Homework 1
2024-01-06
Metka Pintar
RQ: Does the total amount of a transaction differ between the gender?
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 30Unit 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).
2. Analysis
summary(mydata) #Showing the descriptive statistics## Transaction.ID Date Customer.ID
## Min. : 1.0 Length:1000 Length:1000
## 1st Qu.: 250.8 Class :character Class :character
## Median : 500.5 Mode :character Mode :character
## Mean : 500.5
## 3rd Qu.: 750.2
## Max. :1000.0
## Gender Age Product.Category
## Length:1000 Min. :18.00 Length:1000
## Class :character 1st Qu.:29.00 Class :character
## Mode :character Median :42.00 Mode :character
## Mean :41.39
## 3rd Qu.:53.00
## Max. :64.00
## Quantity Price.per.Unit Total.Amount
## Min. :1.000 Min. : 25.0 Min. : 25
## 1st Qu.:1.000 1st Qu.: 30.0 1st Qu.: 60
## Median :3.000 Median : 50.0 Median : 135
## Mean :2.514 Mean :179.9 Mean : 456
## 3rd Qu.:4.000 3rd Qu.:300.0 3rd Qu.: 900
## Max. :4.000 Max. :500.0 Max. :2000Explanation of the descriptive statistics:
- Max Age = 64; The oldest customer was 64 years old.
- Median Quantity = 3; Half of the customers purchased up to 3 products, the other half purchased more than 3 items.
- Mean Total.Amount = 456; The average total monetary value of the transaction is 456 monetary units.
- 3rd quantile Price.per.Unit = 300; 75% of the products has a price per unit up to 300 units, the price per unit of the other 25% of the products is higher than 300 units.
mydata2 <- mydata[, c(4,9)] #Including only 4th and 9th column (only needed data)
head(mydata2)## Gender Total.Amount
## 1 Male 150
## 2 Female 1000
## 3 Male 30
## 4 Male 500
## 5 Male 100
## 6 Female 30set.seed(1) #Setting initial point of sampling
mydata2 <- mydata2[sample(nrow(mydata2), 100, replace = TRUE),] #Random sample of 100 unitslibrary(psych)
describeBy(mydata2$Total.Amount, g = mydata2$Gender)#Showing descriptive statistics separately for males and females##
## Descriptive statistics by group
## group: Female
## vars n mean sd median trimmed mad min max range skew
## X1 1 53 348.68 471.83 100 252.09 103.78 25 2000 1975 1.75
## kurtosis se
## X1 2.23 64.81
## ----------------------------------------------------
## group: Male
## vars n mean sd median trimmed mad min max range skew
## X1 1 47 424.79 527.89 100 342.18 103.78 30 2000 1970 1.25
## kurtosis se
## X1 0.32 77Positive skewness indicate that the distribution is asymmetrical to the right.
library(ggplot2) ##
## Attaching package: 'ggplot2'## The following objects are masked from 'package:psych':
##
## %+%, alphaggplot(mydata2, aes(x = Total.Amount)) +
geom_histogram(binwidth = 30, colour = "royalblue2", fill = "steelblue3") +
facet_wrap(~Gender, ncol = 1) +
ylab("Frequency") #Graphical presentation of the total amount transaction for males and females
From the graph we can also clearly see that both distributions are asymmetrical to the right.
Testing the hypothesis
Parametric test: Welch’s t-test
t.test(mydata2$Total.Amount ~ mydata2$Gender,
paired = FALSE,
var.equal = FALSE,
alternative = "two.sided") #Independent t.test with Welch correction##
## Welch Two Sample t-test
##
## data: mydata2$Total.Amount by mydata2$Gender
## t = -0.7562, df = 92.982, p-value = 0.4514
## alternative hypothesis: true difference in means between group Female and group Male is not equal to 0
## 95 percent confidence interval:
## -275.9706 123.7546
## sample estimates:
## mean in group Female mean in group Male
## 348.6792 424.7872- H0: mu_male - mu_female = 0
- H1: mu_male - mu_female =/ 0
We can not reject H0 (p value: 0.4514 > 0.05). We can not say that there is a difference in the total transaction amount between males and females.
library(rstatix)##
## Attaching package: 'rstatix'## The following object is masked from 'package:stats':
##
## filtermydata2 %>%
group_by(Gender) %>%
shapiro_test(Total.Amount) #Checking whether variable is normally distributed## # A tibble: 2 × 4
## Gender variable statistic p
## <chr> <chr> <dbl> <dbl>
## 1 Female Total.Amount 0.692 0.00000000300
## 2 Male Total.Amount 0.740 0.0000000892- H0: Variable is normally distributed.
- H1: Variable is not normally distributed.
We reject HO at p<0.001 and accept H1, variable total amount of a transaction is not normally distributed.
Checking the assumptions
- Numerical variable -> YES (total amount of transaction is in money unit)
- Normal distribution -> NO (not normally distributed based on Shapiro-Wilk normality test)
- Variances of salaries are the same between both departments -> NO -> Welch correction
Since the assumption for normality is not met, we can’t use parametric test. Non-parametric test is more appropriate however, there is reduced statistical power compared to parametric tests.
Non-parametric test: Wilcoxon Rank Sum Test
wilcox.test(mydata2$Total.Amount ~ mydata2$Gender,
paired = FALSE,
correct = FALSE,
exact = FALSE,
alternative = "two.sided") #Applying alternative non-parametrical test##
## Wilcoxon rank sum test
##
## data: mydata2$Total.Amount by mydata2$Gender
## W = 1147, p-value = 0.4944
## alternative hypothesis: true location shift is not equal to 0- H0: Location distribution of total amount is the same for male and females.
- H1: Location distribution of total amount is not the same for male and females.
We can not reject H0 (p value > 0.005). Based on the sample we can not say that location distribution of total amount is not the same for males and females.
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':
##
## phieffectsize(wilcox.test(mydata2$Total.Amount ~ mydata2$Gender,
paired = FALSE,
correct = FALSE,
exact = FALSE,
alternative = "two.sided")) #Calculating the effect size## r (rank biserial) | 95% CI
## ---------------------------------
## -0.08 | [-0.30, 0.15]interpret_rank_biserial(0.01) #Interpreting the effect size## [1] "tiny"
## (Rules: funder2019)3. Conclusion
Using the sample data, we are unable to say that the total amount of transactions differed between male and female customers (p value > 0.005). The effect size is tiny, r = 0.08; the difference is not significant.