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

$$\$$chi^2$$ = \sum \frac{(\text{observed} - \text{expected})^2$}{\text{expected}}$$

Q: What is the value of Cramer’s V for a contingency table with $$\$$chi^2$$ = 8.33$$, $$n = 200$$, $$r = 2$$, $$c = 2$$?

$$\nu = \sqrt{\frac{8.33}{200 \times (2 - 1)}} = \sqrt{\frac{8.33}{200}} \approx 0.204$$

Question 1

Which of the following best describes a contingency table?

Accepted Answer

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

Question 2

In the context of contingency tables, what is a marginal distribution?

Accepted Answer

The distribution of totals for each categorical variable separately, appearing in the margins of the table.

Question 3

Given the following contingency table for Host and Purchase, what is the conditional purchase rate for Comcast?

$$	ext{Purchase Yes for Comcast} = \frac{27}{295}$$

Accepted Answer

9.15%

Question 4

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

Accepted Answer

Stacked bar chart

Question 5

What does a mosaic plot represent in the context of categorical data analysis?

Accepted Answer

The size of each tile is 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 data are separated into groups defined by a third variable.

Question 7

In the shipping example, why does Orange Arrow appear to be a better shipper before adjusting for weight?

Accepted Answer

Because a lurking variable (weight) is not accounted for, affecting the apparent relationship.

Question 8

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

Accepted Answer

$$\$$chi^2$$ = \sum \frac{(	ext{observed} - 	ext{expected})^2$}{	ext{expected}}$$

Question 9

Given the following observed and expected counts for a cell: observed = 30, expected = 40. What is the contribution to the Chi-Squared statistic from this cell?

Accepted Answer

$$\frac{(30 - 40)^2$}{40} = \frac{100}{40} = 2.5$$

Question 10

What is the value of Cramer’s V for a contingency table with $$\$$chi^2$$ = 8.33$$, $$n = 200$$, $$r = 2$$, $$c = 2$$?

Accepted Answer

$$
u = \sqrt{\frac{8.33}{200 	imes (2 - 1)}} = \sqrt{\frac{8.33}{200}} \approx 0.204$$

Question 11

Which of the following is NOT a requirement for using the Chi-Squared test for association?

Accepted Answer

Variables must be continuous.

Question 12

A company wants to analyze whether shirt size is associated with shirt style. Which statistical tool should they use?

Accepted Answer

Contingency table and Chi-Squared test

Question 13

If a stacked bar chart shows equal proportions for each group across categories, what does this indicate?

Accepted Answer

There is no association between the variables.

Question 14

Which of the following best describes a lurking variable?

Accepted Answer

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

Question 15

In the shipping example, after adjusting for weight, which service has a higher rate of damaged packages for heavy shipments?

Accepted Answer

Brown Box

Question 16

Which step is necessary before analyzing a contingency table in JMP?

Accepted Answer

Remove the 'Total' column and row.

Question 17

A mosaic plot shows that the tiles for 'Large' size and 'Button-Down' style are much bigger than other combinations. What does this indicate?

Accepted Answer

There is a strong association between 'Large' size and 'Button-Down' style.

Question 18

If the Chi-Squared test returns a p-value of 0.0039, what does this imply about the association between the variables?

Accepted Answer

There is strong evidence of association between the variables.

Question 19

Which of the following is a real-world example of Simpson’s Paradox?

Accepted Answer

A university’s overall admission rate appears higher for one gender, but when separated by department, the other gender has higher rates in each department.

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

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