Chi_square_tests (1)

# Chi_square_tests (1) - Chi-square tests Chi-square testing...

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Chi-square tests

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Chi-square testing Goodness of fit testing Test for Independence
Chi-square goodness of fit tests Consider an experiment where each of n randomly selected items is placed into k different groups. Let f i = number of items classified into group i ( i th observed frequency) E i = np i = expected number in i th group if p i is probability of being in group i ( i th expected frequency)

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Chi-square goodness of fit tests H 0 : Probabilities of classification into the cells are p 1 , p 2 , … , p k H a : at least one of the probabilities differs from p 1 , p 2 , … , p k Test Statistic is: Reject H 0 if χ 2 > χ a 2 or if p-value < a * Note: χ 2 and the p-value are based on (k-1) degrees of freedom and the test is always one-sided (i.e. always look at area to the right for p-value calculation) 2 2 1 ( ) k i i i i f E = E = - χ
Chi-square distribution

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Example Are the market shares of 4 different brands of microwave ovens the same in Cleveland and Milwaukee?
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## This note was uploaded on 04/03/2012 for the course BUAD 310 taught by Professor Lv during the Spring '07 term at USC.

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Chi_square_tests (1) - Chi-square tests Chi-square testing...

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