# 34 - The chi-square statistic is a measure of how far the...

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Any difference among the four distributions of living arrangements in the population of all young adults means that the null hypothesis is false and the alternative hypothesis is true. The alternative hypothesis is not one-sided or two-sided. We might call it “many-sided” because it allows any kind of difference. Our general null hypothesis H0 is that there is no relationship between the two categorical variables that label the rows and columns of a two-way table. To test H0, we compare the observed counts in the table with the expected counts, the counts we would expect—except for random variation—if H0 were true. If the observed counts are far from the expected counts, that is evidence against H0. It is easy to find the expected counts. The expected count in any cell of a two-way table when H0 is true is
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Unformatted text preview: The chi-square statistic is a measure of how far the observed counts in a two-way table are from the expected counts. The formula for the statistic is The chi-square statistic is a sum of terms, one for each cell in the table. Cell counts required for the Chi-squared test: You can safely use the chi-square test with critical values from the chi-square distribution when no more than 20% of the expected counts are less than 5 and all individual expected counts are 1 or greater. In particular, all four expected counts in a 2 2 table should be 5 or greater. The expected counts are the counts we expect if all the proportions are equal. A large chi-square test statistic supports the alternative hypothesis. Check conditions: 1. SRS or random allocation 2. All expected counts>=5...
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## This note was uploaded on 02/27/2012 for the course STAT 121 taught by Professor Patticolling during the Winter '11 term at BYU.

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