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notes515fall10chap13 - STAT 515 - Chapter 13: Categorical...

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STAT 515 -- Chapter 13: Categorical Data Recall we have studied binomial data, in which each trial falls into one of 2 categories (success/failure). Many studies allow for more than 2 categories. Example 1: Voters are asked which of 6 candidates they prefer. Example 2: Residents are surveyed about which part of Columbia they live in. (Downtown, NW, NE, SW, SE) Multinomial Experiment (Extension of a binomial experiment → from 2 to k possible outcomes) (1) Consists of n identical trials (2) There are k possible outcomes (categories) for each trial (3) The probabilities for the k outcomes, denoted p 1 , p 2 , …, p k , are the same for each trial (and p 1 + p 2 + … + p k = 1) (4) The trials are independent The cell counts, n 1 , n 2 , …, n k , which are the number of observations falling in each category, are the random variables which follow a multinomial distribution.
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Analyzing a One-Way Table Suppose we have a single categorical variable with k categories. The cell counts from a multinomial experiment can be arranged in a one-way table . Example 1: Adults were surveyed about their favorite sport. There were 6 categories. p
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notes515fall10chap13 - STAT 515 - Chapter 13: Categorical...

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