Business
2025-09-29
#task 2
Importing data:
library(readxl)
business <- read_xlsx("Business School.xlsx")
business <- as.data.frame(business)Showng basic parameters:
summary(business)## Student ID Undergrad Degree Undergrad Grade MBA Grade
## Min. : 1.00 Length:100 Min. : 61.20 Min. :58.14
## 1st Qu.: 25.75 Class :character 1st Qu.: 71.47 1st Qu.:71.14
## Median : 50.50 Mode :character Median : 76.65 Median :76.38
## Mean : 50.50 Mean : 76.90 Mean :76.04
## 3rd Qu.: 75.25 3rd Qu.: 81.70 3rd Qu.:82.15
## Max. :100.00 Max. :100.00 Max. :95.00
## Work Experience Employability (Before) Employability (After)
## Length:100 Min. :101.0 Min. :119.0
## Class :character 1st Qu.:245.8 1st Qu.:312.0
## Mode :character Median :256.8 Median :435.6
## Mean :257.9 Mean :422.7
## 3rd Qu.:261.0 3rd Qu.:529.0
## Max. :421.0 Max. :631.0
## Status Annual Salary
## Length:100 Min. : 20000
## Class :character 1st Qu.: 87125
## Mode :character Median :103500
## Mean :109058
## 3rd Qu.:124000
## Max. :340000Taking out variables that are not numeric:
summary(business[ , -c(1,2,5,8)])## Undergrad Grade MBA Grade Employability (Before) Employability (After)
## Min. : 61.20 Min. :58.14 Min. :101.0 Min. :119.0
## 1st Qu.: 71.47 1st Qu.:71.14 1st Qu.:245.8 1st Qu.:312.0
## Median : 76.65 Median :76.38 Median :256.8 Median :435.6
## Mean : 76.90 Mean :76.04 Mean :257.9 Mean :422.7
## 3rd Qu.: 81.70 3rd Qu.:82.15 3rd Qu.:261.0 3rd Qu.:529.0
## Max. :100.00 Max. :95.00 Max. :421.0 Max. :631.0
## Annual Salary
## Min. : 20000
## 1st Qu.: 87125
## Median :103500
## Mean :109058
## 3rd Qu.:124000
## Max. :340000library(pastecs)
stat.desc(business[ , -c(1,2,5,8)])## Undergrad Grade MBA Grade Employability (Before)
## nbr.val 100.0000000 100.0000000 100.000000
## nbr.null 0.0000000 0.0000000 0.000000
## nbr.na 0.0000000 0.0000000 0.000000
## min 61.2000000 58.1400000 101.000000
## max 100.0000000 95.0000000 421.000000
## range 38.8000000 36.8600000 320.000000
## sum 7689.9000000 7604.0550000 25793.080510
## median 76.6500000 76.3800000 256.831735
## mean 76.8990000 76.0405500 257.930805
## SE.mean 0.7461856 0.7675114 5.934729
## CI.mean.0.95 1.4805941 1.5229091 11.775790
## var 55.6792919 58.9073727 3522.101083
## std.dev 7.4618558 7.6751139 59.347292
## coef.var 0.0970345 0.1009345 0.230090
## Employability (After) Annual Salary
## nbr.val 1.000000e+02 1.000000e+02
## nbr.null 0.000000e+00 0.000000e+00
## nbr.na 0.000000e+00 0.000000e+00
## min 1.190000e+02 2.000000e+04
## max 6.310322e+02 3.400000e+05
## range 5.120322e+02 3.200000e+05
## sum 4.226906e+04 1.090580e+07
## median 4.356379e+02 1.035000e+05
## mean 4.226906e+02 1.090580e+05
## SE.mean 1.292335e+01 4.150149e+03
## CI.mean.0.95 2.564273e+01 8.234796e+03
## var 1.670130e+04 1.722373e+09
## std.dev 1.292335e+02 4.150149e+04
## coef.var 3.057402e-01 3.805451e-01round(stat.desc(business[ , -c(1,2,5,8)]))## Undergrad Grade MBA Grade Employability (Before)
## nbr.val 100 100 100
## nbr.null 0 0 0
## nbr.na 0 0 0
## min 61 58 101
## max 100 95 421
## range 39 37 320
## sum 7690 7604 25793
## median 77 76 257
## mean 77 76 258
## SE.mean 1 1 6
## CI.mean.0.95 1 2 12
## var 56 59 3522
## std.dev 7 8 59
## coef.var 0 0 0
## Employability (After) Annual Salary
## nbr.val 100 100
## nbr.null 0 0
## nbr.na 0 0
## min 119 20000
## max 631 340000
## range 512 320000
## sum 42269 10905800
## median 436 103500
## mean 423 109058
## SE.mean 13 4150
## CI.mean.0.95 26 8235
## var 16701 1722373475
## std.dev 129 41501
## coef.var 0 0Calculating descriptive statistics.
stat.desc(business$`Annual Salary`)## nbr.val nbr.null nbr.na min max range
## 1.000000e+02 0.000000e+00 0.000000e+00 2.000000e+04 3.400000e+05 3.200000e+05
## sum median mean SE.mean CI.mean.0.95 var
## 1.090580e+07 1.035000e+05 1.090580e+05 4.150149e+03 8.234796e+03 1.722373e+09
## std.dev coef.var
## 4.150149e+04 3.805451e-01round(stat.desc(business$`Annual Salary`),1)## nbr.val nbr.null nbr.na min max range
## 100.0 0.0 0.0 20000.0 340000.0 320000.0
## sum median mean SE.mean CI.mean.0.95 var
## 10905800.0 103500.0 109058.0 4150.1 8234.8 1722373474.7
## std.dev coef.var
## 41501.5 0.4Calculating frequency for each degree:
table(business$`Undergrad Degree`)##
## Art Business Computer Science Engineering
## 6 35 25 9
## Finance
## 25Creating new data frame in second window to be able to use frequency data in chart:
freq <- as.data.frame(table(business$`Undergrad Degree`))
colnames(freq) <- c("Diploma", "Count")Making a histogram using ggplot to show frequency od undergrad degrees among students.
library(ggplot2)
ggplot(freq, aes(x = reorder(Diploma, -Count), y = Count)) +
geom_col(fill = "steelblue") +
geom_text(aes(label = Count), vjust = -0.3) +
labs(title = "Frequency of Degrees",
x = "Degree",
y = "Amount of students") +
theme_minimal()
From the chart we are able to see that data is asymmetrical to the right.
Continuing with t test for the average grade of MBA students.
Null hypothesis: Average grade in the population is equal to 74. Alternative hypothesis: Average grade in population is different to 74.
Using t.test function to get the p value.
t.test(business$`MBA Grade`,
mu = 74,
alternative = "two.sided")##
## One Sample t-test
##
## data: business$`MBA Grade`
## t = 2.6587, df = 99, p-value = 0.00915
## alternative hypothesis: true mean is not equal to 74
## 95 percent confidence interval:
## 74.51764 77.56346
## sample estimates:
## mean of x
## 76.04055If we take alpha to be 5%, we can see that p value is smaller than 0.05, meaning we cannot except null hypothesis. This means we must accept the alternative hypothesis. Meaning average grade has changed from last year.
Calculating effect size:
library(effectsize)
cohens_d(business$`MBA Grade`, mu = 74)## Cohen's d | 95% CI
## ------------------------
## 0.27 | [0.07, 0.46]
##
## - Deviation from a difference of 74.interpreting the result:
library(effectsize)
effectsize::interpret_cohens_d(0,27, rules = "cohen1988")## [1] "very small"
## (Rules: cohen1988)From the interpretation function we are able to see that the effect size is very small, meaning that the change in arithmetic mean from last years students to this years was very small.
We know that the average grade has changed, but to check if it increased or decreased, we have to calculate the arithmetic mean of our population.
mean(business$`MBA Grade`)## [1] 76.04055Because the arithmetic mean of the sample is larger, we can conclude that the average grade increased.