User_Data <- read.table("./User_Data.csv", header = TRUE, sep = ",")
head(User_Data)

##    User.ID Gender Age EstimatedSalary Purchased
## 1 15624510   Male  19           19000         0
## 2 15810944   Male  35           20000         0
## 3 15668575 Female  26           43000         0
## 4 15603246 Female  27           57000         0
## 5 15804002   Male  19           76000         0
## 6 15728773   Male  27           58000         0

General

-The dataset contains a sample of 400 observations and 5 variables

- The population is the entire userbase of an online e-commerce platform

-The unit of observation is an individual user of the platform

Variables:

1: User Id

-Unique identification code of platform user

-Type:Categorical (Nominal)

2: Gender

-Gender (Male/Female) of user

-Type: Categorical (Nominal)

3: Age

-Age of user in years

-Type: Numeric (Ratio)

-Unit: Years

4: Estimated Salary

-Estimated annual salary of user

-Type: Numeric (Ratio)

-Unit: Currency

5: Purchased

-Indicates wether a user has purchased any quantity of a specific product

-Type: Categorical (Binary)

Source: Kaggle.com (2025) “User_Data”

Data Manipulation/Descriptive Statistics

User_Data$Gender <- factor(User_Data$Gender,
                            levels = c("Male", "Female"),
                            labels = c("Male", "Female"))
str(User_Data)

## 'data.frame':    400 obs. of  5 variables:
##  $ User.ID        : int  15624510 15810944 15668575 15603246 15804002 15728773 15598044 15694829 15600575 15727311 ...
##  $ Gender         : Factor w/ 2 levels "Male","Female": 1 1 2 2 1 1 2 2 1 2 ...
##  $ Age            : int  19 35 26 27 19 27 27 32 25 35 ...
##  $ EstimatedSalary: int  19000 20000 43000 57000 76000 58000 84000 150000 33000 65000 ...
##  $ Purchased      : int  0 0 0 0 0 0 0 1 0 0 ...

summary(User_Data[,-c(1,5)])

##     Gender         Age        EstimatedSalary 
##  Male  :196   Min.   :18.00   Min.   : 15000  
##  Female:204   1st Qu.:29.75   1st Qu.: 43000  
##               Median :37.00   Median : 70000  
##               Mean   :37.66   Mean   : 69742  
##               3rd Qu.:46.00   3rd Qu.: 88000  
##               Max.   :60.00   Max.   :150000


``` r
library(psych)
describeBy(User_Data$EstimatedSalary, User_Data$Gender)

## 
##  Descriptive statistics by group 
## group: Male
##    vars   n     mean       sd median  trimmed     mad   min    max  range skew
## X1    1 196 67642.86 32421.82  68000 65468.35 28910.7 15000 150000 135000 0.49
##    kurtosis      se
## X1    -0.14 2315.84
## ------------------------------------------------------------ 
## group: Female
##    vars   n    mean       sd median  trimmed     mad   min    max  range skew
## X1    1 204 71759.8 35595.24  70500 69536.59 37806.3 15000 150000 135000 0.46
##    kurtosis      se
## X1     -0.7 2492.17

library(ggplot2)

## 
## Attaching package: 'ggplot2'

## The following objects are masked from 'package:psych':
## 
##     %+%, alpha

library(ggpubr)

Salary_Male <- ggplot(User_Data[User_Data$Gender == "Male", ], aes(x = EstimatedSalary)) +
  geom_histogram(binwidth = 5000, col = "black", fill = "blue") +
  xlab("Estimated Salary") +
  ylab("Frequency") +
  ggtitle("Salary Distribution - Male Employees")


Salary_Female <- ggplot(User_Data[User_Data$Gender == "Female", ], aes(x = EstimatedSalary)) +
  geom_histogram(binwidth = 5000, col = "black", fill = "red") +
  xlab("Estimated Salary") +
  ylab("Frequency") +
  ggtitle("Salary Distribution - Female Employees")


ggarrange(Salary_Male, Salary_Female, ncol = 2, nrow = 1)

library(ggpubr)
ggqqplot(User_Data,
         "EstimatedSalary",
         facet.by = "Gender")

Mean: Females have a higher estimated average salary ($71,759.80) then males ($67,642.86) across the sample

Median: According to the median, half of users make $70,000 or less and half of users make more than $70,000

Standard Deviation: Female estimated salary (35,595.24) has a higher Standard Deviation then male estimated salaries (32,421.82), suggesting higher variance for females

Skew: The distributions of males and females for estimated salary are positively skewed to the right, indicating that they are not normally distributed and that a few higher earners are influencing the mean upward

Research Question:

Is there a statistically significant difference between the expected salaries of males and females who use the site?

#Variance Test

library(car)

## Loading required package: carData

## 
## Attaching package: 'car'

## The following object is masked from 'package:psych':
## 
##     logit

leveneTest(User_Data$EstimatedSalary, group = User_Data$Gender)

## Levene's Test for Homogeneity of Variance (center = median)
##        Df F value  Pr(>F)  
## group   1  2.7631 0.09725 .
##       398                  
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1

#Normality Test

library (dplyr)

## 
## Attaching package: 'dplyr'

## The following object is masked from 'package:car':
## 
##     recode

## The following objects are masked from 'package:stats':
## 
##     filter, lag

## The following objects are masked from 'package:base':
## 
##     intersect, setdiff, setequal, union

library (rstatix)

## 
## Attaching package: 'rstatix'

## The following object is masked from 'package:stats':
## 
##     filter

User_Data %>%
      group_by(Gender) %>%
      shapiro_test (EstimatedSalary)

## # A tibble: 2 × 4
##   Gender variable        statistic          p
##   <fct>  <chr>               <dbl>      <dbl>
## 1 Male   EstimatedSalary     0.962 0.0000349 
## 2 Female EstimatedSalary     0.954 0.00000416

#Parametric Test

t.test(User_Data$EstimatedSalary ~ User_Data$Gender,
       var.equal = TRUE,
       alternative = "two.sided")

## 
##  Two Sample t-test
## 
## data:  User_Data$EstimatedSalary by User_Data$Gender
## t = -1.2079, df = 398, p-value = 0.2278
## alternative hypothesis: true difference in means between group Male and group Female is not equal to 0
## 95 percent confidence interval:
##  -10817.701   2583.807
## sample estimates:
##   mean in group Male mean in group Female 
##             67642.86             71759.80

#Non-Parametric Test

wilcox.test(User_Data$EstimatedSalary ~ User_Data$Gender,
            correct = FALSE,
            exact = FALSE,
            alternative = "two.sided")

## 
##  Wilcoxon rank sum test
## 
## data:  User_Data$EstimatedSalary by User_Data$Gender
## W = 18983, p-value = 0.3827
## alternative hypothesis: true location shift is not equal to 0

- In this case, the non-parametric test is more suitable.

- The assumption of normal distribution across both samples needed to perform parametric Independent samples t-test’s is violated

- the P value for both males and females resulting from the Shapiro test is less then 0.05, rejecting the null hypothesis that both males and females are normally distributed

#Effect size

library(effectsize)

## 
## Attaching package: 'effectsize'

## The following objects are masked from 'package:rstatix':
## 
##     cohens_d, eta_squared

## The following object is masked from 'package:psych':
## 
##     phi

effectsize(wilcox.test(User_Data$EstimatedSalary ~ User_Data$Gender,
            correct = FALSE,
            exact = FALSE,
            alternative = "two.sided"))

## r (rank biserial) |        95% CI
## ---------------------------------
## -0.05             | [-0.16, 0.06]

interpret_rank_biserial(0.05)

## [1] "very small"
## (Rules: funder2019)

The effect size of 0.05 is categorized as “very small” and indicates that gender there is no meaningful relationship between estimated salary and gender

Answering the research question:

- Accordng to the results of the Wilcoxon Rank Sum Test we fail to reject the null hypothesis that the mean estimated salary for males and females on the platform is the same

- The P-Value of 0.3827 output of the test is far greater then 0.05,

- The difference in sample means is highly likely to be a result of random variation and is not indicative of the larger population

- The effect size of 0.05 further concludes that gender is not a relevant factor in the determination of estimated salary

Salary_Data

2025-03-28

General

-The dataset contains a sample of 400 observations and 5 variables

- The population is the entire userbase of an online e-commerce platform

-The unit of observation is an individual user of the platform

Variables:

1: User Id

-Unique identification code of platform user

-Type:Categorical (Nominal)

2: Gender

-Gender (Male/Female) of user

-Type: Categorical (Nominal)

3: Age

-Age of user in years

-Type: Numeric (Ratio)

-Unit: Years

4: Estimated Salary

-Estimated annual salary of user

-Type: Numeric (Ratio)

-Unit: Currency

5: Purchased

-Indicates wether a user has purchased any quantity of a specific product

-Type: Categorical (Binary)

Source: Kaggle.com (2025) “User_Data”

Data Manipulation/Descriptive Statistics

Mean: Females have a higher estimated average salary ($71,759.80) then males ($67,642.86) across the sample

Median: According to the median, half of users make $70,000 or less and half of users make more than $70,000

Standard Deviation: Female estimated salary (35,595.24) has a higher Standard Deviation then male estimated salaries (32,421.82), suggesting higher variance for females

Skew: The distributions of males and females for estimated salary are positively skewed to the right, indicating that they are not normally distributed and that a few higher earners are influencing the mean upward

Research Question:

Is there a statistically significant difference between the expected salaries of males and females who use the site?

- In this case, the non-parametric test is more suitable.

- The assumption of normal distribution across both samples needed to perform parametric Independent samples t-test’s is violated

- the P value for both males and females resulting from the Shapiro test is less then 0.05, rejecting the null hypothesis that both males and females are normally distributed

The effect size of 0.05 is categorized as “very small” and indicates that gender there is no meaningful relationship between estimated salary and gender

Answering the research question:

- Accordng to the results of the Wilcoxon Rank Sum Test we fail to reject the null hypothesis that the mean estimated salary for males and females on the platform is the same

- The P-Value of 0.3827 output of the test is far greater then 0.05,

- The difference in sample means is highly likely to be a result of random variation and is not indicative of the larger population

- The effect size of 0.05 further concludes that gender is not a relevant factor in the determination of estimated salary