Q: Which formula is used to calculate the expected frequency in a contingency table for the Chi-square test of independence?

$$\text{Expected frequency} = \frac{\text{Row total} \times \text{Column total}}{\text{Grand total}}$$

Q: Given a contingency table with 2 rows and 3 columns, what are the degrees of freedom for the Chi-square test?

$$df = (2 - 1) \times (3 - 1) = 2$$

Question 1

Which of the following best describes a categorical (qualitative) variable?

Accepted Answer

A variable that is nominal or ordinal, such as gender, blood group, or employment category.

Question 2

In a study examining the association between gender (male/female) and crash involvement (yes/no), which statistical test is most appropriate?

Accepted Answer

Chi-square test of independence ($$\$$chi^2$$)

Question 3

Which formula is used to calculate the expected frequency in a contingency table for the Chi-square test of independence?

Accepted Answer

$$	ext{Expected frequency} = \frac{	ext{Row total} 	imes 	ext{Column total}}{	ext{Grand total}}$$

Question 4

The Chi-square statistic ($$\$$chi^2$$) is calculated by:

Accepted Answer

$$\$$chi^2$$ = \sum \frac{(O - E)^2$}{E}$$, where $$O is $$observed frequency and $$E is $$expected frequency.

Question 5

Which of the following is an assumption of the Chi-square test of independence?

Accepted Answer

Observations must be independent of each other.

Question 6

If more than 20% of the cells in a contingency table have expected frequencies less than 5, what should you do?

Accepted Answer

Use Fisher's Exact Test instead.

Question 7

Which effect size measure is commonly reported with the Chi-square test of independence?

Accepted Answer

Cramér's V

Question 8

Given a contingency table with 2 rows and 3 columns, what are the degrees of freedom for the Chi-square test?

Accepted Answer

$$df = (2 - 1) 	imes (3 - 1) = 2$$

Question 9

A researcher finds a significant association between age group and survival status in a COVID-19 study using the Chi-square test. What does this result imply?

Accepted Answer

There is a relationship between age group and survival status.

Question 10

Which of the following statements about the Chi-square distribution is correct?

Accepted Answer

It is positively skewed, especially for low degrees of freedom.

Question 11

In a contingency table, the observed frequency for a cell is 20, and the expected frequency is 15. What is the contribution of this cell to the Chi-square statistic?

Accepted Answer

$$\frac{(20 - 15)^2$}{15} = 1.67$$

Question 12

Which scenario would violate the independence assumption of the Chi-square test?

Accepted Answer

Using repeated measures from the same individuals.

Question 13

A Chi-square test yields $$p = 0.03$$ for the association between smoking status (smoker/non-smoker) and lung disease (yes/no). What is the correct interpretation at $$\alpha = 0.05$$?

Accepted Answer

There is a statistically significant association between smoking status and lung disease.

Question 14

Which guideline is used to interpret the strength of association using Cramér's V?

Accepted Answer

Small: $$V \u003c 0.1$$, Moderate: $$0.1 \leq V \u003c 0.3$$, Large: $$V \geq 0.3$$

Question 15

Which of the following is NOT a valid use of the Chi-square test of independence?

Accepted Answer

Testing the association between two continuous variables.

Question 16

A contingency table for a study on COVID-19 survival has 3 age groups and 2 survival outcomes. What is the degrees of freedom for the Chi-square test?

Accepted Answer

$$df = (3 - 1) 	imes (2 - 1) = 2$$

Question 17

Which of the following would be an appropriate real-world application of the Chi-square test?

Accepted Answer

Testing the association between blood type and susceptibility to a disease.

Question 18

If the calculated Chi-square statistic is greater than the critical value from the Chi-square distribution table, what is the correct conclusion?

Accepted Answer

Reject the null hypothesis; there is a significant association.

Question 19

Which of the following is a contingency table?

Accepted Answer

A table displaying the frequencies of combinations of two categorical variables.

Applied Statistics for the Health Sciences: Associations Between Categorical Variables and the Chi-Square Test

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