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FemaleMaleTotal Assistant Profs.126213339 Associate Profs.149411560 Full Profs.60662722 Total3351,2861,621 What statements can you make based on the table above?

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FemaleMaleTotal Assistant Profs.126213339 Associate Profs.149411560 Full Profs.60662722 Total3351,2861,621 FemaleMaleTotal Assistant Profs.126/339 = 37%213/339 = 63%339 Associate Profs.149/560 = 27%411/560 = 73%560 Full Profs.60/722 = 8%662/722 = 92%722 Total335/1621 = 21%1286/1621 = 79%1621 Any other observations?

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In this two way table, two categorical variables (qualitative variables) are used: gender and rank. The order of the rank goes from lowest to highest. We could also calculate the breakdown of percentages of gender by rank (out of 335 for female; 1286 for male)

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A university offers only 2 degree programs: one in electrical engineering and one in English. Admission in these programs is competitive, and the womens caucus suspects discrimination against women in the admissions process. The caucus obtains the following data from the university: MaleFemale Admit3520 Deny4540 Total8060

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Since more male students were denied admission than female students, does that mean that female students had a higher admission rate? What is the percent of male applicants admitted? 44% What is the percent of female applicants admitted? 33%

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A three way table adds another variable. These are the same 80 male and 60 female students from the earlier example. EngineeringEnglish MaleFemaleMaleFemale Admit3010Admit510 Deny3010Deny1530 Total6020Total2040 What does this table show?

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When you look at the three way table, you should notice the following: Exactly half of the male applicants and exactly half of the female applicants were admitted to the engineering program. Exactly one fourth of the male applicants and exactly one fourth of the female applicants were admitted to the English program. Because there is now no difference between male and female applicants percentages, Simpsons Paradox has occurred…

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States that an association or comparison that holds for all of several groups can disappear or even reverse direction when the data are combined to form a single group. When it was a two way table, the male applicants seemed to be favored over the female applicants; when the data was presented as a three way table, it was determined that the two applicant groups were treated the same.

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See the worksheet being handed out…

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