Deans Dilemma Case

Shikhar Kohli - PGP32117
03.10.2017

Question 1: Median salary of all students

deansdilemma.df <- read.csv(paste("datasets/DeansDilemmaData.csv", sep=""))
placed <- subset(deansdilemma.df, Placement == "Placed")
median(deansdilemma.df$Salary)

[1] 240000

Question 2: What percentage of students were placed?

mytable <- with(deansdilemma.df, table(Placement))
mytable

Placement
Not Placed     Placed 
        79        312

round(prop.table(mytable)[2]*100,2)

Placed 
  79.8

Question 3 & 4: Create dataframe 'placed' & find median salary

placed <- subset(deansdilemma.df, Placement == "Placed")
median(placed$Salary)

[1] 260000

Question 5: Create a table showing the mean salary of males and females, who were placed.

placed <- subset(deansdilemma.df, Placement == "Placed")
by(placed$Salary, placed$Gender, median)

placed$Gender: F
[1] 240000
-------------------------------------------------------- 
placed$Gender: M
[1] 265000

Question 6: Histogram showing a breakup of the MBA performance of the students who were placed.

placed <- subset(deansdilemma.df, Placement == "Placed")
hist(placed$Percent_MBA, 
     freq=TRUE, 
     breaks=6, 
     xlab="MBA Percentage")

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Question 7 Create a dataframe called 'notplaced', that contains a subset of only those students who were NOT placed after their MBA

notplaced <- subset(deansdilemma.df, deansdilemma.df$Placement == "Not Placed")

Question 8** Generate two histograms side-by-side, visually comparing the MBA performance of Placed and Not Placed students, as shown below.

library(lattice)
histogram(~ deansdilemma.df$Percent_MBA | deansdilemma.df$Placement, data = deansdilemma.df)

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Question 9 Generate two boxplots, one below the other, comparing the distribution of salaries of males and females who were placed, as shown below

boxplot( deansdilemma.df$Salary ~ deansdilemma.df$Gender, data = deansdilemma.df, plot=TRUE, staplewex = TRUE, horizontal = TRUE, names = c("Females","Males"))

plot of chunk unnamed-chunk-8

Question 10

Create a dataframe called 'placedET', representing students who were placed after the MBA and who also gave some MBA entrance test before admission into the MBA program

placedET <- subset(x = deansdilemma.df, subset = deansdilemma.df$Placement == "Placed" & deansdilemma.df$Entrance_Test != "None")

Question 11

Draw a Scatter Plot Matrix for 3 variables – {Salary, Percent_MBA, Percentile_ET} using the dataframe placedET, as shown below.

placed <- subset(deansdilemma.df, Placement == "Placed")
placedET <- subset(placed, placed$S.TEST == 1)
library(car)

scatterplotMatrix(~Salary + Percent_MBA + Percentile_ET, data=placedET,
                  spread=FALSE, smoother.args=list(lty=2),
                  main="Scatter Plot Matrix via Deans Dilemma data")

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Question 12

What is mean salary of all the students who were placed?

mean(placed$Salary)

[1] 274550

```

Question 13

Test whether the distribution of salaries is normal

shapiro.test(deansdilemma.df$Salary)


    Shapiro-Wilk normality test

data:  deansdilemma.df$Salary
W = 0.89789, p-value = 1.619e-15

qqnorm(deansdilemma.df$Salary)
qqline(deansdilemma.df$Salary)

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Since the p-value is less than 0.05, we reject the null hypothesis that the population is normally distributed

Question 14 Create a table giving the mean salary of the men and the women MBAs who were placed?

by(deansdilemma.df$Salary, deansdilemma.df$Gender, mean)

deansdilemma.df$Gender: F
[1] 193288.2
-------------------------------------------------------- 
deansdilemma.df$Gender: M
[1] 231484.8

```

Question 15 Visualize the mean salary of men and women who were placed, using plotmeans()

gplots::plotmeans(deansdilemma.df$Salary ~ deansdilemma.df$Gender, data = deansdilemma.df)

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Question 16 Create a table giving the variance of the salary of the men and women MBAs who were placed?

by(data = deansdilemma.df$Salary,  deansdilemma.df$Gender, FUN = var)

deansdilemma.df$Gender: F
[1] 15840147717
-------------------------------------------------------- 
deansdilemma.df$Gender: M
[1] 20303338173

Question 17 Use a suitable statistical test to compare whether the variances are significantly different?

placed <- subset(deansdilemma.df, Placement == "Placed")
res.ftest <- var.test(placed$Salary ~ placed$Gender, data = placed)
res.ftest


    F test to compare two variances

data:  placed$Salary by placed$Gender
F = 0.55675, num df = 96, denom df = 214, p-value = 0.00135
alternative hypothesis: true ratio of variances is not equal to 1
95 percent confidence interval:
 0.3999212 0.7927360
sample estimates:
ratio of variances 
         0.5567478

Question 18 Use a suitable statistical test to compare whether there is a significant difference between the salaries of men and women?

res.ttest <- t.test(placed$Salary ~ placed$Gender, data = placed)
res.ttest


    Welch Two Sample t-test

data:  placed$Salary by placed$Gender
t = -3.0757, df = 243.03, p-value = 0.00234
alternative hypothesis: true difference in means is not equal to 0
95 percent confidence interval:
 -51138.42 -11209.22
sample estimates:
mean in group F mean in group M 
       253068.0        284241.9

Create data frames for engineers and non-engineers

nonengineering.df <- subset(deansdilemma.df, deansdilemma.df$Course_Degree != "Engineering")
engineering.df <- subset(deansdilemma.df, deansdilemma.df$Course_Degree == "Engineering")

ENGINEERING

Question 14 Create a table giving the mean salary of the men and the women MBAs who were placed?

by(engineering.df$Salary, engineering.df$Gender, mean)

engineering.df$Gender: F
[1] 187000
-------------------------------------------------------- 
engineering.df$Gender: M
[1] 292074.1

Question 15 Visualize the mean salary of men and women who were placed, using plotmeans()

gplots::plotmeans(engineering.df$Salary ~ engineering.df$Gender, data = engineering.df)

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Question 16 Create a table giving the variance of the salary of the men and women MBAs who were placed?

by(data = engineering.df$Salary,  engineering.df$Gender, FUN = var)

engineering.df$Gender: F
[1] 19312222222
-------------------------------------------------------- 
engineering.df$Gender: M
[1] 27796148148

Question 17 Use a suitable statistical test to compare whether the variances are significantly different?

placed <- subset(engineering.df, Placement == "Placed")
res.ftest <- var.test(placed$Salary ~ placed$Gender, data = placed)
res.ftest


    F test to compare two variances

data:  placed$Salary by placed$Gender
F = 0.27253, num df = 6, denom df = 22, p-value = 0.1122
alternative hypothesis: true ratio of variances is not equal to 1
95 percent confidence interval:
 0.08921974 1.40097801
sample estimates:
ratio of variances 
         0.2725341

Question 18 Use a suitable statistical test to compare whether there is a significant difference between the salaries of men and women?

res.ttest <- t.test(placed$Salary ~ placed$Gender, data = placed)
res.ttest


    Welch Two Sample t-test

data:  placed$Salary by placed$Gender
t = -2.18, df = 20.06, p-value = 0.04134
alternative hypothesis: true difference in means is not equal to 0
95 percent confidence interval:
 -148173.503   -3279.913
sample estimates:
mean in group F mean in group M 
       267142.9        342869.6

NON ENGINEERING

Question 14 Create a table giving the mean salary of the men and the women MBAs who were placed?

by(nonengineering.df$Salary, nonengineering.df$Gender, mean)

nonengineering.df$Gender: F
[1] 193825.6
-------------------------------------------------------- 
nonengineering.df$Gender: M
[1] 224582.3

Question 15 Visualize the mean salary of men and women who were placed, using plotmeans()

gplots::plotmeans(nonengineering.df$Salary ~ nonengineering.df$Gender, data = nonengineering.df)

plot of chunk unnamed-chunk-26

Question 16 Create a table giving the variance of the salary of the men and women MBAs who were placed?

by(data = nonengineering.df$Salary,  nonengineering.df$Gender, FUN = var)

nonengineering.df$Gender: F
[1] 15703615544
-------------------------------------------------------- 
nonengineering.df$Gender: M
[1] 19096049346

Question 17 Use a suitable statistical test to compare whether the variances are significantly different?

placed <- subset(nonengineering.df, Placement == "Placed")
res.ftest <- var.test(placed$Salary ~ placed$Gender, data = placed)
res.ftest


    F test to compare two variances

data:  placed$Salary by placed$Gender
F = 0.63307, num df = 89, denom df = 191, p-value = 0.01571
alternative hypothesis: true ratio of variances is not equal to 1
95 percent confidence interval:
 0.4479942 0.9159224
sample estimates:
ratio of variances 
         0.6330683

Question 18 Use a suitable statistical test to compare whether there is a significant difference between the salaries of men and women?

res.ttest <- t.test(placed$Salary ~ placed$Gender, data = placed)
res.ttest


    Welch Two Sample t-test

data:  placed$Salary by placed$Gender
t = -2.4149, df = 214.74, p-value = 0.01658
alternative hypothesis: true difference in means is not equal to 0
95 percent confidence interval:
 -45851.09  -4639.74
sample estimates:
mean in group F mean in group M 
       251973.3        277218.8