When comparing several population proportions the chi

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When comparing several population proportions, the chi-square degrees of freedom are equal to the number of explanatory variable categories minus 1, c ± 1. This makes sense because once we specify the number of observations in c ± 1 of the categories, the last category is forced to assume the value that allows the observed counts to sum to the sample size. For large sample sizes, we will use the chi-square distribution to approximate the p-value. Technology Detour Chi-square Probabilities In R: The iscamchisqprob function takes the following inputs x xval = the observed value of the test statistic x df = degrees of freedom for the chi-square distribution In Minitab: Choose Graph > Probability Distribution Plot (View Probability) . Then select the Chi-Square distribution with Degrees of freedom = 6. Select the Shaded Area tab, and specify the X value , with Right Tail , to be 62.68. Press OK . (r) How does this p-value compare to the empirical p-value you determined in (n)?
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Chance/Rossman, 2015 ISCAM III Investigation 5.1 325 Discussion: If the null hypothesis is rejected, the conclusion we draw is that at least one of the population proportions differs from the rest, but we don’t have much information about which one. It could be that one explanatory variable group is behaving much differently than the rest or they could all be different. One way to gain more information about the nature of the differences between the S i values is to compare the components of the chi-square statistic sum. (s) Return to the sum you calculated in (i). Which cell comparison(s) provide the largest (standardized) discrepancy between the observed counts and the expected counts? (t) For the cells identified in (s), which is larger, the observed counts or the expected counts? Explain the implications of this comparison. (u ) Which judge do you believe tried Dr. Spock’s case? Explain. Study Conclusions One judge clearly stood out compared to the others in these sample data. If we consider these results to be representative of the overall jury selection process, the very small p-value indicates that if in fact the judges’ selections of jurors were independent random processes with the same probability of selecting a woman, then it would be almost impossible to observe sample proportions differing by this much by chance alone. Thus, the sample data provide strong evidence that the long-run probability of a juror being female is not the same among all seven judges. The largest contributions to the X 2 test statistic, by far, come from judge 7, who has many more men than would be expected and many fewer women than would be expected on his jury lists. This was indeed Judge Ford, the judge assigned to Dr. Spock’s case. In fact, there are two issues with this judge: The sampling from the city directory led to a far smaller percentage of women (29%) than the city population (53%) across all the judges, and then the proportion of women selected by Judge Ford dipped even lower to around 15% women. (By the way, the Court
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