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chap18_2010

# chap18_2010 - Chapter 18 Chi-Square Tests 2 Distribution...

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Chapter 18 Chi-Square Tests

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2 Distribution Let x1, x2, .. xn be a random sample from a normal distribution with  and 2, and let s2 be the sample variance, then the random variable (n-1)s2/2 has 2 distribution with n-1 degrees of freedom. Probability Density Function, with k degrees of freedom, Mean Variance Mode = k-2 (when k 3) 0 ) 2 ( 2 1 ) ( 2 / 1 ) 2 / ( 2 Γ = - - x e x k x f x k k k x E = ) ( k x V 2 ) ( =

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2 Distribution Goodness-of-fit Tests Tests of Independence Tests of Homogeneity
Multinominal Experiments A Multinomial experiment is a statistical experiment that has the following properties: It consists of n repeated trials (repetitions). Each trial can result in one of k possible outcomes. The trials are independent. The probabilities of the various events remain constant for each trial.

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Goodness-of-fit Test Observed Frequencies (Oi): Frequencies obtained from the actual performance of an experiment. Goodness-of-fit Test: Test of null hypothesis that the observed frequencies follow certain pattern or theoretical distributions, expressed by the Expected Frequencies (Ei).
Goodness-of-fit Test for Multinominal Experiments Degree of freedom = k -1, where k is the number of categories Chi-square goodness-of-fit test is always a right-tailed test Sample size should be large enough so that the expected frequency for each category is at least 5.

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