lecture_07 - Two-Way Contingency Tables Lecture 07 ILRST...

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    Two-Way Contingency Tables Lecture 07 ILRST 411
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           Chi-Square Requirements    Chi-square has the following requirements: The sample must be randomly drawn from the population. Data must be reported in raw frequencies (not percentages) Measured variables must be independent Values/categories on independent and dependent variables  must be mutually exclusive and exhaustive. Observed frequencies cannot be small.
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            Chi-square tests of independence Now that we understand the distribution under the null, we  can start looking at some statistics for testing statistical  independence between variables X and Y.       We’ll discuss two tests:  Pearson chi-squared statistic  The likelihood ratio statistic
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                  Pearson chi-squared statistic It was proposed in 1900 by Karl Pearson, the British  statistician known also for the Pearson product-moment  correlation, among his many contributions. The Pearson chi-squared statistic for testing a null  hypothesis, H 0  is a function of the observed counts and the  expected frequencies under the null hypothesis:    where: = observed frequency     = expected (theoretical) frequency - = ij ij ij n μ 2 2 ) ( X
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            Pearson chi-squared statistic Under the null hypothesis, this statistic has an asymptotic  chi-square distribution with degrees of freedom equal to the  difference in the number of parameters between the null and  alternative hypotheses.  (For contingency tables with all μ ij  ≥ 5, the chi-squared  distribution is a good approximation for the sampling  distribution.) For a fixed sample size, greater differences between {n ij and {μ ij } produce larger   X values and stronger evidence  against Ho.  Since larger  X 2   values are more contradictory   to Ho. The  X 2   statistic has approximately a chi-squared distribution for  large sample sizes. 
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             Pearson chi-squared statistic Pearson's chi-square is used to assess two types of  comparison: tests of goodness of fit and tests of  independence.  A test of goodness of fit establishes whether or not an  observed frequency distribution differs from a theoretical  distribution.  A test of independence assesses whether paired  observations on two variables, expressed in a contingency  table, are independent of each other  for example, whether people from different regions differ in  the frequency with which they report that they support a  political candidate.
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    Chi-square test-goodness of fit Problem1: In a consumer marketing , a common problem 
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lecture_07 - Two-Way Contingency Tables Lecture 07 ILRST...

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