Question 1

Which of the following best describes a contingency table?

Accepted Answer

A table that displays the frequencies of two categorical variables simultaneously.

Question 2

In a study examining the relationship between smoking status (smoker/non-smoker) and survival status (alive/dead), which is the response variable?

Accepted Answer

Survival status

Question 3

Given the following data from a food study: 29 out of 127 organic foods and 19,485 out of 26,571 conventional foods contain pesticide residues. What is the conditional proportion of conventional foods with pesticide residues?

Accepted Answer

$$ \frac{19,485}{26,571} = 0.73 $$

Question 4

If there is no association between two categorical variables, what would you expect about the conditional proportions for the response variable across the groups defined by the explanatory variable?

Accepted Answer

The conditional proportions would be the same for each group.

Question 5

Which of the following is the correct formula for the difference of proportions when comparing two groups?

Accepted Answer

$$ p_1$ - p_2$ $$

Question 6

In a medical study, 40% of patients receiving a new drug recover, while 25% of patients receiving a placebo recover. What is the risk ratio (relative risk) of recovery for the drug group compared to the placebo group?

Accepted Answer

$$ \frac{0.40}{0.25} = 1.6 $$

Question 7

A study finds that the odds of lung cancer among smokers is 10:1, and among non-smokers is 2:1. What is the odds ratio of lung cancer for smokers compared to non-smokers?

Accepted Answer

$$ \frac{10}{2} = 5 $$

Question 8

Which of the following best describes a response variable in the context of a statistical study?

Accepted Answer

It is the outcome variable on which comparisons are made for different values of the explanatory variable.

Question 9

Suppose you are comparing the proportion of students who pass an exam between two teaching methods. If 60 out of 100 students pass with Method A and 45 out of 100 pass with Method B, what is the difference in proportions?

Accepted Answer

$$ \frac{60}{100} - \frac{45}{100} = 0.15 $$

Question 10

Which of the following statements about the odds ratio is correct?

Accepted Answer

The odds ratio compares the odds of an event occurring in one group to the odds in another group.

Question 11

In a contingency table, what does a marginal proportion represent?

Accepted Answer

The proportion of all sampled items that fall into a particular category, regardless of the other variable.

Question 12

A researcher wants to compare the effect of two diets (Diet A and Diet B) on weight loss. Which is the explanatory variable?

Accepted Answer

Type of diet (Diet A or Diet B)

Question 13

If the risk ratio (relative risk) between two groups is 1, what does this indicate about the association between the explanatory and response variables?

Accepted Answer

There is no association between the variables.

Question 14

Which of the following is a correct interpretation of a risk ratio of 3.2 in a food safety study?

Accepted Answer

The risk of pesticide residue is 3.2 times higher in one group compared to the other.

Question 15

A side-by-side bar chart is most useful for:

Accepted Answer

Comparing conditional proportions across groups.

Question 16

In a study, 80 out of 200 patients treated with Drug X recover, while 40 out of 200 patients given a placebo recover. What is the odds ratio of recovery for Drug X compared to placebo?

Accepted Answer

$$ \frac{\frac{80}{120}}{\frac{40}{160}} = \frac{0.6667}{0.25} = 2.67 $$

Question 17

Which of the following is NOT a correct way to measure the strength of association between two categorical variables?

Accepted Answer

Calculating the correlation coefficient.

Question 18

A researcher finds that the conditional proportion of disease in the exposed group is 0.20 and in the unexposed group is 0.05. What is the risk ratio?

Accepted Answer

$$ \frac{0.20}{0.05} = 4 $$

Question 19

Which of the following best describes a conditional proportion?

Accepted Answer

A proportion calculated within a specific group defined by the explanatory variable.

(Lecture 6) Association Between Two Categorical Variables: Contingency Tables, Conditional Proportions, and Measures of Association

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