Final Project
DATA Statistics and Probability for Data Analytics
CUNY MSDS DATA 606
Date: 2018/05/08
Author: Rose Koh
Introduction
Research Question
"Does obtaining master’s degree and beyond leads to higher prevailing wage determination?"
\[H_0: \beta_1 = 0\]
The difference of estimated wage between Master’s degree holder and non-holder is zero.
\[H_a: \beta_1 \neq 0\]
The difference of estimated wage between Master’s degree holder and non-holder is not zero – there is difference.
For any foreign employees who would pursue the employer sponsored green card, may wonder whether higher academic achievements is an open ticket that could lead them to an advantage when it comes to prevailing wage determination.
Employer Sponsored Green Card – PERM, is the process for obtaining labor certification, the first step of the green card process for foreign nationals seeking permanent residence through their employment. The U.S. employer requests a permanent labor certification by completing an Application for Permanent Employment Certification (“ETA Form 9089”).
Data
Data collection
Data is provided by US department of labor.
The Office of Foreign Labor Certification (OFLC) generates program data of processing of labor certification and labor attestation applications that is essential both for internal assessment of program effectiveness and for providing the Department’s external stakeholders with useful information about the immigration programs administered by OFLC.
Cases
Each case represents a case of PERM application in the US in 2017. There are 97603 observations in the dataset. For the research question we selected, the total number of relative observations are 50023
Variables
Explanatory variable:
edumaster’s degree (categorical)Response variable:
payprevailing wage determination (numerical)
Type of study
This is an observational study – There was no process or experimental design in the process of gathering the information.
Scope of inference - generalizability, causality
This is an observational study. This is not an experiment as the information was collected aggregating the application papers. Since this is an observational data, specifically limited to PERM applicants, I would not generalize the conclusion because correlation doesn’t mean causation.
Exploratory data analysis
Summary description of wage determination according to education backgrounds.
## # A tibble: 2 x 7
## edu n mean sd median min max
## <chr> <int> <dbl> <dbl> <dbl> <dbl> <dbl>
## 1 n 26009 92526. 30890. 90646. 14560. 233355.
## 2 y 24014 97114. 26487. 95846. 17080. 233355.##
## Call:
## lm(formula = pay ~ edu, data = df)
##
## Residuals:
## Min 1Q Median 3Q Max
## -80034 -19019 -1788 16662 140829
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 92526.4 179.0 517.04 <2e-16 ***
## eduy 4587.3 258.3 17.76 <2e-16 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 28860 on 50021 degrees of freedom
## Multiple R-squared: 0.006267, Adjusted R-squared: 0.006247
## F-statistic: 315.5 on 1 and 50021 DF, p-value: < 2.2e-16
##
## Two Sample t-test
##
## data: pay by edu
## t = -17.761, df = 50021, p-value < 2.2e-16
## alternative hypothesis: true difference in means is not equal to 0
## 95 percent confidence interval:
## -5093.557 -4081.094
## sample estimates:
## mean in group n mean in group y
## 92526.37 97113.69
The exploratory analysis suggests:
- Linearity: There seem to be linearity in the scatter plot.
- Near normal residuals: The residuals appear to be nearly normal.
- Constant variability: Residual plots shows constant variability.
- Independent observations: There is no obvious pattern that suggests these observations were dependent on each other.
The variability among the employees are about equal and the distribution is symmetric. With these conditions satisfied, it is reasonable to apply the linear regression model.
Conclusion
The goal of this research project was to study whether obtaining the master’s degree affects on the level of determination of prevailing wage when it comes to PERM applications.
The Hypothesis was to test whether Obtaining Master's degree leads to an advantage of earning higher wage.
T-test was implemented to compare the two groups (edu$y = master’s degree and higher, edu$n = bachelor’s degree and lower.)
The variable edu is coded 1 if the employee is master’s degree holder and 0 if not.
The summary table shows the results of a linear regression predicting the average wage of employees, based on academic backgrounds of the employees.
It appears from the Two sample t-test summary, the p-value was extremely small at near 0, which is a strong evidence that indeed having Master’s degree does lead to an advantage of earning higer wage for PERM applicants.
The equation of the regression line is as follows:
\[\widehat{wage\_masters\_true} = 92526.4 + 4587.3 * 1 = 97113.7\]
\[\widehat{wage\_masters\_false} = 92526.4 + 4587.3 * 0 = 92526.4\]
The slope (USD 4587.3) is the difference of predicted wages of applicants of who are master’s degree holder and non-holder.
The p-value corresponds to the two-sided test and as the p-value is very small, we reject the null hypothesis (that there is no difference between master’s degree holder and non-holder on wages) and conclude that there is a statistically significant association between the academic backgrounds and wages.
For possible future research, it would be interesting to add more variables such as number of years of work experience, industries etc along with education backgrounds and build better predictive model.