lecture14note - Psych 100A Winter 2010 Categorical data...

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1 Psych 100A Winter 2010 Lecture 14: Statistical Inference Categorical data Multinomial experiment Chi-square test Contingency table Categorical data Previous inference methods applicable to quantitative data. Inference on qualitative data. Number of observations at each level of a qualitative variable = count or enumeration data. Population: individuals can be placed into various categories according to some characteristic. Sample: count of number of individuals who fall into each category. Data is characteristic of multinomial experiment. 1. Multinomial experiment. A natural extension of a binomial experiment Multinomial experiments are defined by the following conditions: 1. Experiment consists of n iid trials 2 Polychotomous outcome on each trial: each 2. Polychotomous outcome on each trial: each trial results in one of k outcomes 3. Pr(outcome i) = i , i = 1,…,k; constant from trial to trial;  I = 1. 4. Variables of interest are n i = the number of trials with outcome i observed during the n trials. Formula: Pr(outcomes) in a multinomial experiment Probability for the number of observations resulting in each of the k outcomes is given by  k n n n k k n n n n n n n 3 2 1 2 1 2 1 2 1 ! ! ! ! , , , Pr where n = number of trials i = probability of i th outcome n i = number of i th outcomes x! = x(x-1)(x-2)…(2)(1) Multinomial experiment (cont.) One use is to test specified probabilities ( iO ) for each outcome in a categorical study. In an study with k outcomes, the expected number of outcomes of type I in n trials equals: E i = n iO In 1900, Pearson devised a test statistic to test specified categorical probabilities called the 2 (chi-square) goodness-of-fit statistic: where n i ’s = observed cell counts and E i ’s = expected cell counts.
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This note was uploaded on 03/15/2010 for the course PSYCHOLOGY 100B taught by Professor Firstenberg,i. during the Winter '10 term at UCLA.

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lecture14note - Psych 100A Winter 2010 Categorical data...

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