Q: Given a 2x3 contingency table, what is the correct formula for the degrees of freedom for a chi-square test for independence?

$$ df = (k_{row} - 1) \times (k_{column} - 1) $$

Question 1

Which of the following scenarios would most appropriately require the use of a nonparametric test rather than a parametric test?

Accepted Answer

A study examining whether the frequency of eye color (blue, brown, green) differs from what would be expected by chance.

Question 2

What is the main limitation of nonparametric tests compared to parametric tests?

Accepted Answer

They have less statistical power, increasing the likelihood of a Type II error.

Question 3

Which formula correctly represents the calculation of the chi-square test statistic?

Accepted Answer

$$ \chi^2 = \sum \frac{(O-E)^2}{E} $$

Question 4

A researcher wants to test if the distribution of favorite ice cream flavors (chocolate, vanilla, strawberry) in a sample matches the general population. Which test should be used?

Accepted Answer

Chi-square test for goodness of fit

Question 5

Which of the following is NOT an assumption for the chi-square test for independence?

Accepted Answer

The sample must be normally distributed.

Question 6

Given a 2x3 contingency table, what is the correct formula for the degrees of freedom for a chi-square test for independence?

Accepted Answer

$$ df = (k_{row} - 1) 	imes (k_{column} - 1) $$

Question 7

A chi-square test for independence is performed on a 3x2 table with a sample size of 120. What are the degrees of freedom?

Accepted Answer

2

Question 8

Which of the following best describes Cramér's V (Phi) in the context of chi-square tests?

Accepted Answer

A measure of the effect size for chi-square tests for independence.

Question 9

If a chi-square test for independence yields a test statistic greater than the critical value at $\alpha = 0.05$, what is the correct conclusion?

Accepted Answer

Reject the null hypothesis; there is evidence of an association.

Question 10

Which of the following real-world scenarios would be best analyzed using a chi-square test for independence?

Accepted Answer

Testing whether the proportion of smokers differs by gender in a hospital sample.

Question 11

What is the main purpose of calculating adjusted standardized residuals in a chi-square test?

Accepted Answer

To determine which cells contribute most to the chi-square statistic.

Question 12

Relative risk in the context of chi-square tests is best described as:

Accepted Answer

The ratio of two conditional proportions to quantify the likelihood of an outcome between groups.

Question 13

A researcher finds $\chi^2 = 8.2$ with $df = 2$ and $\alpha = 0.05$. Using the critical value table, what is the correct decision?

Accepted Answer

Reject the null hypothesis.

Question 14

Which of the following is a correct interpretation of a significant chi-square test for goodness of fit?

Accepted Answer

The observed frequencies differ significantly from the expected frequencies under the null hypothesis.

Question 15

Which of the following is NOT a step in the six-step hypothesis testing procedure for chi-square tests?

Accepted Answer

Calculate the mean and standard deviation of the sample.

Question 16

If the expected frequency in a cell is less than 5, what is the most appropriate action?

Accepted Answer

Combine categories to increase expected frequencies.

Question 17

Which of the following best describes a Type II error in the context of chi-square tests?

Accepted Answer

Failing to reject the null hypothesis when it is false.

Question 18

Which formula is used to calculate Cramér's V for effect size in a chi-square test for independence?

Accepted Answer

$$ \phi = \sqrt{\frac{\chi^2}{N 	imes df_{row/column}}} $$

Question 19

A study finds that the relative risk of developing a condition is 3.0 for Group A compared to Group B. What does this mean?

Accepted Answer

Group A is three times as likely to develop the condition as Group B.

Chi-Square Tests and Nonparametric Statistics: A Study Guide

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