Quiz 3: Two-way Tables 📊

Test your knowledge of the material on two-way tables in the following quiz to see how much you learned. This is entirely private for you---no records are kept of your performance.

Questions

1. What is the best way to test the significance of the association between two categorical variables in a two-way frequency table?

Using a chi-square test Using a t-test Using a one-way ANOVA Using a linear regression

Explanation

The chi-square test (either Pearson or likelihood ratio) is the standard test for assessing the statistical significance of association between two categorical variables in a two-way frequency table. T-tests, ANOVA, and linear regression are designed for continuous outcomes.

2. What is the best measure used to quantify the strength of association between two categorical variables in a two-way frequency table?

Chi-square test Cramer's V Pearson's correlation coefficient Odds ratio None of the above

Explanation

Cramer's V is a measure of effect size that quantifies the strength of association between categorical variables, ranging from 0 (no association) to 1 (perfect association). The chi-square test only tests for significance, not strength. Pearson's correlation is for continuous variables, and odds ratios are typically used for 2×2 tables.

3. What is the null hypothesis for a chi-square test of independence in a two-way frequency table?

The two variables are independent The two variables are dependent The two variables are correlated The two variables are not correlated

Explanation

The null hypothesis for a chi-square test of independence states that the two variables are independent (not associated). This means knowing the value of one variable provides no information about the other.

4. What is the alternative hypothesis for a chi-square test for independence in a two-way frequency table?

The two variables are independent The two variables are dependent The two variables are uncorrelated None of the above

Explanation

The alternative hypothesis is the complement of the null hypothesis. If the null is independence, then the alternative is that the two variables are dependent (associated).

5. What are the assumptions for the validity of a chi-square test for independence in a two-way frequency table?

The observations are independent and randomly sampled The expected frequencies for each cell in the table are greater than 5 The variables are categorical All of the above

Explanation

All three assumptions are necessary: (1) observations must be independent and randomly sampled, (2) expected frequencies should be ≥5 in each cell (to ensure validity of the chi-square approximation), and (3) the variables must be categorical.

6. When interpreting the results of a chi-square test for independence in a two-way frequency table, what does a p-value of less than 0.05 indicate?

There is evidence of association between the two variables There is no evidence of association between the two variables The variables are correlated The variables are uncorrelated

Explanation

A p-value less than 0.05 (the conventional significance level) provides evidence to reject the null hypothesis of independence, suggesting there is an association between the two variables.

7. How do you interpret the p-value in a chi-squared test for independence in a two-way frequency table?

A small p-value indicates evidence against the null hypothesis A large p-value indicates evidence against the null hypothesis A small p-value indicates evidence in favor of the null hypothesis A large p-value indicates evidence in favor of the null hypothesis

Explanation

A small p-value indicates that the observed data would be unlikely if the null hypothesis were true, thus providing evidence against the null hypothesis. Conversely, a large p-value suggests the data are consistent with the null hypothesis.

8. When both variables are ordered in a two-way frequency table, the most focused test for association is:

The Pearson chi-squared test The Likelihood ratio chi-squared test The CMH test for general association The CMH test for non-zero correlation

Explanation

The Cochran-Mantel-Haenszel (CMH) test for non-zero correlation takes advantage of the ordering in both variables and is more powerful than general association tests when both variables are ordinal. It tests for a linear trend in the association.