Chapter 10 - Part II

Chapter 10 - Part II - Advantages of 2 χ statistic over z...

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Unformatted text preview: Advantages of 2 χ statistic over z statistic : A statistic can only be used to compare a estimate to its hypotheses value i.e for hypotheses like : H : or H : This is only possible in tables as we saw above. For contingency tables with more than rows and/or columns, we need more than hypotheses to describe the association. Eg : Suppose we want to compare the effectiveness of Advil, Tylenol and Excedrin in reducing headaches. Our contingency table would then look like : Medicine Headache ? Y N Advil p 1 1- p 1 Tylenol p 2 1- p 2 Excedrin p 3 1- p 3 Here is the population proportion of patients taking Advil whose headache was reduced. Similarly for p 2 and p 3. Here the explanatory variable ( ) has categories corresponding to the three medicines used. So, the null hypotheses for independence will be H : We can rewrite this hypotheses as H 01 : and H 02 : Now, in order to test H 01 and H 02 we have to use z statistics (one for each). On the other hand, only 2 χ statistic (with 2 df) will be enough to test this . So, crudely speaking, statistics are easier to use when we have large contingency tables. Limitations of the Chi-square test : We have seen that a p – value corresponding to a...
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This note was uploaded on 04/18/2008 for the course EXP 3116 taught by Professor Fasig during the Spring '08 term at University of Florida.

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Chapter 10 - Part II - Advantages of 2 χ statistic over z...

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