10. Introduction to multivariate relationships

# 10. Introduction to multivariate relationships - 10...

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10. Introduction to Multivariate Relationships Bivariate analyses are informative, but we usually need to take into account many variables. Many explanatory variables have an influence on any particular response variable. The effect of an explanatory variable on a response variable may change when we take into account other variables. Example (Ch.11, pp. 322-323): Florida county-wide data on x = education (% with at least a high school degree) and y = crime rate

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Example : Y = whether admitted into grad school at U. California, Berkeley (for the 6 largest departments) X = gender Whether admitted Gender Yes No Total %yes Female 550 1285 1835 30% Male 1184 1507 2691 44% Difference of sample proportions = 0.44 – 0.30 = 0.14 has se = 0.014, Pearson • 2 = 90.8 (df = 1) , P- value = 0.00000…. There is very strong evidence of a higher probability of admission for men than for women.
• Now let X 1 = gender and X 2 = department to which the person applied. e.g., for Department A, Whether admitted Gender Yes No Total %yes Female 89 19 108 82% Male 511 314 825 62% Now, • 2 = 17.4 (df = 1), but difference is 0.62 – 0.82 = -0.20. T he strong evidence is that there is a higher probability of being admitted for women than men . What happens with other departments?

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Female Male Difference of Dept. Total %admitted Total %admitted proportions 2 A 108 82% 825 62% -0.20 17.4 B 25 68% 560 63% -0.05 0.25 C 593 34% 325 37% 0.03 0.75 D 375 35% 417 33% -0.02 0.3 E 393 24% 191 28% 0.04 1.0 F 341 7% 273 6% -0.01 0.4 Total 1835 30% 2691 44% 0.14 90.8 There are 6 “partial tables,” which summed give the original “bivariate” table. How can the partial table results be so different from the bivariate table?
Partial tables – display association between two

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## This note was uploaded on 07/12/2011 for the course STA 3030 taught by Professor Agresti during the Spring '11 term at University of Florida.

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10. Introduction to multivariate relationships - 10...

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