BIOST 512WINTER 2013Homework 8 key

Question 1. Part A Test statistic = 4.31 (df = 2)p = 0.01At the 5% significance level, I reject the null hypothesis. The data provide strong evidence that the association between sex and salary depends on the field and vice versa.

Part BRatio of geometric mean salaries of Males to Females inEstimate (95% CI)

Arts1 (0.94, 1.07)

Professional1.03 (0.96, 1.12)

Other1.10 (1.07, 1.14)

Part CTest statistic = 7.37 (df=1)p = 0.007At the 5% significance level, I reject the null hypothesis. The data provide strong evidence that the association between sex and salary depends on the number of years of experience and vice versa.

ExperienceRatio of geometric means comparing males to females, adjusting for rank and field

51.0 (0.97, 1.05)

101.03 (1.0, 1.06)

201.07 (1.04, 1.10)

301.11 (1.06, 1.16)

Part D

Note: The ratio of geometric means increases as we increase the experience. This is expected since the coefficient of the interaction term (sex*experience) is greater than zero.

Part E

A graph of the residuals versus the fitted values does not indicate any deviations from our assumptions of linearity and homoscedasticity.An analysis of the delta betas will provide us with information about any outliers.

LogsalaryFitted valueExperienceFieldRankSexID

8.158.4227OtherAssistantFemale1600

9.048.403OtherAssistantFemale334

There are no outliers with respect to rank, field or the interaction between sex and experience in this model. The largest absolute changes in the coefficient (delta betas) are less than 5% of the regression coefficient for all of the above variables. There are two outliers with regard to experience (1600) and sex (334) as noted in the table above.