Where does it pay to attend college?
Preregistration of analyses
Analysis #1
Our first analysis intends to identify if there is a difference in the starting salary and mid-career salary for different regions. This could be analyzed using a hypothesis test where we try to identify if the salaries differ in the different regions across the USA. Since there are more than 2 regions, (there’s 5; California, Northeastern, Midwestern, Southern and Western), a simple hypothesis test would not work unless all possible combinations where compared to one another. A better test to understand if there is a difference in the salaries across regions would be to use test of Analysis of Variance, also called an ANOVA test. ANOVA tests whether there is a difference on the means of some quantitative variable, in this case starting salary or mid-career salary, at different levels, or in this case Regions.
The null and alternative Hypothesis will be:
\[ H_0: \text{There is no difference in mean starting or mid-career salary across different regions.} \] \[ H_A: \text{There is a difference in mean starting or mid-career salary across different regions.} \]
If there is enough statistical evidence to reject H_o at ⍺ = 0.05, then we need to find what regions have a difference in mean salaries. We shall do this by comparing Regions to each other.
Information on Anova Using INFER:
Analysis #2
For our second analysis, we will analyze whether there is a statistical significance at \(\alpha = 0.05\) in the starting and mid-career salaries for different types of schools. To accomplish this, we can run two p-test between the starting/mid-career salaries for Ivy League colleges and state colleges.
\[ H_0: \mu_{ivy} - \mu_{state} = 0\\ H_A: \mu_{ivy} - \mu_{state} \neq 0 \]
To compare multiple different types of colleges, we can run an ANOVA test at \[\alpha = 0.05\] between the different school types, similar to as described in Analysis #1 above. In that case, the null and alternative hypotheses will be:
\[ H_0: \text{There is no difference in mean starting/mid-career salary across different school types.} \\ H_A: \text{There is a difference in mean starting/mid-career salary across different school types.} \]