HW2

Metka Pintar

RQ1: Is there a relationship between age of a customer and the total amount of a transaction they make?

RQ2: Is there a relationship between gender and the category of a product they purchase?

1. Data

Source of the data: https://www.kaggle.com/datasets/mohammadtalib786/retail-sales-dataset/data

mydata <- read.table("./retail_sales_dataset.csv", header=TRUE, sep = ",", dec = ",") #Reading the data
head(mydata) #Showing first 6 rows of the data

##   Transaction.ID       Date Customer.ID Gender Age Product.Category
## 1              1 2023-11-24     CUST001   Male  34           Beauty
## 2              2 2023-02-27     CUST002 Female  26         Clothing
## 3              3 2023-01-13     CUST003   Male  50      Electronics
## 4              4 2023-05-21     CUST004   Male  37         Clothing
## 5              5 2023-05-06     CUST005   Male  30           Beauty
## 6              6 2023-04-25     CUST006 Female  45           Beauty
##   Quantity Price.per.Unit Total.Amount
## 1        3             50          150
## 2        2            500         1000
## 3        1             30           30
## 4        1            500          500
## 5        2             50          100
## 6        1             30           30

Unit of observation: 1 customer (not specified where, when; crafted data)

Sample size: 1000

Definition and units of variables:

Transaction.ID: A unique identifier for each transaction.
Date: The date when the transaction occurred (year, month, day).
Customer ID: A unique identifier for each customer.
Gender: The gender of the customer (Male,Female).
Age: The age of the customer (years).
Product.Category:The category of the purchased product (Electronics, Clothing, Beauty).
Quantity: The number of units of the product purchased.
Price.per.Unit: The price of one unit of the product(money unit is not specified).
Total.Amount: The total monetary value of the transaction (money unit is not specified).

mydata3 <- mydata[, c(4,5,6,9)] #Including only 4th, 5th, 6th and 9th column (only needed data)
head(mydata3)

##   Gender Age Product.Category Total.Amount
## 1   Male  34           Beauty          150
## 2 Female  26         Clothing         1000
## 3   Male  50      Electronics           30
## 4   Male  37         Clothing          500
## 5   Male  30           Beauty          100
## 6 Female  45           Beauty           30

#Creating a factor variable for product category
mydata3$Product.CategoryFactor <- factor(mydata3$Product.Category, 
                                levels = c("Beauty", "Clothing", "Electronics"), 
                                labels = c("Beauty", "Clothing", "Electronics")) 

#Creating a factor variable for gender
mydata3$GenderFactor <- factor(mydata3$Gender, 
                                levels = c("Female", "Male"), 
                                labels = c("Female", "Male")) 
   
head(mydata3, 6)

##   Gender Age Product.Category Total.Amount Product.CategoryFactor
## 1   Male  34           Beauty          150                 Beauty
## 2 Female  26         Clothing         1000               Clothing
## 3   Male  50      Electronics           30            Electronics
## 4   Male  37         Clothing          500               Clothing
## 5   Male  30           Beauty          100                 Beauty
## 6 Female  45           Beauty           30                 Beauty
##   GenderFactor
## 1         Male
## 2       Female
## 3         Male
## 4         Male
## 5         Male
## 6       Female

summary(mydata3) #Showing the descriptive statistics

##     Gender               Age        Product.Category    Total.Amount 
##  Length:1000        Min.   :18.00   Length:1000        Min.   :  25  
##  Class :character   1st Qu.:29.00   Class :character   1st Qu.:  60  
##  Mode  :character   Median :42.00   Mode  :character   Median : 135  
##                     Mean   :41.39                      Mean   : 456  
##                     3rd Qu.:53.00                      3rd Qu.: 900  
##                     Max.   :64.00                      Max.   :2000  
##  Product.CategoryFactor GenderFactor
##  Beauty     :307        Female:510  
##  Clothing   :351        Male  :490  
##  Electronics:342                    
##                                     
##                                     
##

Explanation of the descriptive statistics:

Max Age = 64; The oldest customer was 64 years old.
Median Age = 42; Half of the customers were up to 42 years old, the other half were more than 42 years old.
Mean Total.Amount = 456; The average total monetary value of the transaction is 456 monetary units.
3rd quantile Total.Amount = 900; 75% of the customers have a total amount up to 900 monetary units, the total amount of the other 25% of the customers is higher than 900 monetary units.

2. Analysis

RQ1: Is there a relationship between age and total amount of a transaction?

#install.packages("psych")
library(car)

## Loading required package: carData

scatterplot(mydata3$Age, mydata3$Total.Amount, 
            ylim = c(20, 2005),
            xlim = c(15,70),
            col = "darkgreen",
            ylab = "Total amount of a transaction",
            xlab = "Age",
            smooth=FALSE) #showing the scatterplot

shapiro.test(mydata3$Total.Amount) #checking the normality distribution for variable total amount

## 
##  Shapiro-Wilk normality test
## 
## data:  mydata3$Total.Amount
## W = 0.74891, p-value < 2.2e-16

H0: The amount of total transaction is normally distributed

H1: The amount of total transaction is not normally distributed

We reject H0 (p<0.001). We can not say that the amount of total transaction is normally distributed.

shapiro.test(mydata3$Age) #checking the normality distribution for variable gender

## 
##  Shapiro-Wilk normality test
## 
## data:  mydata3$Age
## W = 0.95241, p-value < 2.2e-16

H0: Age is normally distributed

H1: Age is not normally distributed

We reject H0 (p<0.001). We can not say that age is normally distributed.

The assumption of normality of both variables is violated. I need to use the non-parametric version, Spearman correlation coefficient.

library(Hmisc)

## 
## Attaching package: 'Hmisc'

## The following objects are masked from 'package:base':
## 
##     format.pval, units

cor(mydata3$`Age`, mydata3$`Total.Amount`, 
      method= "pearson") #Pearson correlation coefficient

## [1] -0.06056802

cor.test(mydata3$`Age`, mydata3$`Total.Amount`,
         method = "pearson",
         exact = FALSE)

## 
##  Pearson's product-moment correlation
## 
## data:  mydata3$Age and mydata3$Total.Amount
## t = -1.9169, df = 998, p-value = 0.05553
## alternative hypothesis: true correlation is not equal to 0
## 95 percent confidence interval:
##  -0.12210264  0.00143043
## sample estimates:
##         cor 
## -0.06056802

As I said, Pearson correlation coefficient is not appropriate, we use Spearman correlation coefficient.

cor(mydata3$`Age`, mydata3$`Total.Amount`, 
      method= "spearman")

## [1] -0.03786403

cor.test(mydata3$`Age`, mydata3$`Total.Amount`,
         method = "spearman",
         exact = FALSE) #Spearman correlation coefficient

## 
##  Spearman's rank correlation rho
## 
## data:  mydata3$Age and mydata3$Total.Amount
## S = 172977165, p-value = 0.2316
## alternative hypothesis: true rho is not equal to 0
## sample estimates:
##         rho 
## -0.03786403

H0: There is no correlation between age and the amount of total transaction.

H1: There is a correlation between age and the amount of total transaction.

We can not reject H0 (p value is too high). We can not say that there is a statistically significant correlation between age and the total amount of a transaction.

Linear relationship between age and the total amount of a transaction is negative and very weak (Spearman correlation coefficient is -0.038)

RQ2: Is there a relationship between gender and the category of a product?

results <- chisq.test(mydata3$GenderFactor, mydata3$Product.CategoryFactor, 
                      correct = TRUE) # Pearson Chi2 test

results

## 
##  Pearson's Chi-squared test
## 
## data:  mydata3$GenderFactor and mydata3$Product.CategoryFactor
## X-squared = 1.6738, df = 2, p-value = 0.433

H0:There is no association between the category of a product and gender.

H1:There is association between the category of a product and gender.

We can not reject H0 (p value is too high). Based on the sample data we can not say that there is an association between gender and the category of a product.

addmargins(results$observed) #Checking empirical frequencies

##                     mydata3$Product.CategoryFactor
## mydata3$GenderFactor Beauty Clothing Electronics  Sum
##               Female    166      174         170  510
##               Male      141      177         172  490
##               Sum       307      351         342 1000

round(results$expected) #Checking expected frequencies

##                     mydata3$Product.CategoryFactor
## mydata3$GenderFactor Beauty Clothing Electronics
##               Female    157      179         174
##               Male      150      172         168

Assumptions

Observations must be independent. - Assumption is met.
All expected frequencies are greater than 1. - Assumption is met.
Max 20% of frequencies can be between 1 and 5. - Assumption is met.

round(results$res, 2) #Checking residuals

##                     mydata3$Product.CategoryFactor
## mydata3$GenderFactor Beauty Clothing Electronics
##               Female   0.75    -0.37       -0.33
##               Male    -0.77     0.38        0.34

All std. residuals are below 1.96 critical value, deviations are not statistically significant.

There is more than expected females that buy beauty products and less than expected females that buy clothes and electronics products.
There is less than expected males that buy beauty products and more than expected males that buy clothes and electronics products

addmargins(round(prop.table(results$observed), 3))

##                     mydata3$Product.CategoryFactor
## mydata3$GenderFactor Beauty Clothing Electronics   Sum
##               Female  0.166    0.174       0.170 0.510
##               Male    0.141    0.177       0.172 0.490
##               Sum     0.307    0.351       0.342 1.000

Explanation of Female/Beauty = 0.166:

Out of 1000 people, there is 16.6% of them that are female and buy beauty products.

addmargins(round(prop.table(results$observed, 1), 3), 2)

##                     mydata3$Product.CategoryFactor
## mydata3$GenderFactor Beauty Clothing Electronics   Sum
##               Female  0.325    0.341       0.333 0.999
##               Male    0.288    0.361       0.351 1.000

Explanation of Male/Electronics = 0.351:

Out of all males, 35.1% of them buy electronics products. .

addmargins(round(prop.table(results$observed, 2), 3), 1)

##                     mydata3$Product.CategoryFactor
## mydata3$GenderFactor Beauty Clothing Electronics
##               Female  0.541    0.496       0.497
##               Male    0.459    0.504       0.503
##               Sum     1.000    1.000       1.000

Explanation of Female/Beauty = 0.541:

Out of all people that buy beauty products, 54.1% of them are females.

library(effectsize)
effectsize::cramers_v(mydata3$Product.CategoryFactor, mydata3$GenderFactor) #Calculating the effect size; Cramer's V statistics

## Cramer's V (adj.) |       95% CI
## --------------------------------
## 0.00              | [0.00, 1.00]
## 
## - One-sided CIs: upper bound fixed at [1.00].

interpret_cramers_v(0.00)

## [1] "tiny"
## (Rules: funder2019)

fisher.test(mydata3$Product.CategoryFactor, mydata3$GenderFactor) #Fisher test for robustness

## 
##  Fisher's Exact Test for Count Data
## 
## data:  mydata3$Product.CategoryFactor and mydata3$GenderFactor
## p-value = 0.4355
## alternative hypothesis: two.sided

H0: Odds ratio = 1

H1: Odds ratio =/ 1

Based on the sample data we can not reject H0 (p value is too high). Both genders have equal odds for the product category.

3. Conclusion

RQ1: We can not reject H0 (p value is too high). We can not say that there is a statistically significant correlation between age and the total amount of a transaction.