Q: Which of the following is the correct formula for the Chi-square test statistic used to test the association between two categorical variables?

$$\sum_{\text{cells}} \frac{(O - E)^2$}{E}$$

Question 1

Which of the following is the correct formula for the Chi-square test statistic used to test the association between two categorical variables?

Accepted Answer

$$\sum_{	ext{cells}} \frac{(O - E)^2$}{E}$$

Question 2

In the Titanic example, what was the null hypothesis ($$H_0) $$for the Chi-square test of association between passenger class and survival?

Accepted Answer

There is no association between survival and passenger class.

Question 3

Given the following observed and expected frequencies for a cell in a contingency table: $$O = 80$$, $$E = 133$$, what is the contribution of this cell to the Chi-square statistic?

Accepted Answer

$$\frac{(80 - 133)^2$}{133} = 20.98$$

Question 4

Which of the following is an important assumption for the validity of the Chi-square test?

Accepted Answer

No more than 20% of the cells should have expected frequencies less than 5.

Question 5

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

Accepted Answer

Combine categories to reduce the number of cells.

Question 6

What is Simpson’s Paradox?

Accepted Answer

A phenomenon where a trend appears in several groups but reverses when the groups are combined.

Question 7

In the context of the Titanic data, which group had the highest survival rate?

Accepted Answer

First class females

Question 8

A bank’s AI algorithm predicted 9,000 true frauds and 88,000 false frauds out of 97,000 predicted frauds. What is the positive predictive value (PPV) of the algorithm?

Accepted Answer

$$\frac{9000}{97000} = 0.0928 or$$ $$9.28\%$$

Question 9

In a medical test, 15 people with the illness test positive, and 5 with the illness test negative. What is the sensitivity of the test?

Accepted Answer

$$\frac{15}{20} = 0.75 or$$ $$75\%$$

Question 10

Which of the following best describes specificity in the context of a diagnostic test?

Accepted Answer

The percentage of people without the illness who are correctly identified as not having the illness.

Question 11

In the Berkeley admissions example, why did the overall data initially appear to show gender discrimination?

Accepted Answer

Females applied in higher numbers to departments with lower admission rates.

Question 12

Which of the following is the correct formula for accuracy in a prediction context?

Accepted Answer

$$\frac{TP + TN}{TP + TN + FP + FN}$$

Question 13

A medical test for a disease has 15 true positives, 95 false positives, 5 false negatives, and 885 true negatives. What is the specificity?

Accepted Answer

$$\frac{885}{980} = 0.903 or$$ $$90.3\%$$

Question 14

Which of the following statements about the Chi-square test is FALSE?

Accepted Answer

It can be used for continuous data without categorization.

Question 15

In the context of prediction accuracy, what does a high sensitivity but low positive predictive value indicate?

Accepted Answer

Many true positives are detected, but there are also many false positives.

Question 16

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

Accepted Answer

Reject the null hypothesis and conclude there is an association.

Question 17

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

Accepted Answer

A treatment appears effective in each subgroup but ineffective in the combined group.

Question 18

In the context of the Titanic data, what is the main insight from the Chi-square test results?

Accepted Answer

There is a strong association between passenger class and survival.

Question 19

Why is it important to check the expected frequencies before performing a Chi-square test?

Accepted Answer

To ensure the validity of the test results.

Question 20

A study finds that 76.2% of smokers and 68.6% of non-smokers are alive after 30 years. What is a possible explanation for this counter-intuitive result?

Accepted Answer

There may be confounding variables such as age or health status.

Chi-Square Tests, Simpson’s Paradox, and Assessing Prediction Accuracy

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