Research Scenario 4

DEPENDENT T-TEST & WILCOXON SIGN RANK

NULL HYPOTHESIS (H0)
There is no difference between sales before campaign and after campaign.

ALTERNATE HYPOTHESIS (H1)
There is a difference between the sales before campaign and after campaign

LOAD THE PACKAGE

library(readxl)

IMPORT EXCEL FILE INTO R STUDIO

dataset <- read_excel("C:\\Users\\burug\\Downloads\\A6R4.xlsx")

CALCULATE THE DIFFERENCE SCORES

Before <- dataset$PreCampaignSales
After <- dataset$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

QUESTION 2: Did the histogram look too flat, too tall, or did it have a proper bell curve?
ANSWER: Too flat

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: The data is abnormally distributed (p< 0.04).

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 Dot

QUESTION 2: Where are the dots in your boxplot?
One dot far to whiskers

QUESTION 3: Based on the dots and there location, is the data normal?
The data is not normal, dot is far away from whiskers.

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

LOAD THE PACKAGE

library(rstatix)

## 
## Attaching package: 'rstatix'

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

library(coin)

## Loading required package: survival

## 
## Attaching package: 'coin'

## The following objects are masked from 'package:rstatix':
## 
##     chisq_test, friedman_test, kruskal_test, sign_test, wilcox_test

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

Q1) What is the size of the effect?
A Rank Biserial Correlation of 0.261 indicates the difference between the sales before campaign and after campaign is moderate.
Q2) Which group had the higher average score?
The sales were moderately higher after campaign.

REPORT
A Wilcoxon Signed-Rank Test was conducted to compare sales before campaign and after campaign. among 60 clothing stores. Median before campaign were significantly lower (Md = 24624) than Median after campaign (Md = 25086), V = 640, p = .0433. These results indicate that the sales are moderately higher after campaign. The effect size was r = 0.261, indicating a moderate effect.