 ambidextrous. Using  = .05 as the level of significance, what is the correct result and conclusion for this analysis:
2 = 0.875; The distribution in the class is not different from the population. b. 2 = 125.00; The distribution in the class is significantly different from the
population, with fewer right handed students than expected.
2 = 5.99: The distribution in the class is not different from the population. d. 2 = 12.50: The distribution in the class is significantly different from the
population, with more left-handed students than expected.

Answer 7

D
Rationale: The value of chi-square is based on expected frequencies of 160 right handed, 30 left handed, and 10 ambidextrous. The calculated value of 2 is 12.50 which is significant (the critical value is 2(2) = 5.99 at p = .05 with 2 degrees of freedom- see Appendix Table A-5). Therefore, there is a difference between the expected and observed frequencies. The number of left handed students is larger than expected (45 observed, 30 expected). The number of right handed students is less than expected (140 observed, 160 expected). The number of ambidextrous is slightly higher than expected (15 observed, 10 expected).

Question 8

A study is designed to test if children of parents who smoke also smoke. In a sample of 1000 parent/child pairs, each was asked if they currently smoke. Data were recorded as yes/no. To analyze these data, we would need to use:
a. Fisher exact test c. McNemar test
b. Chi-square d. A uniform goodness of fit test

Answer 8

C

Rationale: McNemar is used because the data are paired (correlated). Chi-square, Fisher or goodness of fit cannot be used because the scores are not independent.

Question 9

A study is designed to look at the association between pain (absent, mild, severe) and sleep (poor, moderate, good), using a 3  3 contingency table. The result is 2 = 5.68. What is the critical value of 2 and is this a significant test at .05?
a. The critical value is 3.84 and the test is not significant.
b. The critical value is 9.49 and the test is significant.
c. The critical value is 5.99 and the test is not significant.
d. The critical value is 7.82 and the test is significant.

Answer 9

B

Rationale: The critical value of 2 at .05 for 4df is 9.49. significant (see Appendix Table A-5).