invest_3ed.pdf

When comparing several population proportions the chi

• 429
• 60% (5) 3 out of 5 people found this document helpful

This preview shows pages 325–327. Sign up to view the full content.

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)?

This preview has intentionally blurred sections. Sign up to view the full version.

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
This is the end of the preview. Sign up to access the rest of the document.
• Spring '14
• -STAFF

{[ snackBarMessage ]}

What students are saying

• As a current student on this bumpy collegiate pathway, I stumbled upon Course Hero, where I can find study resources for nearly all my courses, get online help from tutors 24/7, and even share my old projects, papers, and lecture notes with other students.

Kiran Temple University Fox School of Business ‘17, Course Hero Intern

• I cannot even describe how much Course Hero helped me this summer. It’s truly become something I can always rely on and help me. In the end, I was not only able to survive summer classes, but I was able to thrive thanks to Course Hero.

Dana University of Pennsylvania ‘17, Course Hero Intern

• The ability to access any university’s resources through Course Hero proved invaluable in my case. I was behind on Tulane coursework and actually used UCLA’s materials to help me move forward and get everything together on time.

Jill Tulane University ‘16, Course Hero Intern