t-Test
Aswathy Gunadeep
11 December 2017
T-Test Analysis based on “A Dean’s Dilemma: Selection of Students for the MBA Program”
This is a report on the t-Test analysis on the salaries of placed male and female MBAs, based on the Dean’s dilemma dataset.
setwd("D:/desktop/Data Analytics internship-sameer mathur/work/datasets")
mba.df<-read.csv(paste("Data - Deans Dilemma.csv", sep=""))
View(mba.df)3b: table showing the average salary of males and females, who were placed
placed.df <- subset(mba.df, mba.df$Placement_B==1 )
placed.salary.mean <- aggregate(placed.df$Salary, list(placed.df$Gender), mean)
colnames(placed.salary.mean)[2] <- "Mean Salary"
colnames(placed.salary.mean)[1] <- "Gender"
placed.salary.mean## Gender Mean Salary
## 1 F 253068.0
## 2 M 284241.93c: t-Test:
H1: The average salary of the male MBAs is higher than the average salary of female MBAs.
- Inspecting the structure of the data
head(placed.df)## SlNo Gender Gender.B Percent_SSC Board_SSC Board_CBSE Board_ICSE
## 1 1 M 0 62.00 Others 0 0
## 2 2 M 0 76.33 ICSE 0 1
## 3 3 M 0 72.00 Others 0 0
## 4 4 M 0 60.00 CBSE 1 0
## 5 5 M 0 61.00 CBSE 1 0
## 6 6 M 0 55.00 ICSE 0 1
## Percent_HSC Board_HSC Stream_HSC Percent_Degree Course_Degree
## 1 88.00 Others Commerce 52.00 Science
## 2 75.33 Others Science 75.48 Computer Applications
## 3 78.00 Others Commerce 66.63 Engineering
## 4 63.00 CBSE Arts 58.00 Management
## 5 55.00 ISC Science 54.00 Engineering
## 6 64.00 CBSE Commerce 50.00 Commerce
## Degree_Engg Experience_Yrs Entrance_Test S.TEST Percentile_ET
## 1 0 0 MAT 1 55.0
## 2 0 1 MAT 1 86.5
## 3 1 0 None 0 0.0
## 4 0 0 MAT 1 75.0
## 5 1 1 MAT 1 66.0
## 6 0 0 None 0 0.0
## S.TEST.SCORE Percent_MBA Specialization_MBA Marks_Communication
## 1 55.0 58.80 Marketing & HR 50
## 2 86.5 66.28 Marketing & Finance 69
## 3 0.0 52.91 Marketing & Finance 50
## 4 75.0 57.80 Marketing & Finance 54
## 5 66.0 59.43 Marketing & HR 52
## 6 0.0 56.81 Marketing & Finance 53
## Marks_Projectwork Marks_BOCA Placement Placement_B Salary
## 1 65 74 Placed 1 270000
## 2 70 75 Placed 1 200000
## 3 61 59 Placed 1 240000
## 4 66 62 Placed 1 250000
## 5 65 67 Placed 1 180000
## 6 70 53 Placed 1 300000- summary statistics
table(placed.df$Gender)##
## F M
## 97 215summary(placed.df$Salary)## Min. 1st Qu. Median Mean 3rd Qu. Max.
## 120000 220000 260000 274600 300000 940000- Average salaries of female and male MBAs placed.
placed.salary.mean## Gender Mean Salary
## 1 F 253068.0
## 2 M 284241.9- Graphical represenation
boxplot(Salary ~ Gender, data=placed.df, yaxt="n", horizontal = TRUE, ylab="Gender",
xlab="Salary", main="Comparison of salaries of Males and Females", col=c("lightblue", "pink"))
axis(side=2, at=c(1,2), labels=c("Males" , "Females"))
log.transformed.salary = log(placed.df$Salary)Hypothesis 1: The average salary of the male MBAs is higher than the average salary of female MBAs.
NULL hypothesis: -" there is no significant difference between average salary of the MBA and female MBA "
t.test(log.transformed.salary~placed.df$Gender,var.equal = TRUE)##
## Two Sample t-test
##
## data: log.transformed.salary by placed.df$Gender
## t = -2.8142, df = 310, p-value = 0.005203
## alternative hypothesis: true difference in means is not equal to 0
## 95 percent confidence interval:
## -0.17482594 -0.03094897
## sample estimates:
## mean in group F mean in group M
## 12.40435 12.50723- Since the p-value is less than 0.05, we reject the null hypothesis that there’s no difference between the means and conclude that a significant difference does exist.In this case, it is the salaries of male and female MBAs and that we would reject our NULL hypothesis and accept the hypothesis H1.
- Mean salary of male MBAs is 284241.9 rupees as compared to female MBAs which had a mean of 253068.0 rupees.
- The box plot revealed the presence of a few outliners in case of salaries of female MBAs.
3d: (1)
placed.salary.mean## Gender Mean Salary
## 1 F 253068.0
## 2 M 284241.93d: (2)
placed.salary.mean[2,2]## [1] 284241.93d: (3)
placed.salary.mean[1,2]## [1] 2530683d: (4)
t.test(log.transformed.salary~placed.df$Gender,var.equal = TRUE)##
## Two Sample t-test
##
## data: log.transformed.salary by placed.df$Gender
## t = -2.8142, df = 310, p-value = 0.005203
## alternative hypothesis: true difference in means is not equal to 0
## 95 percent confidence interval:
## -0.17482594 -0.03094897
## sample estimates:
## mean in group F mean in group M
## 12.40435 12.50723The p-value is 0.005203.
3d: (5)
- Since the p-value is less than 0.05, we reject the null hypothesis that there’s no difference between the means and conclude that a significant difference does exist.In this case, it is the salaries of male and female MBAs and that we would reject our NULL hypothesis and accept the hypothesis H1.
- Mean salary of male MBAs is 284241.9 rupees as compared to female MBAs which had a mean of 253068.0 rupees.
- The box plot revealed the presence of a few outliners in case of salaries of female MBAs.