Chapter Thirteen

# Chapter Thirteen - Lecture Notes Chapter Thirteen...

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Lecture Notes Chapter Thirteen: Categorical Data Analysis Randall Miller 1 | Page 1. Categorical Data and the Multinomial Experiment Properties of the Multinomial Experiment 1. The experiment consists of n identical trials 2. There are k possible outcomes to each trial. These outcomes are sometimes called classes , categories , or cells . 3. The probabilities of the k outcomes, denoted by 12 ,..., k pp p , where ... 1 k p + ++ = , remain the same from trial to trial. 4. The trails are independent. 5. The random variables of interest are the cell counts , ,..., k nn n of the number of observations that fall into each of the k categories. 2. Testing Categorical Probabilities: One-Way Table A Test of a Hypothesis about Multinomial Probabilities: One-Way Table 0 1 1,0 2 2,0 ,0 : , ,..., kk Hp pp p p p = = Where 1,0 , ,..., k p represent the hypothesized values of the multinomial probabilities : a H At least one of the multinomial probabilities does not equal its hypothesized value Test statistic : [ ] 2 2 1 n ii i i nE E χ = = where E np = is the expected cell count

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Chapter Thirteen - Lecture Notes Chapter Thirteen...

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