1. AP STATISTICS LESSON 4 – 3 ( DAY 1 )
RELATIONS IN CATAGORICAL DATA

2. ESSENTIAL QUESTION: What relationships do categorical variables have?
To analyze two way tables.
To create marginal distributions.
To explain the phenomena known as Simpson’s Paradox.

3. Analyzing Categorical Data
To analyze categorical data we use counts or percents of individuals that fall into various categories.
Two way tables contain two variables, one represented in the rows and one in the columns.

4. Definitions
Marginal distributions – The totals of each row and column that appear in the margins are referred to the marginal distributions.
Roundoff error – The difference between actual and the marginal distributions do to rounding of the sums.
Conditional distribution – The counts or percents of a given categorical variable.

5. Simpson’s Paradox
Simpson’s paradox refers to the reversal of the direction of a comparison or an association when data from several groups are combined to form a single group.

6. Describing Relationships
To describe relationships among categorical variables, calculate appropriate percents from the counts given. We use percents because counts are often hard to compare.
A bar graph compares the sizes of different items. The horizontal axis of a bar graph need not have any measurement scale but simply identify the items being compared.