Wiki Page, Math 13 - Perez Sandbox : Module 10 - Wrap Up “Relationships in Categorical Data with Intro to Probability Review”

Wiki Page
2026-01-17T21:15:09-08:00

Let’s Summarize

A Relationship Between Two Categorical Variables

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 values of the explanatory variable. For example, we investigated the relationship between body image and gender. We compared males to females. For each gender, we determined the percentage who felt their body weight was about right, overweight, or underweight.

Keys Ideas from Our Work with Probability

We used a two-way table to estimate a conditional probability:

A conditional probability is calculated the same way that we calculate a conditional percentage. The difference lies in the interpretation. For example, to calculate the probability that a Health Science major smokes, we look first at all Health Science majors, then identify the smokers in that group.

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).

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