AP Statistics RELATIONS IN CATEGORICAL DATA Categorical Data

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AP Statistics RELATIONS IN CATEGORICAL DATA

AP Statistics RELATIONS IN CATEGORICAL DATA

Categorical Data � Can be naturally formed (gender, ethnicity, eye-color, etc). � Can be

Categorical Data � Can be naturally formed (gender, ethnicity, eye-color, etc). � Can be formed by grouping quantitative variables into classes (Old: 50+, Middleage: 30 -49, Young: 15 -29) � Can be expressed as either counts or percents.

Categorical Data � Data is often organized into two-way contingency tables. Heart Attack No

Categorical Data � Data is often organized into two-way contingency tables. Heart Attack No Heart Attack Total Aspirin 104 10, 933 11, 037 Placebo 189 10, 845 11, 034 Total 293 21, 778 22, 071 Values in red represent the marginal distributions. � 22, 071 is the grand total. Both marginal distributions add up to the grand total. �

Marginal Distributions Relates to the total number of values that fall into any one

Marginal Distributions Relates to the total number of values that fall into any one category. May also be calculated as a percent. � Example: Calculate the marginal distribution of the medical occurrence (heart attack or not) in percent. � Medical Occurrence Heart Attack No Heart Attack Percent 1. 33% 98. 67% 293/22, 071 21, 778/22, 071

Conditional Distribution � Recall the original distribution: What percent of people who had heart

Conditional Distribution � Recall the original distribution: What percent of people who had heart attacks had taken aspirin? (This is a conditional distribution question. ) � 104/293 × 100 = 35. 5% �

Example � Myers-Briggs Personality Preference and Area of Study Arts and Sciences Business Allied

Example � Myers-Briggs Personality Preference and Area of Study Arts and Sciences Business Allied Health Total in 64 15 17 96 en 82 42 30 154 is 68 35 12 115 es 75 42 37 134 Total 289 134 96 519 “in” is “introvert/intuition (idealist)”. � “en” is “extrovert/intuition (idealist)”. � “is” is “introvert/sensing (realist)”. � “es” is “extrovert/sensing (realist)”. �

Example Continued � Find the marginal distribution of personality preferences. Personality Preference in en

Example Continued � Find the marginal distribution of personality preferences. Personality Preference in en is es Percent 18. 5% 29. 67% 22. 16% 25. 8% 96/519 154/519 115/519 134/519

Example Continued � What percent of Allied Health majors have “is” personalities? � 12/95

Example Continued � What percent of Allied Health majors have “is” personalities? � 12/95 = 12. 5%

Example Continued � What percent of each major have “is” personalities? Major Arts and

Example Continued � What percent of each major have “is” personalities? Major Arts and Sciences Business Allied Health Percent 23. 5% 26. 1% 12. 5% 68/289 35/134 12/96

Graphical Displays � Since the data is categorical, a bar graph can be used

Graphical Displays � Since the data is categorical, a bar graph can be used for quick and easy interpretation.

Homework � Textbook: review 4. 51, 4. 53 -4. 58, chapter 4

Homework � Textbook: review 4. 51, 4. 53 -4. 58, chapter 4