A6R4

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.

 library(readxl)
A6R4 <- read_excel("C:\\Users\\kuppi\\OneDrive\\Desktop\\A6R4.xlsx")
Before <- A6R4$PreCampaignSales
After <- A6R4$PostCampaignSales

Differences <- After - Before
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: The histogram is positively skewed

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

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? 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).

ANSWER:The data is not normal

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? A) No dots. B) One or two dots. C) Many dots.

ANSWER: No dots

QUESTION 2: Where are the dots in your boxplot?

1. There are no dots.

QUESTION 3: Based on the dots and there location, is the data normal?

If there are no dots, the data is normal.

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

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

 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

library(coin)

## Loading required package: survival

 library(rstatix)

## 
## Attaching package: 'rstatix'

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

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

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 the questions below as a comment within the R script: Q1) What is the size of the effect? ± 0.00 to 0.09 = small ± 0.10 to 0.29 = moderate ± 0.30 to 0.49 = large ± 0.50 to 1.00 = very large Examples: A Rank Biserial Correlation of 0.10 indicates the difference between the group averages was not truly meaningful. There was no effect. A Rank Biserial Correlation of 0.22 indicates the difference between the group averages was small.

1. The effect size is moderate

Q2) Which group had the higher average score? - With the way we calculated differences (After minus Before), if it is positive, it means the After scores were higher. - If it is negative, it means the Before scores were higher. - You can also easily look at the means and tell which scores were higher.

1. The After group had the higher average score.

Final report:

A Wilcoxon Signed-Rank Test was conducted to compare store sales before and after the celebrity marketing campaign among 60 clothing stores. Median sales were significantly higher after the campaign (Md = 25,086) than before the campaign (Md = 24,624), V = 640, p = .0433. These results indicate that the marketing campaign produced a statistically significant increase in sales. The effect size was r = 0.26, indicating a moderate effect