$$\frac{45}{300} \times 100 = 15\%$$

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

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 the web shopping contingency table, what is the conditional distribution of purchases for Comcast?

Accepted Answer

Comcast: $$\frac{27}{295} = 9.15\%$$ purchased, $$\frac{268}{295} = 90.85\%$$ did not purchase.

Question 3

What is a marginal distribution in a contingency table?

Accepted Answer

The distribution of counts for one categorical variable, ignoring the other variable.

Question 4

Which visualization is best for showing conditional distributions in a contingency table?

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

Which scenario best illustrates Simpson’s Paradox?

Accepted Answer

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

Question 7

Given the shipping contingency table, what is the percentage of damaged packages for Orange Arrow?

Accepted Answer

$$\frac{45}{300} 	imes 100 = 15\%$$

Question 8

What is a lurking variable?

Accepted Answer

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

Question 9

After adjusting for weight in the shipping example, what happens to the apparent association between service and package status?

Accepted Answer

Orange Arrow no longer appears to be the better shipper.

Question 10

Which formula is used to calculate 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 11

What is the formula for the chi-squared statistic?

Accepted Answer

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

Question 12

If the chi-squared statistic is large and the p-value is small, what does this indicate about the association between two categorical variables?

Accepted Answer

There is likely a strong association between the variables.

Question 13

What is Cramer’s V used for?

Accepted Answer

To measure the strength of association between two categorical variables.

Question 14

Which value of Cramer’s V indicates perfect association?

Accepted Answer

$$1$$

Question 15

In the shirt size and style contingency table, which size is most common for the Button-Down style?

Accepted Answer

Large

Question 16

Which of the following is NOT a step in preparing data for JMP analysis of a contingency table?

Accepted Answer

Combine all counts into a single cell.

Question 17

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 between the variables.

Question 18

Which checklist item is essential before calculating the chi-squared statistic?

Accepted Answer

Verify that variables are categorical.

Question 19

A company wants to compare the purchase rates from three hosts. Which statistical method should they use?

Accepted Answer

Contingency table analysis with chi-squared test.

Ch 5. Association Between Categorical Variables: Contingency Tables, Lurking Variables, and Strength of Association

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