DEPENDENT T-TEST & WILCOXON SIGN RANK

Used to test if there is a difference between Before scores and After scores (comparing the means).

NULL HYPOTHESIS (H0)

The null hypothesis is ALWAYS used.

There is no difference in sales after the Campaign.

ALTERNATE HYPOTHESIS (H1)

Choose ONE of the three options below (based on your research scenario):

2) DIRECTIONAL ALTERNATE HYPOTHESES: There is a difference in sales after the campaign

IMPORT EXCEL FILE

Purpose: Import your Excel dataset into R to conduct analyses.

install.packages(“readxl”)

library(readxl)

dataset <- read_excel("/Users/mac/Downloads/A6R4.xlsx")

CALCULATE THE DIFFERENCE SCORES

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.

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

WRITE THE REPORT

Answer the questions below as a comment within the R script:

Q1) Is the histograms symmetrical, positively skewed, or negatively skewed?

#It is positively skewed # Q2) Did the histogram look too flat, too tall, or did it have a proper bell curve? # It is too flat

SHAPIRO-WILK TEST

Check the normality for the difference between the groups.

CONDUCT SHAPIRO-WILK TEST

shapiro.test(Differences)

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

QUESTIONS

Answer the questions below as a comment within the R script:

Q1)Was the data normally distributed or abnormally distributed?

It was 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).

BOXPLOT

Check for any outliers impacting the mean.

CREATE THE BOXPLOT

Boxplot of Difference Scores

boxplot(Before, After,
        names = c("Before", "After"),
        main = "Boxplot of Before and After Scores",
        col = c("lightblue", "lightgreen"))

QUESTIONS

Answer the questions below as a comment within the R script:

Q1) Were there any dots outside of the boxplot? Are these dots close to the whiskers of the boxplot or are they very far away?yes

If there are no dots, continue with Dependent t-test

If there are a few dots (two or less), and they are close to the whiskers, continue with Dependent t-test.

If there are a few dots (two or less), and they are far away from the whiskers, consider switching to Wilcoxon Sign Rank.

If there are many dots (more than one or two) and they are very far away from the whiskers, you should switch to a Wilcoxon Sign Rank. .

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

Summary Paragraph:

The Wilcoxon Signed-Rank Test was used to compare the sales during the campaign with those after the campaign to compare the sales of 60 individuals. The findings indicated that the sales were positively significantly higher during the post-campaign period (Median = 25,086) as compared to pre-campaign period (Median = 24,624) V = 640, p =.043. The effect size = 0.26 which is moderate. According to these findings, the campaign had statistically significant impact on increase in sales.