Wiki Page, Math 13 - Perez Sandbox : Unit 4 - Relationships in Categorical Data with Intro to Probability Review

Wiki Page
2026-01-17T21:16:12-08:00

This concludes the lessons for Unit 4 (Module 10).

Let’s Summarize

To summarize the relationship between two categorical variables, use:

A data display: A two-way table

Numerical summaries: Conditional percentages

When we investigate the relationship between two categorical variables, we use the values of the explanatory variable to define the comparison groups. We then compare the distributions of the response variable for values of the explanatory variable. In particular, we look at how the pattern of conditional percentages differs between the different values of the explanatory variable.

For example, we investigated the relationship between body image and gender. We compared males to females. For each gender (the explanatory variable), we determined the percentage who felt their body weight was about right, overweight, or underweight. P(body image “about right” | male) is compared to P(body image “about right” | female).

Keys Ideas from Our Work with Probability

We defined three kinds of probabilities related to a two-way table:

A conditional probability is the probability of a categorical variable taking on a particular value given the condition that the other categorical variable has some particular value. For example, P(Health Sciences given female) means we look first at all females, then identify the female students who are Health Science students. In calculating the probability, we use only a subset of the data. The condition determines the subset of data we use. If our condition relates to female students, then we consider only the information in the table pertaining to females.

When we calculate the probability of a negative outcome, we often refer to the probability as a risk. We compare risk by calculating the percentage change (divide difference in risks by risk in placebo group).

You are now ready to put it all together and practice what you learned in this unit by working through a StatCrunch lab.

Mark this page as done, then click the "Next" or > button to continue.

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