Quantitative Methods – Group 1
Correction of Final Examination
December 2008
For the past two decades, there has been increased interest in the wage gap between men and women. Common knowledge says that in Europe the gap is decreasing, but as of today, we are not so sure of whether wage differences persist or not. Hence a recent commision has been appointed by EU President Nicolas Sarkosy to analyse more in depth the actual wage differential between men and women. As the quantitative expert of the commision, you have been asked to evaluate the wage gap using on a random sample of 474 employees drawn from all European countries. This sample is representative of all workers employed in Europe. For each employee we have the following information:
Table 1. Variable list and description Label Variable Name Unit Type
Employee ID id - QL 0 Male Gender female QL 1 Female 0 No Minority minority 1 Yes QL 9 (missing) Level of education (years) educ_years In years QT 0 0 (Missing) 1 Secretary Employee category job_cat QL 2 Management staff 3 Executive officer Wage wage In Euro QT
Wage at hiring date ini_wage In Euro QT
Months since Hire months_hire In months QT
Past experience (years) exp In years QT Note: Education level is considered as a quantitatiuve variable
In order to facilitate your empirical investigation, you have decomposed the research into three parts. Part I is designed to report wage differentials. Part II reports the differences between men and women in the relationship between education, experience and wage. Part III seeks to understand the sources of wage differentials. Part I. Descriptive statistics on wage statistics 1. Importing the file and producing descriptive statitsics. a. The source file is an excel file which can be found at my webpage b. Provide and comment descriptive statitsics for wage, initial wage, years of education and experience
Descriptive Statistics
N Minimum Maximum Mean Std. Deviation educ_years 474 7 21 13.44 2.759 wage 474 15750 135000 34419.57 17075.661 ini_wage 474 9000 79980 17016.09 7870.638 exp 474 0 476 95.86 104.586 Valid N (listwise) 474
The average number of years of education is 13.44 months, with a low standard deviation. On average, the first annual salary is 17 thousand Euros a year, and the sample average wage is 34,5 thousand Euros.The average length of experience is 95 months.
c. Provide and comment frequency table for gender and women job types
female
Cumulative Frequency Percent Valid Percent Percent Valid 0 258 54.4 54.4 54.4 1 216 45.6 45.6 100.0 Total 474 100.0 100.0
job_cat
Cumulative Frequency Percent Valid Percent Percent Valid 1 353 74.5 74.5 74.5 2 36 7.6 7.6 82.1 3 85 17.9 17.9 100.0 Total 474 100.0 100.0
2. Reporting differences in wages a. Test initial wage differential i. Write out H0 and H1 H0: No difference between men and women in terms of initial wage differential H1: Significant difference between men and women in terms of initial wage differential
ii. Carry out test You can either carry out a T test or an Anova. T test Group Statistics
Std. Error female N Mean Std. Deviation Mean ini_wage 1 216 13091.97 2935.599 199.742 0 258 20301.40 9111.781 567.275
Independent Samples T Test
t-test for Equality of Means 95% Confidence Interval t df Sig. (2-tailed) of the Difference Lower Upper ini_wage Equal variances assumed -11.152 472 .000 -8479.698 -5939.158
ANOVA Descriptives ini_wage 95% Confidence Interval for N Mean Std. Deviation Std. Error Mean Lower Upper Upper Bound Bound Lower Bound Bound Lower Bound Upper Bound 0 258 20301.40 9111.781 567.275 19184.30 21418.49 1 216 13091.97 2935.599 199.742 12698.26 13485.67 Total 474 17016.09 7870.638 361.510 16305.72 17726.45
ANOVA ini_wage Sum of Squares df Mean Square F Sig. Between Groups 611078077 6110780779.0 1 124.376 .000 9.007 07 Within Groups 231901241 472 49131619.039 86.448 Total 293009049 473 65.454
iii. Conclude There are significant differences between mena nd women in terms of initial wage. The mean difference in wage is about 7000 euros in annual wage.
b. Test actual wage differential (we report T test results only) i. Write out H0 and H1 H0: No difference between men and women in terms of actual wage differential H1: Significant difference between men and women in terms of actual wage differential ii. Carry out test
Group Statistics
Std. Error female N Mean Std. Deviation Mean wage 1 216 26031.92 7558.021 514.258 0 258 41441.78 19499.214 1213.968
Independent Samples Test
t-test for Equality of Means 95% Confidence Interval t df Sig. (2-tailed) of the Difference Upper Lower wage Equal variances - -10.945 472 .000 -12643.322 assumed 18176.401
iii. Conclude
There are significant differences between mena nd women in terms of actual wage. The mean difference in wage is about 15000 euros in annual wage.
3. Conclusion on part I
As of our sample, there are significant differences in terms of actual and initial wages between mena dn women. The difference is present from the first wage onwards, and is increasing with experience. Part II. Relationship between education, experience and wage 4. Report the effect of a one-year increase in education on initail wage for all employees. a. Carry out test Model Summary
Adjusted R Std. Error of Model R R Square Square the Estimate 1 .505(a) .255 .253 6802.609 a Predictors: (Constant), educ_years
ANOVA(b)
Sum of Model Squares df Mean Square F Sig. 1 Regression 745887688 7458876888.5 1 161.184 .000(a) 8.510 10 Residual 218420280 472 46275483.214 76.944 Total 293009049 473 65.454 a Predictors: (Constant), educ_years b Dependent Variable: ini_wage
Coefficients(a)
Unstandardized Standardized Coefficients Coefficients
Model B Std. Error Beta t Sig. 1 (Constant) -2323.274 1554.999 -1.494 .136 educ_years 1439.293 113.367 .505 12.696 .000 a Dependent Variable: ini_wage
b. Conclusion
A one-year increase in education is associated with a 1439 Euro increase in annual initial salary.
5. Report the effect of a one-month increase in experience in the company on wage for all employees. a. Carry out test
Model Summary
Adjusted R Std. Error of Model R R Square Square the Estimate 1 .084(a) .007 .005 17033.194 a Predictors: (Constant), months_hire
ANOVA(b) Sum of Model Squares df Mean Square F Sig. 1 Regression 975277786 975277786.35 1 3.362 .067(a) .350 0 Residual 136941217 290129698.41 472 649.990 1 Total 137916495 473 436.340 a Predictors: (Constant), months_hire b Dependent Variable: wage
Coefficients(a)
Unstandardized Standardized Coefficients Coefficients
Model B Std. Error Beta t Sig. 1 (Constant) 22843.324 6362.214 3.590 .000 months_hire 142.723 77.844 .084 1.833 .067 a Dependent Variable: wage
b. Conclusion
A one-month increase in the company is very loosely associated with a 142 Euro increase in initial salary. This relationship is not signbificant at 5% level.
6. Repeat steps 4 and 5 for both men and women (Hint: use the data - spilt file option)
STEP 4
Model Summary
Adjusted R Std. Error of female Model R R Square Square the Estimate 0 1 .625(a) .391 .388 7126.948 1 1 .533(a) .285 .281 2488.804 a Predictors: (Constant), educ_years
ANOVA(b)
Sum of female Model Squares df Mean Square F Sig. 0 1 Regression 833420114 8334201147.5 1 164.080 .000(a) 7.577 77 Residual 130031083 256 50793391.993 50.098 Total 213373094 257 97.675 1 1 Regression 527267248 527267248.06 1 85.123 .000(a) .064 4 Residual 132554744 214 6194146.919 0.710 Total 185281468 215 8.774 a Predictors: (Constant), educ_years b Dependent Variable: ini_wage Coefficients(a)
Unstandardized Standardized Coefficients Coefficients
female Model B Std. Error Beta t Sig. 0 1 (Constant) -5368.827 2052.548 -2.616 .009 educ_years 1911.376 149.217 .625 12.809 .000 1 1 (Constant) 4592.710 936.641 4.903 .000 educ_years 632.176 68.519 .533 9.226 .000 a Dependent Variable: ini_wage
STEP 5
Model Summary
Adjusted R Std. Error of female Model R R Square Square the Estimate 0 1 .059(a) .003 .000 19503.086 1 1 .085(a) .007 .003 7548.245 a Predictors: (Constant), months_hire
ANOVA(b)
Sum of female Model Squares df Mean Square F Sig. 0 1 Regression 341558736 341558736.07 1 .898 .344(a) .071 1 Residual 973748106 380370354.27 256 93.775 3 Total 977163694 257 29.845 1 1 Regression 88729997. 1 88729997.558 1.557 .213(a) 558 Residual 121928629 214 56975995.234 80.104 Total 122815929 215 77.663 a Predictors: (Constant), months_hire b Dependent Variable: wage
Coefficients(a)
Unstandardized Standardized Coefficients Coefficients
female Model B Std. Error Beta t Sig. 0 1 (Constant) 32340.213 9681.214 3.341 .001 months_hire 111.374 117.531 .059 .948 .344 1 1 (Constant) 20695.502 4306.958 4.805 .000 months_hire 66.390 53.200 .085 1.248 .213 a Dependent Variable: wage
7. Conclusion on part II
There is an tight relationship between education and first salary. A one-year increase in education is associated with a 1439 Euro increase in annual initial salary. There is a very loose relationship between time spent in a company and actual salary. A one-month increase in the company is very loosely associated with a 142 Euro increase in initial salary. In both cases, the relationship is tighter more beneficial for men. Especially in the education / initial wage relationship, the gender division is most striking: a one-year increase in education is associated with a 1911 Euro increase in annual initial salary for men, whereas this relationship decreases to 632 Euros. Thus education pays off three times as much for men than for women. Part III. Understanding the sources of wage differences. 8. Is the level of education is gender-specific ? a. Write out H0 and H1 H0: No difference between men and women in terms of level of education H1: Significant difference between men and women in terms of level of education
b. Carry out test
Group Statistics
Std. Error female N Mean Std. Deviation Mean educ_years 1 216 13.44 2.477 .169 0 258 13.43 2.979 .185
Independent Samples Test
t-test for Equality of Means 95% Confidence Interval t df Sig. (2-tailed) of the Difference Lower Upper Lower educ_years Equal variances assumed .056 472 .956 -.486 .515
c. Conclusion There is no significant difference between men and women in terms of level of education
9. Are job types gender specific a. Write out H0 and H1 H0: there is independece between job types and gender H1: there is dependece between job types and gender
b. Carry out test female * job_cat Crosstabulation
job_cat 1 2 3 Total female 0 Count 157 27 74 258 Expected Count 192.1 19.6 46.3 258.0 1 Count 196 9 11 216 Expected Count 160.9 16.4 38.7 216.0 Total Count 353 36 85 474 Expected Count 353.0 36.0 85.0 474.0 Chi-Square Tests
Asymp. Sig. Value df (2-sided) Pearson Chi-Square 56.727(a) 2 .000 a 0 cells (.0%) have expected count less than 5. The minimum expected count is 16.41.
c. Conclusion There is dependece between job types and gender
10. At equal job, are initial wage differences are due to gender ? (use the data - spilt file option). Conclude
Descriptives ini_wage 95% Confidence Interval for job_cat N Mean Std. Deviation Std. Error Mean Lower Upper Upper Bound Bound Lower Bound Bound Lower Bound Upper Bound 1 0 157 15861.21 2564.694 204.685 15456.90 16265.52 1 196 12707.93 2386.167 170.440 12371.79 13044.08 Total 353 14110.38 2920.916 155.465 13804.63 14416.14 2 0 27 15077.78 1341.235 258.121 14547.20 15608.35 1 9 13516.67 2594.224 864.741 11522.57 15510.76 Total 36 14687.50 1828.832 304.805 14068.71 15306.29 3 0 74 31627.70 9749.813 1133.393 29368.85 33886.55 1 11 19587.27 4405.415 1328.283 16627.67 22546.87 Total 85 30069.53 10072.176 1092.481 27897.01 32242.05
ANOVA ini_wage
job_cat Sum of Squares df Mean Square F Sig. 1 Between Groups 866772515.170 1 866772515.170 142.406 .000 Within Groups 2136403058.202 351 6086618.399 Total 3003175573.372 352 2 Between Groups 16450208.333 1 16450208.333 5.559 .024 Within Groups 100611666.667 34 2959166.667 Total 117061875.000 35 3 Between Groups 1388319653.536 1 1388319653.536 16.154 .000 Within Groups 7133372927.642 83 85944252.140 Total 8521692581.177 84
Overall conclusion For all types of job there are significant differences between men and women. Hence, not only there is inequal access to jobs, there are also differences in initial wages at equal level of education and equal job.