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Lesson 12 - 2

Lesson 12 - 2. Contingency Tables and Association. Objectives. Compute the marginal distribution of a variable Use the conditional distribution to identify association among categorical data. Vocabulary. Contingency Table – relates to categories of data

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Lesson 12 - 2

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  1. Lesson 12 - 2 Contingency Tables and Association

  2. Objectives • Compute the marginal distribution of a variable • Use the conditional distribution to identify association among categorical data

  3. Vocabulary • Contingency Table – relates to categories of data • Marginal Distribution – a frequency or relative frequency of either the row or column variable in the contingency table • Conditional Distribution – lists the relative frequency of each category of a variable, given a specific value of the other variable in the contingency table.

  4. Requirements To describe the association between two categorical variables, relative frequencies (percentages) must be used, because there will likely be different numbers of observations for each of the categories

  5. Contingency Table Conditional distributions Totals by color of M&M Totals by type of M&M Marginal distributions

  6. Conditional Distribution graph Problem #11, page 650 Abortions in thousands completed in a year, by age and year Percentages in total cells represents the marginal distributions Percentages in other cells represent theconditional distributions (cell ⁄column total) Total numbers going down; conditional % under 19decreasing; conditional % over 25 increasing; conditional % between 20 – 24 pretty constant An alternative graph

  7. Summary and Homework • Summary • Contingency tables are categorical data that have a specific structure • A row variable • A column variable • There are counts associated with each combination of row variable value and column variable value • Various row and column totals and row and column frequencies can be used to summarize this data • Homework • pg 647 – 651: 1, 3, 4, 7, 11, 13

  8. Comments • Since the data is population data no inferential statistical comparisions are done. • Since many of the data is observational, beware of making any statements regarding causations.

  9. Even Homework Answers • 4: since each category could have different total numbers in them, the only safe way to compare is through percentages (or relative frequencies).

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