Q: Which of the following is the correct formula for the expected count in a cell of a contingency table?

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

Question 1

Which of the following best describes a contingency table?

Accepted Answer

A table that shows counts of cases on one categorical variable contingent on the value of another categorical variable.

Question 2

In the context of the web shopping data, what does the conditional distribution of 'Purchase' for each 'Host' reveal?

Accepted Answer

That Comcast has the highest rate of purchases, more than twice that of Nextag.

Question 3

Which of the following is a lurking variable?

Accepted Answer

A variable that is not included in the analysis but affects the relationship between the variables studied.

Question 4

Simpson’s Paradox occurs when:

Accepted Answer

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

Question 5

Given the following contingency table for shirt size and style, what is the marginal total for 'Medium' size?

Accepted Answer

$$175$$

Question 6

Which graphical display is best for visualizing the association between two categorical variables when the size of each group is important?

Accepted Answer

Mosaic plot

Question 7

If the conditional distribution of 'Purchase' by 'Region' is nearly identical across all regions, what does this suggest?

Accepted Answer

There is no association between Purchase and Region.

Question 8

Which of the following is the correct formula for 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

The chi-squared statistic is calculated by:

Accepted Answer

$$\sum \frac{(O - E)^2$}{E}$$, where $$O is $$the observed count and $$E is $$the expected count for each cell.

Question 10

Cramer’s V is used to:

Accepted Answer

Measure the strength of association between two categorical variables.

Question 11

Which of the following values of Cramer’s V indicates the strongest association?

Accepted Answer

$$0.95$$

Question 12

A company compares two shipping services and finds that Orange Arrow appears to have fewer damaged packages overall. However, when separating the data by package weight, Brown Box is better for both heavy and light packages. What statistical phenomenon is this?

Accepted Answer

Simpson’s Paradox

Question 13

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

Accepted Answer

Assign numerical codes to all categorical variables.

Question 14

Given the following observed and expected counts for a cell: $$O = 30$$, $$E = 40$$, what is the contribution of this cell to the chi-squared statistic?

Accepted Answer

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

Question 15

Which of the following is a key checklist item before using the chi-squared test?

Accepted Answer

Verify that variables are categorical.

Question 16

If a stacked bar chart shows that the proportion of 'Yes' purchases is much higher for Comcast than for Nextag, what does this indicate?

Accepted Answer

There is an association between Host and Purchase.

Question 17

Which of the following best describes a marginal distribution?

Accepted Answer

The distribution of totals for each categorical variable separately, found in the margins of a contingency table.

Question 18

A mosaic plot shows that the size of the 'Large' tile for 'Button Down' style is much bigger than for 'Small Print' style. What does this suggest?

Accepted Answer

There is an association between shirt size and style.

Question 19

Which of the following formulas is used to calculate Cramer’s V?

Accepted Answer

$$V = \sqrt{\frac{\$$chi^2$$}{n(k-1)}}$$

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

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