Transcription of Chapter 7 Pearson’s chi-square test
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Chapter 7 Pearson’s chi-square test
Chapter 7 pearson s chi-square Null hypothesis asymptoticsLetX1,X2, be independent from a multinomial(1,p) distribution, wherepis ak-vectorwith nonnegative entries that sum to one. That is,P(Xij= 1) = 1 P(Xij= 0) =pjfor all 1 j k( )and eachXiconsists of exactlyk 1 zeros and a single one, where the one is in the componentof the success category at triali. Note that the multinomial distribution is a generalizationof the binomial distribution to the case in which there arekcategories of outcome insteadof only purpose of this section is to derive the asymptotic distribution of the pearson chi-squarestatistic 2=k j=1(nj npj)2npj,( )wherenjis the random variablenXj, the number of successes in thejth category for trials1.
Pearson’s chi-square test 7.1 Null hypothesis asymptotics Let X 1,X 2,··· be independent from a multinomial(1,p) distribution, where p is a k-vector with nonnegative entries that sum to one. That is, P(X ij = 1) = 1−P(X ij = 0) = p j for all 1 ≤ j ≤ k (7.1) and each X i consists of exactly k−1 zeros and a single one, where the one ...
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