Scenario 4

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?

NULL HYPOTHESIS (H0)

There is no difference between the Before scores and After scores.

ALTERNATE HYPOTHESIS (H1)

There is a difference between the Before scores and After scores.

IMPORT EXCEL FILE

Import your Excel dataset into R to conduct analyses.

INSTALL AND LOAD REQUIRED PACKAGE

# install.packages("readxl")
library(readxl)
## Warning: package 'readxl' was built under R version 4.5.2

IMPORT EXCEL FILE INTO R STUDIO

dataset <- read_excel("C:/Users/Murari_Lakshman/Downloads/A6R4.xlsx")

CALCULATE THE DIFFERENCE SCORES

Purpose: Calculate the difference between the Before scores versus the after scores.

Before <- dataset$PreCampaignSales
After <- dataset$PostCampaignSales

Differences <- After - Before

HISTOGRAM

Create a histogram for difference scores to visually check skewness and kurtosis.

CREATE THE HISTOGRAMS

You do not need to edit this code.

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

QUESTIONS

QUESTION 1: Is the histograms symmetrical, positively skewed, or negatively skewed?
A) The histogram looks positively skewed

QUESTION 2: Did the histogram look too flat, too tall, or did it have a proper bell curve?
A) The histogram does not have a proper bell-shaped curve.

SHAPIRO-WILK TEST

Check the normality for the difference between the groups.

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

QUESTION

QUESTION 1: Was the data normally distributed or abnormally distributed?
[NOTE: If p > 0.05 (P-value is GREATER than .05) this means the data is NORMAL (continue with Dependent t-test). If p < 0.05 (P-value is LESS than .05) this means the data is NOT normal (switch to Wilcoxon Sign Rank).]
A) The data is abnormally distributed because p < .05.

BOXPLOT

Check for any outliers impacting the mean.

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

QUESTIONS

QUESTION 1: How many dots are in your boxplot?
A) One or two dots.

QUESTION 2: Where are the dots in your boxplot?
A) Far away from the whiskers.

QUESTION 3: Based on the dots and there location, is the data normal?
A) Based on the box plot, we cannot determine if the data is normal or abnormal.

DESCRIPTIVE STATISTICS

Calculate the mean, median, SD, and sample size for each group.

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

DETERMINE STATISTICAL SIGNIFICANCE

If results were statistically significant (p < .05), continue to effect size section below.
If results were NOT statistically significant (p > .05), skip to reporting section below.
NOTE: Getting results that are not statistically significant does NOT mean you switch to Wilcoxon Sign Rank. The Wilcoxon Sign Rank test is only for abnormally distributed data — not based on outcome significance.

EFFECT SIZE FOR WILCOXON SIGN RANK TEST

Purpose: Determine how big of a difference there was between the group means.

INSTALL AND LOAD REQUIRED PACKAGE

# install.packages("rstatix")
library(rstatix)
## Warning: package 'rstatix' was built under R version 4.5.2
## 
## 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

Q1) What is the size of the effect?
A) A Rank Biserial Correlation of 0.261 indicates the difference between the group averages was moderate

Q2) Which group had the higher average score?
A) The post campaign sales have higher average score.

SUMMARY OF RESULTS

A Wilcoxon Signed-Rank Test was conducted to compare the sales before and after a marketing campaign of a clothing company. Median sales were significantly lower before the campaign (Md = 24624) than after (Md = 25086), V = 640, p = 0.0433. These results indicate that the campaign has successfully managed to increase the clothing brand’s sales. The effect size was r = 0.261, indicating a moderate effect.