Question

Table 10.7 lists the mean salary, in thousands of dollars, of faculty on nine-month contracts in U.S. institutions of higher education in 2013-2014, by gender and academic rank.

(a) Suppose that gender is the explanatory variable. Identify the response variable and the control variable.

(b) Describe the bivariate relationship between gender and salary.

(c) Describe the relationship between gender and salary, controlling for academic rank.

(d) A hypothesis of interest for these variable is "Controlling for academic rank, annual salary and gender are independent." Draw a causal diagram that is consistent with this hypothesis. Refer to your interpretation inpart (c), and commeng on whether the gypthesis seems plausible.

(e) Is it possible that the overall difference between mean income of men and women could be larger than the difference for each academic rank? (It nearly is.) Explain how or how not.

Academic Rank

Gender	Professor	Associate	Assistant	Instructor	Overall
Men	115.5	81.2	68.5	59.6	85.5
Women	98.1	75.4	63.6	56.9	70.4

Answer 1

a)

Let us denote the explanatory variable be X1, so X1 = gender

Let us denote the response variable be Y, and mean salary, in thousands of dollars, of faculty is the response variable

Let us denote the control variable as X2, and academic rank is the control variable.

(b) Describe the bivariate relationship between gender and salary.

Mean salary, in thousands of dollars of faculty on 9-month contract in the US is higher for men as compared to women. As concluded from the overall mean salary of men is 85.5 and the overall mean salary of women is 70.4.

(c) Describe the relationship between gender and salary, controlling for academic rank.

For each academic rank, the mean salary is higher for men as compared to women. as concluded from the table, with the academic rank of professor mean salary of men is 111.5 while that of women is 98.1, with the academic rank of professor mean salary of men is 111.5 while that of women is 98.1, with the academic rank of associate mean salary of men is 81.2 while that of women is 75.4, with the academic rank of assistant mean salary of men is 68.5 while that of women is 63.6, with the academic rank of instructor mean salary of men is 59.6 while that of women is 56.9.

(d) A hypothesis of interest for these variables is "Controlling for academic rank, annual salary and gender are independent." Draw a causal diagram that is consistent with this hypothesis. Refer to your interpretation in part (c), and comment on whether the hypothesis seems plausible.

It is the statistical interaction relationship because the difference in men and women salary differ on the level of academic rank.

Gender	Professor	Associate	Assistant	Instructor	Overall
Men	115.5	81.2	68.5	59.6	85.5
Women	98.1	75.4	63.6	56.9	70.4
Difference	17.4	5.8	4.9	2.7	15.1

The difference is high for when academic rank is professor and difference though it is present decreases for academic ranks.

Gender effects mean salary and also academic rank effects mean salary of the faculty too.