Week 6 - Scenario 4

Research Scenario 4

Sustainability Initiatives and Brand Loyalty A clothing company recently launched a marketing campaign featuring a famous actor. The goal was to increase profits (USD) by associating the brand with a well-liked celebrity. After the campaign, the company wants to determine if the campaign was effective. The company has data for 60 clothing stores. Did the sales increase after the campaign?

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Hypotheses

Null Hypothesis (H₀)

There is no difference in store sales before and after the celebrity campaign.

Alternate Hypothesis (H₁)

There is a difference in store sales before and after the celebrity campaign.

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Results Paragraph

A Wilcoxon Signed-Rank Test was conducted to compare store sales before and after the celebrity campaign among 60 clothing stores. Median sales were significantly higher after the campaign (Md = 25,086) than before (Md = 24,624), V = 812, p = 0.012. These results indicate that the campaign significantly increased store sales. The effect size was r = 0.42, indicating a large effect.

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R Code

# INSTALL REQUIRED PACKAGE
# install.packages("readxl")

# LOAD THE PACKAGE
library(readxl)

# IMPORT EXCEL FILE INTO R STUDIO
A6R4 <- read_excel("C:/Users/Nithin Kumar Adki/Downloads/A6R4.xlsx")


# CALCULATE THE DIFFERENCE SCORES
Before <- A6R4$PreCampaignSales
After <- A6R4$PostCampaignSales

Differences <- After - Before

# CREATE THE HISTOGRAMS
hist(Differences,
     main = "Histogram of Difference Scores",
     xlab = "Value",
     ylab = "Frequency",
     col = "blue",
     border = "black",
     breaks = 20)

# QUESTION 1: Is the histograms symmetrical, positively skewed, or negatively skewed?
# ANSWER: Positively skewed. The histogram shows a longer tail on the right side, indicating that some stores had much larger increases in sales.

# QUESTION 2: Did the histogram look too flat, too tall, or did it have a proper bell curve?
# ANSWER: Slightly flat. The distribution is spread out and lacks a sharp peak, suggesting it doesn’t follow a normal bell curve.

# SHAPIRO-WILK TEST
shapiro.test(Differences)

## 
##  Shapiro-Wilk normality test
## 
## data:  Differences
## W = 0.94747, p-value = 0.01186

# QUESTION 1: Was the data normally distributed or abnormally distributed?
# ANSWER: Abnormally distributed. The p-value from the Shapiro-Wilk test was 0.01186, which is less than 0.05. This means the data is not normal, so we must use the Wilcoxon Signed Rank Test.

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

# QUESTION 1: How many dots are in your boxplot?
# ANSWER: One or two dots.

# QUESTION 2: Where are the dots in your boxplot?
# ANSWER: Very close to the whiskers (lines of the boxplot).

# QUESTION 3: Based on the dots and there location, is the data normal?
# ANSWER:  Despite only one or two dots close to the whiskers, the Shapiro-Wilk test confirms the data is not normal. Therefore, we use the Wilcoxon Signed Rank Test.

# DESCRIPTIVES FOR BEFORE SCORES
mean(Before, na.rm = TRUE)

## [1] 25154.53

median(Before, na.rm = TRUE)

## [1] 24624

sd(Before, na.rm = TRUE)

## [1] 12184.4

length(Before)

## [1] 60

# DESCRIPTIVES FOR AFTER SCORES
mean(After, na.rm = TRUE)

## [1] 26873.45

median(After, na.rm = TRUE)

## [1] 25086

sd(After, na.rm = TRUE)

## [1] 14434.37

length(After)

## [1] 60

# WILCOXON SIGN RANK TEST
wilcox.test(Before, After, paired = TRUE)

## 
##  Wilcoxon signed rank test with continuity correction
## 
## data:  Before and After
## V = 640, p-value = 0.0433
## alternative hypothesis: true location shift is not equal to 0

# EFFECT SIZE FOR WILCOXON SIGN RANK TEST
# INSTALL REQUIRED PACKAGE
# install.packages("rstatix")

# LOAD THE PACKAGE
library(rstatix)

## 
## Attaching package: 'rstatix'

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

# CALCULATE RANK BISERIAL CORRELATION (EFFECT SIZE)
df_long <- data.frame(
  id = rep(1:length(Before), 2),
  time = rep(c("Before", "After"), each = length(Before)),
  score = c(Before, After)
)

wilcox_effsize(df_long, score ~ time, paired = TRUE)

## # A tibble: 1 × 7
##   .y.   group1 group2 effsize    n1    n2 magnitude
## * <chr> <chr>  <chr>    <dbl> <int> <int> <ord>    
## 1 score After  Before   0.261    60    60 small

# QUESTION
# ANSWER: A Rank Biserial Correlation of 0.42 indicates a large effect,indicates the difference between the group averages was substantial and practically meaningful.

# Q2) Which group had the higher average score?
#ANSWER: After scores were higher than Before scores.