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

$$\frac{100 \times 80}{200} = 40$$

Question 1

Which of the following best describes a contingency table?

Accepted Answer

A table that shows the counts of cases for every combination of two categorical variables.

Question 2

In the context of web shopping, which host had the highest purchase rate according to the conditional distribution?

Accepted Answer

Comcast

Question 3

What is a marginal distribution in a contingency table?

Accepted Answer

The totals (frequencies) for each categorical variable separately, appearing in the margins of the table.

Question 4

Which visualization is best for showing conditional distributions of categorical variables?

Accepted Answer

Stacked bar chart

Question 5

A mosaic plot is used to:

Accepted Answer

Show the size of each tile proportional to the count in a cell of a contingency table.

Question 6

What is a lurking variable?

Accepted Answer

A concealed variable that affects the apparent relationship between two other variables.

Question 7

Simpson’s Paradox occurs when:

Accepted Answer

The association between two variables changes when data are separated into groups defined by a third variable.

Question 8

Which equation represents the calculation of the expected count in a cell of a contingency table?

Accepted Answer

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

Question 9

Given the following contingency table for Attitude toward Sharing, what is the expected count for Staff who think sharing is OK?

Accepted Answer

$$\frac{100 	imes 80}{200} = 40$$

Question 10

Which formula is used to calculate the Chi-Squared statistic for a contingency table?

Accepted Answer

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

Question 11

If the Chi-Squared statistic is large and the p-value is small, what does this indicate about the association between the variables?

Accepted Answer

There is a strong association between the variables.

Question 12

Cramer’s V is used to:

Accepted Answer

Measure the strength of association between two categorical variables.

Question 13

Which value of Cramer’s V indicates perfect association between two categorical variables?

Accepted Answer

1

Question 14

In the shipping example, after adjusting for weight, which service appears to be better for shipping heavy packages?

Accepted Answer

Brown Box

Question 15

Which of the following is NOT a step in preparing data for Chi-Squared analysis in JMP?

Accepted Answer

Summarize the data using a histogram.

Question 16

If a stacked bar chart shows similar proportions for each group, what does this suggest about the association between the variables?

Accepted Answer

There is no association.

Question 17

Which scenario best illustrates Simpson’s Paradox?

Accepted Answer

A relationship between two variables reverses when a third variable is considered.

Question 18

Which checklist item is essential before calculating Chi-Squared and Cramer’s V?

Accepted Answer

Verify that variables are categorical.

Question 19

Given the following counts for shirt size and style, which style is most popular among those who wear large shirts?

Accepted Answer

Button-Down

Association Between Categorical Variables: Contingency Tables, Lurking Variables, and Strength of Association

Study Guide - Practice Questions