A Dean’s Dillemma - t Test Code
Mehul Agrawal
February 5, 2018
Task 3b
Read and View the data using read.csv
data.df <- read.csv(paste("Data - Deans Dilemma.csv", sep=""))
View(data.df)
head(data.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 300000Create a dataframe called placed containing a subset of only those students who were successfully placed
placed <- data.df[which(data.df$Placement_B == 1), ]
head(placed)## SlNo Gender Gender.B Percent_SSC Board_SSC Board_CBSE Board_ICSE
## 1 1 M 0 62.00 Others 0 0
## 2 2 M 0 76.33 ICSE 0 1
## 3 3 M 0 72.00 Others 0 0
## 4 4 M 0 60.00 CBSE 1 0
## 5 5 M 0 61.00 CBSE 1 0
## 6 6 M 0 55.00 ICSE 0 1
## Percent_HSC Board_HSC Stream_HSC Percent_Degree Course_Degree
## 1 88.00 Others Commerce 52.00 Science
## 2 75.33 Others Science 75.48 Computer Applications
## 3 78.00 Others Commerce 66.63 Engineering
## 4 63.00 CBSE Arts 58.00 Management
## 5 55.00 ISC Science 54.00 Engineering
## 6 64.00 CBSE Commerce 50.00 Commerce
## Degree_Engg Experience_Yrs Entrance_Test S.TEST Percentile_ET
## 1 0 0 MAT 1 55.0
## 2 0 1 MAT 1 86.5
## 3 1 0 None 0 0.0
## 4 0 0 MAT 1 75.0
## 5 1 1 MAT 1 66.0
## 6 0 0 None 0 0.0
## S.TEST.SCORE Percent_MBA Specialization_MBA Marks_Communication
## 1 55.0 58.80 Marketing & HR 50
## 2 86.5 66.28 Marketing & Finance 69
## 3 0.0 52.91 Marketing & Finance 50
## 4 75.0 57.80 Marketing & Finance 54
## 5 66.0 59.43 Marketing & HR 52
## 6 0.0 56.81 Marketing & Finance 53
## Marks_Projectwork Marks_BOCA Placement Placement_B Salary
## 1 65 74 Placed 1 270000
## 2 70 75 Placed 1 200000
## 3 61 59 Placed 1 240000
## 4 66 62 Placed 1 250000
## 5 65 67 Placed 1 180000
## 6 70 53 Placed 1 300000Create a table showing the mean salary of males and females, who were placed
mean_sal_gender <- aggregate(placed$Salary, list(placed$Gender), mean)
mean_sal_gender## Group.1 x
## 1 F 253068.0
## 2 M 284241.9Plot box plots for each category to understand data distribution and identify outliers
boxplot(Salary ~ Gender, data = placed, main = "Salary of Males and Females who were placed", xlab = "Gender (Femame/male)",col = (c("green","blue")), ylab = "Salary")
Take the log of Salary data to stabilize variance
log.transformed.Salary = log(placed$Salary)
boxplot(log.transformed.Salary ~ Gender, data = placed, main = "Salary of Males and Females who were placed", xlab = "Gender (Femame/male)",col = (c("green","blue")), ylab = "Log Transformed Salary")
Task 3c
Run a t-test to test the following hypothesis: H1: The average salary of the male MBAs is higher than the average salary of female MBAs.
t.test(log.transformed.Salary ~ Gender, data = placed, var.equal = TRUE)##
## Two Sample t-test
##
## data: log.transformed.Salary by 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 12.50723Task 3d
Interpret the results
- R code that creates a table showing the mean salary of males and females, who were placed is present in Chunk 3.
- Mean Salary for Males who were placed = 284241.9
- Mean Salary for Males who were placed = 253068.0
- t-test for the Hypothesis “The average salary of the male MBAs is higher than the average salary of female MBAs.” is present in Chunk 6.
- The p-value based on the t-test = 0.005203
- Meaning of the t-test, as applied to the average salaries of male and female MBAs -
- The box plots for the salaries of Males and Females reveal presence of any certain outliers. Outliers are more in case of Males.
- The t test showed there was a significant difference in average salaries between males and females. We can now reject the null hypothesis that there is no significant difference between the salaries of males and females. The average salaries of males is greater than that of females.