Goal:

Using data consisting of observations on six variables for 52 tenure-track professors employed by a relatively low-enrollment college, our task was to analyze whether there is gender discrimination in University Professors' salaries.

i. For sl (academic year salary) by sx (sex, coded 0 for male and 1 for female)

ii. For sl (academic year salary) by dg (Highest degree, coded 0 for masters and 1 for doctoral degree)

With a Smooth Line Among Points - sl (academic year salary) by yd (Number of years since highest degree was earned)

With a Smooth Line Among Points - sl (academic year salary) by yr (Number of years in current rank)

Plotted with a linear model, and 95% confidence interval for the model - sl (academic year salary) by yd (Number of years since highest degree was earned).

sl (academic year salary) by yr (Number of years in current rank) grouped by rk (academic rank, coded 1 for assistant professor, 2 for associate professor, and 3 for full professor).

A simple linear regression with sl as the dependent variable and sx, yr, dg, yd, and a recoded rk variable as independent variables.

I read from the findings that:

Multiple R-squared: 0.7863, Adjusted R-squared: 0.763

F-statistic: 33.84 on 5 and 46 DF, p-value: 2.461e-14

If α = .05, then the p-value, 2.461e-14, is less than α. Therefore, I reject the null hypothesis that there is no relationship between the dependent variable and the entire set of independent variables.

I read from the findings that:

Again, if α = .05, then the p-value, 0.59 (rounded), is more than α. Therefore, I fail to reject the null hypothesis that there is no relationship between sl (academic year salary) and sx (sex). In other words, there does not seem to be a relationship between sl and sx in this small sample of University faculty.

Here is the 95% confidence interval for sx:

Since we failed to reject the null hypothesis that there is no relationship between sl and sx, the interpretation of this confidence interval is meaningless.

Our next task was to compute and report a new regression equation with sl as the dependent variable and sx as the sole independent variable. Then compute a t-test of the difference in mean sl by sx. From there, I will describe whether and how the results about the relationship between sl and sx from the regression analysis and from the t-test are similar.

I read from the findings that:

Multiple R-squared: 0.0639, Adjusted R-squared: 0.04518

F-statistic: 3.413 on 1 and 50 DF, p-value: 0.0706

If α = .05, then the p-value, 0.07 (rounded), is more than α. Therefore, I fail to reject the null hypothesis that there is no relationship between sl (academic year salary) and sx (sex). In other words, there does not seem to be a relationship between academic year salary and sex in this small sample of University faculty.

## 
##  Two Sample t-test
## 
## data:  sl by sx
## t = 1.8474, df = 50, p-value = 0.0706
## alternative hypothesis: true difference in means is not equal to 0
## 95 percent confidence interval:
##  -291.257 6970.550
## sample estimates:
## mean in group 0 mean in group 1 
##        24696.79        21357.14

The results of the regression equation with sl as the dependent variable and sx as the sole independent variable is the same as the t-test of the difference in mean sl by sx. Both reveal of p-value of 0.07 (rounded). Since my α = .05, then the p-value, 0.07 (rounded), is more than α. Therefore both test fail to reject the null hypothesis that there is no difference in academic year salary between the men and women. In other words, there does not seem to be a relationship between academic year salary and sex in this small sample of University faculty.