Does customer spending differ before and after a promotional offer?

Packages

library(readxl)
library(ggpubr)

## Loading required package: ggplot2

library(effsize)
library(rstatix)

## 
## Attaching package: 'rstatix'

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

Import Data

FP1 <- read_excel("~/Library/CloudStorage/OneDrive-SaintLouisUniversity/AA-5221-12/Final Project/Dependent t-test (or Wilcoxon Signed Rank)/FP1.xlsx")

Before and After

Before <- FP1$Spending_Before
After <- FP1$Spending_After

Differences <- After - Before

Descriptive Statistics

mean(Before, na.rm = TRUE)

## [1] 109.4618

median(Before, na.rm = TRUE)

## [1] 106.83

sd(Before, na.rm = TRUE)

## [1] 33.83085

mean(After, na.rm = TRUE)

## [1] 122.2797

median(After, na.rm = TRUE)

## [1] 119.265

sd(After, na.rm = TRUE)

## [1] 38.42304

Histogram

hist(Differences,
     breaks = 15,
     col = "blue",
     border = "white")

# Data for the difference scores appears normally distributed.

Boxplot

boxplot(Differences,
        main = "Distribution of Score Differences (After - Before)",
        ylab = "Difference in Scores",
        col = "blue",
        border = "darkblue")

# The difference scores boxplot does not have outliers.

Shapiro-Wilk

shapiro.test(Differences)

## 
##  Shapiro-Wilk normality test
## 
## data:  Differences
## W = 0.98179, p-value = 0.5086

# The difference scores are normally distributed (p = .509).

Dependent t-Test

t.test(Before, After, paired = TRUE, na.action = na.omit)

## 
##  Paired t-test
## 
## data:  Before and After
## t = -4.4733, df = 59, p-value = 3.568e-05
## alternative hypothesis: true mean difference is not equal to 0
## 95 percent confidence interval:
##  -18.551524  -7.084142
## sample estimates:
## mean difference 
##       -12.81783

Effect Size

cohen.d(Before, After, paired = TRUE)

## 
## Cohen's d
## 
## d estimate: -0.347826 (small)
## 95 percent confidence interval:
##      lower      upper 
## -0.5063935 -0.1892585

# A Dependent t-Test was conducted to determine if there was a difference
# in customer spending between Before and After the promotional offer.
# Before scores (M = 109.46, SD = 33.83) were significantly different
# from After scores (M = 122.28, SD = 38.42),
# t(59) = -4.47, p < .001.
# The effect size was small, Cohen's d = -0.348.