Do purchase amounts differ between members and non-members?

Packages

library(readxl)
library(ggpubr)

## Loading required package: ggplot2

library(dplyr)

## 
## Attaching package: 'dplyr'

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

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

library(effectsize)
library(effsize)

Import Data

FP2 <- read_excel("~/Library/CloudStorage/OneDrive-SaintLouisUniversity/AA-5221-12/Final Project/Independent t-test (or Mann-Whitney U)/FP2.xlsx")

Descriptive Statistics

FP2 %>%
  group_by(Membership) %>%
  summarise(
    Mean = mean(Purchase_Amount, na.rm = TRUE),
    Median = median(Purchase_Amount, na.rm = TRUE),
    SD = sd(Purchase_Amount, na.rm = TRUE),
    N = n()
  )

## # A tibble: 2 × 5
##   Membership  Mean Median    SD     N
##   <chr>      <dbl>  <dbl> <dbl> <int>
## 1 Member      73.4   66.9  25.6    60
## 2 Non-member  61.0   58.1  22.0    60

Histograms

hist(FP2$Purchase_Amount[FP2$Membership == "Member"],
     main = "Member",
     breaks = 15,
     col = "skyblue",
     border = "white")

# Data for members appears abnormally distributed.

hist(FP2$Purchase_Amount[FP2$Membership == "Non-member"],
     main = "Non-member",
     breaks = 15,
     col = "firebrick",
     border = "white")

# Data for non-members appears abnormally distributed.

Boxplot

ggboxplot(FP2,
          x = "Membership",
          y = "Purchase_Amount",
          color = "Membership",
          palette = "jco",
          add = "jitter")

# The members boxplot have outliers.
# The non-members boxplot have outliers.

Shapiro-Wilk

shapiro.test(FP2$Purchase_Amount[FP2$Membership == "Member"])

## 
##  Shapiro-Wilk normality test
## 
## data:  FP2$Purchase_Amount[FP2$Membership == "Member"]
## W = 0.90112, p-value = 0.0001446

# Purchase amounts for members were abnormally distributed (p < .001).
shapiro.test(FP2$Purchase_Amount[FP2$Membership == "Non-member"])

## 
##  Shapiro-Wilk normality test
## 
## data:  FP2$Purchase_Amount[FP2$Membership == "Non-member"]
## W = 0.94322, p-value = 0.007564

# Purchase amounts for non-members were abnormally distributed (p = .008).

Mann-Whitney U Test

wilcox.test(Purchase_Amount ~ Membership, data = FP2)

## 
##  Wilcoxon rank sum test with continuity correction
## 
## data:  Purchase_Amount by Membership
## W = 2332, p-value = 0.005276
## alternative hypothesis: true location shift is not equal to 0

Effect Size

mw_effect <- cliff.delta(Purchase_Amount ~ Membership, data = FP2)
print(mw_effect)

## 
## Cliff's Delta
## 
## delta estimate: 0.2955556 (small)
## 95 percent confidence interval:
##      lower      upper 
## 0.08916778 0.47760753

# A Mann-Whitney U Test was conducted to determine whether purchase amounts
# differed between members and non-members.
# Members (Mdn = 66.9) had significantly higher purchase amounts than
# non-members (Mdn = 58.1), W = 2332, p = .005.
# The effect size was small, Cliff's delta = .30.