Discrimination analysis
Cheng-Hsiu Tsai(111078517)
2022-12-29
Hi there! Welcome to my data visualization land. ^^ Today I will use the data to discuss whether there is discrimination against female employees in terms of salary.
Import and Preprocess Data
data1 <- data.table::fread("C:/R-language/PBA/banksalary.csv")
require(tidyverse)## 載入需要的套件：tidyverse## Warning: 套件 'tidyverse' 是用 R 版本 4.2.2 來建造的## ── Attaching packages
## ───────────────────────────────────────
## tidyverse 1.3.2 ──## ✔ ggplot2 3.4.0 ✔ purrr 0.3.5
## ✔ tibble 3.1.8 ✔ dplyr 1.0.10
## ✔ tidyr 1.2.1 ✔ stringr 1.4.1
## ✔ readr 2.1.3 ✔ forcats 0.5.2## Warning: 套件 'ggplot2' 是用 R 版本 4.2.2 來建造的## ── Conflicts ────────────────────────────────────────── tidyverse_conflicts() ──
## ✖ dplyr::filter() masks stats::filter()
## ✖ dplyr::lag() masks stats::lag()glimpse(data1)## Rows: 208
## Columns: 9
## $ Employee <int> 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18…
## $ EducLev <int> 3, 1, 1, 2, 3, 3, 3, 3, 1, 3, 3, 2, 2, 2, 3, 3, 3, 2, 3, 2, 3…
## $ JobGrade <int> 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1…
## $ YrsExper <int> 3, 14, 12, 8, 3, 3, 4, 8, 4, 9, 9, 8, 9, 10, 4, 3, 6, 8, 5, 4…
## $ Age <int> 26, 38, 35, 40, 28, 24, 27, 33, 62, 31, 34, 37, 37, 58, 33, 2…
## $ Gender <chr> "Male", "Female", "Female", "Female", "Male", "Female", "Fema…
## $ YrsPrior <int> 1, 1, 0, 7, 0, 0, 0, 2, 0, 0, 2, 8, 0, 6, 0, 0, 0, 9, 6, 3, 2…
## $ PCJob <chr> "No", "No", "No", "No", "No", "No", "No", "No", "No", "No", "…
## $ Salary <chr> "$32,000 ", "$39,100 ", "$33,200 ", "$30,600 ", "$29,000 ", "…data1$Salary <- str_trim(data1$Salary, side = c("right"))
data1$Salary <- gsub(c("[$]"),"",data1$Salary)
data1$Salary <- gsub(c(","),"",data1$Salary)
data1$Salary <- as.integer(data1$Salary)
summary(data1)## Employee EducLev JobGrade YrsExper
## Min. : 1.00 Min. :1.000 Min. :1.00 Min. : 2.000
## 1st Qu.: 52.75 1st Qu.:2.000 1st Qu.:1.00 1st Qu.: 5.000
## Median :104.50 Median :3.000 Median :3.00 Median : 8.000
## Mean :104.50 Mean :3.159 Mean :2.76 Mean : 9.673
## 3rd Qu.:156.25 3rd Qu.:5.000 3rd Qu.:4.00 3rd Qu.:13.000
## Max. :208.00 Max. :5.000 Max. :6.00 Max. :39.000
## Age Gender YrsPrior PCJob
## Min. :22.00 Length:208 Min. : 0.000 Length:208
## 1st Qu.:32.00 Class :character 1st Qu.: 0.000 Class :character
## Median :38.50 Mode :character Median : 1.000 Mode :character
## Mean :40.39 Mean : 2.375
## 3rd Qu.:47.25 3rd Qu.: 4.000
## Max. :65.00 Max. :18.000
## Salary
## Min. :26700
## 1st Qu.:33000
## Median :37000
## Mean :39922
## 3rd Qu.:44000
## Max. :97000I want to find whether there is a significant difference in average salary between female employees and male employees.
We first assume that there is a equal in average salary between female and male employees.
require(reshape2)## 載入需要的套件：reshape2## Warning: 套件 'reshape2' 是用 R 版本 4.2.2 來建造的##
## 載入套件：'reshape2'## 下列物件被遮斷自 'package:tidyr':
##
## smithsrequire(data.table)## 載入需要的套件：data.table##
## 載入套件：'data.table'## 下列物件被遮斷自 'package:reshape2':
##
## dcast, melt## 下列物件被遮斷自 'package:dplyr':
##
## between, first, last## 下列物件被遮斷自 'package:purrr':
##
## transposeshapiro.test(data1$Salary)##
## Shapiro-Wilk normality test
##
## data: data1$Salary
## W = 0.7792, p-value < 2.2e-16data1[,shapiro.test(Salary),Gender] # match with normal distribution## Gender statistic p.value method data.name
## 1: Male 0.8329482 2.744032e-07 Shapiro-Wilk normality test Salary
## 2: Female 0.9202464 4.814479e-07 Shapiro-Wilk normality test Salaryansari.test(Salary ~ Gender, data1) #variance is not similar##
## Ansari-Bradley test
##
## data: Salary by Gender
## AB = 8024, p-value = 0.0009319
## alternative hypothesis: true ratio of scales is not equal to 1t.test(Salary ~ Gender, data = data1, var.equal = FALSE)##
## Welch Two Sample t-test
##
## data: Salary by Gender
## t = -4.141, df = 78.898, p-value = 8.604e-05
## alternative hypothesis: true difference in means between group Female and group Male is not equal to 0
## 95 percent confidence interval:
## -12282.943 -4308.082
## sample estimates:
## mean in group Female mean in group Male
## 37209.93 45505.44dataSummary <- data1[,.(
Salary.mean=mean(Salary), Salary.sd=sd(Salary),
Lower=mean(Salary) - 2*sd(Salary)/sqrt(NROW(Salary)),
Upper=mean(Salary) + 2*sd(Salary)/sqrt(NROW(Salary))
), Gender]; dataSummary## Gender Salary.mean Salary.sd Lower Upper
## 1: Male 45505.44 15843.218 41662.90 49347.99
## 2: Female 37209.93 6710.867 36075.59 38344.27ggplot(dataSummary, aes(x=Salary.mean, y=Gender)) + geom_point() +
geom_errorbarh(aes(xmin=Lower, xmax=Upper), height=.2) +
theme_bw()
Viewing the number, the p-value of Two sample t-test is lower than 0.05, so we should reject the null hypothesis.
According to the chart, it is shown that two means are not within 2 standard deviation of each other. They are far apart from each other.
As the results, it is noticed that there is indeed a significant difference in average salary between female and male employees.
In addition to observe the relation between salary and gender, I also want to explore more. Therfore, I transform EducLev into several dummy variables. I also transform JobGrade, Gender, and PCJob into dummy variables.
data2 <- data1
data2$EducLev <- as.factor(data2$EducLev)
data2$JobGrade <- as.factor(data2$JobGrade)
data2$Gender <- factor(data2$Gender,levels = c(unique(data2$Gender)))
data2$PCJob <- factor(data2$PCJob,levels = c(unique(data2$PCJob)))
require(fastDummies)## 載入需要的套件：fastDummies## Warning: 套件 'fastDummies' 是用 R 版本 4.2.2 來建造的data_2 <- dummy_cols(data2,select_columns = c("Gender","EducLev","JobGrade","PCJob"))
data_dum <- data_2[,c(-10,-12,-17,-23)];data_dum## Employee EducLev JobGrade YrsExper Age Gender YrsPrior PCJob Salary
## 1: 1 3 1 3 26 Male 1 No 32000
## 2: 2 1 1 14 38 Female 1 No 39100
## 3: 3 1 1 12 35 Female 0 No 33200
## 4: 4 2 1 8 40 Female 7 No 30600
## 5: 5 3 1 3 28 Male 0 No 29000
## ---
## 204: 204 3 6 34 60 Male 0 No 95000
## 205: 205 5 6 36 61 Male 0 No 97000
## 206: 206 5 6 32 62 Male 0 No 88000
## 207: 207 5 6 35 59 Male 0 No 94000
## 208: 208 5 6 33 62 Female 0 No 30000
## Gender_Female EducLev_2 EducLev_3 EducLev_4 EducLev_5 JobGrade_2
## 1: 0 0 1 0 0 0
## 2: 1 0 0 0 0 0
## 3: 1 0 0 0 0 0
## 4: 1 1 0 0 0 0
## 5: 0 0 1 0 0 0
## ---
## 204: 0 0 1 0 0 0
## 205: 0 0 0 0 1 0
## 206: 0 0 0 0 1 0
## 207: 0 0 0 0 1 0
## 208: 1 0 0 0 1 0
## JobGrade_3 JobGrade_4 JobGrade_5 JobGrade_6 PCJob_Yes
## 1: 0 0 0 0 0
## 2: 0 0 0 0 0
## 3: 0 0 0 0 0
## 4: 0 0 0 0 0
## 5: 0 0 0 0 0
## ---
## 204: 0 0 0 1 0
## 205: 0 0 0 1 0
## 206: 0 0 0 1 0
## 207: 0 0 0 1 0
## 208: 0 0 0 1 0I estimate a multiple regression model to support previous justification.
original model
model1 <- lm(Salary ~ YrsExper+Age+YrsPrior+Gender_Female+EducLev_2+EducLev_3+EducLev_4+EducLev_5
+JobGrade_2+JobGrade_3+JobGrade_4+JobGrade_5+JobGrade_6+PCJob_Yes, data = data_dum)
summary(model1)##
## Call:
## lm(formula = Salary ~ YrsExper + Age + YrsPrior + Gender_Female +
## EducLev_2 + EducLev_3 + EducLev_4 + EducLev_5 + JobGrade_2 +
## JobGrade_3 + JobGrade_4 + JobGrade_5 + JobGrade_6 + PCJob_Yes,
## data = data_dum)
##
## Residuals:
## Min 1Q Median 3Q Max
## -40117 -2359 -397 1778 23958
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 29689.935 2490.014 11.924 < 2e-16 ***
## YrsExper 515.583 97.980 5.262 3.77e-07 ***
## Age -8.962 57.699 -0.155 0.8767
## YrsPrior 167.727 140.442 1.194 0.2338
## Gender_Female -2554.474 1011.974 -2.524 0.0124 *
## EducLev_2 -485.552 1398.657 -0.347 0.7289
## EducLev_3 527.915 1357.519 0.389 0.6978
## EducLev_4 285.176 2404.727 0.119 0.9057
## EducLev_5 2690.801 1620.891 1.660 0.0985 .
## JobGrade_2 1564.497 1185.771 1.319 0.1886
## JobGrade_3 5219.358 1262.395 4.134 5.30e-05 ***
## JobGrade_4 8594.833 1496.018 5.745 3.53e-08 ***
## JobGrade_5 13659.409 1874.269 7.288 7.86e-12 ***
## JobGrade_6 23832.391 2799.888 8.512 4.75e-15 ***
## PCJob_Yes 4922.846 1473.825 3.340 0.0010 **
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 5648 on 193 degrees of freedom
## Multiple R-squared: 0.7652, Adjusted R-squared: 0.7482
## F-statistic: 44.94 on 14 and 193 DF, p-value: < 2.2e-16require(stargazer)## 載入需要的套件：stargazer##
## Please cite as:## Hlavac, Marek (2022). stargazer: Well-Formatted Regression and Summary Statistics Tables.## R package version 5.2.3. https://CRAN.R-project.org/package=stargazerstargazer(model1, type = "text")##
## ===============================================
## Dependent variable:
## ---------------------------
## Salary
## -----------------------------------------------
## YrsExper 515.583***
## (97.980)
##
## Age -8.962
## (57.699)
##
## YrsPrior 167.727
## (140.442)
##
## Gender_Female -2,554.474**
## (1,011.974)
##
## EducLev_2 -485.552
## (1,398.657)
##
## EducLev_3 527.915
## (1,357.519)
##
## EducLev_4 285.176
## (2,404.727)
##
## EducLev_5 2,690.801*
## (1,620.891)
##
## JobGrade_2 1,564.497
## (1,185.771)
##
## JobGrade_3 5,219.358***
## (1,262.395)
##
## JobGrade_4 8,594.833***
## (1,496.018)
##
## JobGrade_5 13,659.410***
## (1,874.269)
##
## JobGrade_6 23,832.390***
## (2,799.888)
##
## PCJob_Yes 4,922.846***
## (1,473.825)
##
## Constant 29,689.940***
## (2,490.014)
##
## -----------------------------------------------
## Observations 208
## R2 0.765
## Adjusted R2 0.748
## Residual Std. Error 5,648.080 (df = 193)
## F Statistic 44.939*** (df = 14; 193)
## ===============================================
## Note: *p<0.1; **p<0.05; ***p<0.01require(jtools) # install the package, "jtools", first!## 載入需要的套件：jtools## Warning: 套件 'jtools' 是用 R 版本 4.2.2 來建造的plot_summs(model1)## 載入需要的命名空間：broom.mixed
We found that age has zero effect on the response variable. So, we use the scale function below:
model2 <- lm(Salary ~ YrsExper+scale(Age)+YrsPrior+Gender+EducLev+
JobGrade+PCJob, data = data2)
summary(model2)##
## Call:
## lm(formula = Salary ~ YrsExper + scale(Age) + YrsPrior + Gender +
## EducLev + JobGrade + PCJob, data = data2)
##
## Residuals:
## Min 1Q Median 3Q Max
## -40117 -2359 -397 1778 23958
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 29327.92 1637.94 17.905 < 2e-16 ***
## YrsExper 515.58 97.98 5.262 3.77e-07 ***
## scale(Age) -92.48 595.39 -0.155 0.8767
## YrsPrior 167.73 140.44 1.194 0.2338
## GenderFemale -2554.47 1011.97 -2.524 0.0124 *
## EducLev2 -485.55 1398.66 -0.347 0.7289
## EducLev3 527.91 1357.52 0.389 0.6978
## EducLev4 285.18 2404.73 0.119 0.9057
## EducLev5 2690.80 1620.89 1.660 0.0985 .
## JobGrade2 1564.50 1185.77 1.319 0.1886
## JobGrade3 5219.36 1262.39 4.134 5.30e-05 ***
## JobGrade4 8594.83 1496.02 5.745 3.53e-08 ***
## JobGrade5 13659.41 1874.27 7.288 7.86e-12 ***
## JobGrade6 23832.39 2799.89 8.512 4.75e-15 ***
## PCJobYes 4922.85 1473.82 3.340 0.0010 **
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 5648 on 193 degrees of freedom
## Multiple R-squared: 0.7652, Adjusted R-squared: 0.7482
## F-statistic: 44.94 on 14 and 193 DF, p-value: < 2.2e-16stargazer(model2, type = "text")##
## ===============================================
## Dependent variable:
## ---------------------------
## Salary
## -----------------------------------------------
## YrsExper 515.583***
## (97.980)
##
## scale(Age) -92.480
## (595.393)
##
## YrsPrior 167.727
## (140.442)
##
## GenderFemale -2,554.474**
## (1,011.974)
##
## EducLev2 -485.552
## (1,398.657)
##
## EducLev3 527.915
## (1,357.519)
##
## EducLev4 285.176
## (2,404.727)
##
## EducLev5 2,690.801*
## (1,620.891)
##
## JobGrade2 1,564.497
## (1,185.771)
##
## JobGrade3 5,219.358***
## (1,262.395)
##
## JobGrade4 8,594.833***
## (1,496.018)
##
## JobGrade5 13,659.410***
## (1,874.269)
##
## JobGrade6 23,832.390***
## (2,799.888)
##
## PCJobYes 4,922.846***
## (1,473.825)
##
## Constant 29,327.920***
## (1,637.944)
##
## -----------------------------------------------
## Observations 208
## R2 0.765
## Adjusted R2 0.748
## Residual Std. Error 5,648.080 (df = 193)
## F Statistic 44.939*** (df = 14; 193)
## ===============================================
## Note: *p<0.1; **p<0.05; ***p<0.01plot_summs(model2)## 載入需要的命名空間：broom.mixed
After done the multiple regression and viewing the coefficients, we can say that a variable is significant if their p-value is lower than 0.05, and then the t value will larger than 1.96.
Consequently,it is observed that gender has an impact on Salary(p-value < 0.05), but education_level has no effect on Salary.
Therefore, we can maintain our original justification. Besides that, years_Experience, JobGrade and PCJob also have the great impact on Salary.
However, the second level of jobgrade does not affect Salary significantly. Last but not the least, JobGrade6, which is the highest level of jobgrade, has the largest effect on Salary. We can then view the R-squared, which means that the extent to which the RHS variables in the model explains the variation in Y, is 0.7652. Thus, this model has quite convincing explanation.
Just in case you have a question: Do these data provide evidence that there is discrimination against female employees in terms of salary?
As a result above, we can recognize that there is indeed a significant difference in average salary between female and male employees during two sample t-test.
In addition, after we considered other variables to check whether we have overestimated the impact between Gender and Salary,we found that other variables like YrsExper, PCJob positively affect Salary, but Gender in female still has negatively effect on Salary. (as its p-value < 0.05, which means it is significant.)
In a nutshell, I would tend to say that there is discrimination against female employees in terms of salary.
To find out sufficient provement to do the conclusion, I choose three variable(YrsExper,Gender,JobGrade) to be IV, and suppose they will have an impact on Salary.
lm1 <- lm(Salary ~ YrsExper+Gender+JobGrade, data = data2)
summary(lm1)##
## Call:
## lm(formula = Salary ~ YrsExper + Gender + JobGrade, data = data2)
##
## Residuals:
## Min 1Q Median 3Q Max
## -39461 -2763 -704 2190 24394
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 30531.85 1142.83 26.716 < 2e-16 ***
## YrsExper 406.22 77.79 5.222 4.42e-07 ***
## GenderFemale -1926.52 1005.27 -1.916 0.0567 .
## JobGrade2 2667.72 1180.04 2.261 0.0249 *
## JobGrade3 6420.38 1165.81 5.507 1.11e-07 ***
## JobGrade4 10524.67 1367.86 7.694 6.36e-13 ***
## JobGrade5 16115.28 1557.68 10.346 < 2e-16 ***
## JobGrade6 27450.30 2412.98 11.376 < 2e-16 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 5831 on 200 degrees of freedom
## Multiple R-squared: 0.7407, Adjusted R-squared: 0.7316
## F-statistic: 81.61 on 7 and 200 DF, p-value: < 2.2e-16Gender has an negative impact on Salary marginally when it becomes a female, as its p-value < 0.1.
But both of YrsExper and JobGrade has great impact on Salary, as their p-value far lower than 0.05.
So I pick up Gender to be moderator and do the regression again.
data3 <- data2
data3$JobGrade <- as.integer(data3$JobGrade)
data3 <- dummy_cols(data3,select_columns = "Gender")
data3 <- data3[,-10]
salary1 <- lm(Salary ~ YrsExper+JobGrade,data = data3,subset=(Gender_Female==0))
summary(salary1)##
## Call:
## lm(formula = Salary ~ YrsExper + JobGrade, data = data3, subset = (Gender_Female ==
## 0))
##
## Residuals:
## Min 1Q Median 3Q Max
## -15506.2 -2268.7 287.2 2044.2 15140.4
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 22244.94 1505.05 14.780 < 2e-16 ***
## YrsExper 1054.43 98.48 10.707 5.50e-16 ***
## JobGrade 3627.35 503.92 7.198 7.74e-10 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 5524 on 65 degrees of freedom
## Multiple R-squared: 0.882, Adjusted R-squared: 0.8784
## F-statistic: 243 on 2 and 65 DF, p-value: < 2.2e-16salary2 <- lm(Salary ~ YrsExper+JobGrade,data = data3,subset=(Gender_Female==1))
summary(salary2)##
## Call:
## lm(formula = Salary ~ YrsExper + JobGrade, data = data3, subset = (Gender_Female ==
## 1))
##
## Residuals:
## Min 1Q Median 3Q Max
## -21988.6 -2924.6 -449.6 2071.0 14828.9
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 27877.34 980.98 28.418 <2e-16 ***
## YrsExper 64.45 73.36 0.879 0.381
## JobGrade 3664.06 322.56 11.359 <2e-16 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 4715 on 137 degrees of freedom
## Multiple R-squared: 0.5136, Adjusted R-squared: 0.5065
## F-statistic: 72.32 on 2 and 137 DF, p-value: < 2.2e-16Because two kinds of Gender has imapct on JobGrade, I will do the t-score to testify:
(3627.35-3664.06) / sqrt(98.48^2+73.36^2)## [1] -0.2989398