Research Scenario 2

In order to be more competitive in the market, a technology store wants to start selling their laptops and anti-virus software as a bundle to small businesses. A bundle is when two products are sold together at a lower price than if they were purchased separately. Before offering the bundle, the store wants to make sure the two products are commonly purchased together. The store has data from the past year showing how many laptops and how many anti-virus software licenses each small business bought from them. Analyze the data to determine if there is a positive correlation between the number of laptops purchased and the number of anti-virus licenses purchased.

PURPOSE

Used to test the relationship between two continuous variables.

NULL HYPOTHESIS

There is no relationship between laptops and anti-virus licenses purchased.

ALTERNATE HYPOTHESIS

There is a relationship between laptops and anti-virus licenses purchased.

options(repos = c(CRAN = "https://cloud.r-project.org"))
install.packages("readxl")
## Installing package into 'C:/Users/tsury/AppData/Local/R/win-library/4.5'
## (as 'lib' is unspecified)
## package 'readxl' successfully unpacked and MD5 sums checked
## 
## The downloaded binary packages are in
##  C:\Users\tsury\AppData\Local\Temp\RtmpcjVqjI\downloaded_packages
library(readxl)
dataset <- read_excel("C:\\Users\\tsury\\Downloads\\A5RQ2.xlsx")

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DESCRIPTIVE STATISTICS

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#install.packages("psych")
library(psych)
describe(dataset[, c("Antivirus", "Laptop")])
##           vars   n  mean    sd median trimmed   mad min max range  skew
## Antivirus    1 122 50.18 13.36     49   49.92 12.60  15  83    68  0.15
## Laptop       2 122 40.02 12.30     39   39.93 11.86   8  68    60 -0.01
##           kurtosis   se
## Antivirus    -0.14 1.21
## Laptop       -0.32 1.11

===============================================

CHECK THE NORMALITY OF THE CONTINUOUS VARIABLES

Two methods will be used to check the normality of the continuous variables. First, you will create histograms to visually inspect the normality of the variables. Next, you will conduct a test called the Shapiro-Wilk test to inspect the normality of the variables. It is important to know whether or not the data is normal to determine which inferential test should be used.

CREATE A HISTOGRAM FOR EACH CONTINUOUS VARIABLE

A histogram is used to visually check if the data is normally distributed.

hist(dataset$Antivirus,
     main = "Histogram of Antivirus",
     xlab = "Value",
     ylab = "Frequency",
     col = "lightblue",
     border = "black",
     breaks = 20)

hist(dataset$Laptop,
     main = "Histogram of Laptop",
     xlab = "Value",
     ylab = "Frequency",
     col = "lightgreen",
     border = "black",
     breaks = 20)

QUESTION

Q1) Check the SKEWNESS of the VARIABLE 1 histogram. In your opinion, does the histogram look symmetrical, positively skewed, or negatively skewed? A) The histogram for anti-virus purchases looks symmetrical

Q2) Check the KURTOSIS of the VARIABLE 1 histogram. In your opinion, does the histogram look too flat, too tall, or does it have a proper bell curve? A) After closely checking at the Kurtosis of anti-virus purchases, it has a proper bell-shaped curve

Q3) Check the SKEWNESS of the VARIABLE 2 histogram. In your opinion, does the histogram look symmetrical, positively skewed, or negatively skewed? A) The histogram for laptop purchases looks symmetrical

Q4) Check the KUROTSIS of the VARIABLE 2 histogram. In your opinion, does the histogram look too flat, too tall, or does it have a proper bell curve? A) After closely checking at the Kurtosis of laptop purchases, it has a proper bell-shaped curve

PURPOSE

Use a statistical test to check the normality of the continuous variables. The Shapiro-Wilk Test is a test that checks skewness and kurtosis at the same time. The test is checking “Is this variable the SAME as normal data (null hypothesis) or DIFFERENT from normal data (alternate hypothesis)?” For this test, if p is GREATER than .05 (p > .05), the data is NORMAL. If p is LESS than .05 (p < .05), the data is NOT normal.

shapiro.test(dataset$Antivirus)
## 
##  Shapiro-Wilk normality test
## 
## data:  dataset$Antivirus
## W = 0.99419, p-value = 0.8981
shapiro.test(dataset$Laptop)
## 
##  Shapiro-Wilk normality test
## 
## data:  dataset$Laptop
## W = 0.99362, p-value = 0.8559

QUESTION

Was the data normally distributed for Variable 1? YES

Was the data normally distributed for Variable 2? YES

Since both of variables are normal, change to the Pearson Correlation test.

VISUALLY DISPLAY THE DATA

PURPOSE

A scatterplot visually shows the relationship between two continuous variables.

#install.packages("ggplot2")
install.packages("ggpubr")
## Installing package into 'C:/Users/tsury/AppData/Local/R/win-library/4.5'
## (as 'lib' is unspecified)
## package 'ggpubr' successfully unpacked and MD5 sums checked
## 
## The downloaded binary packages are in
##  C:\Users\tsury\AppData\Local\Temp\RtmpcjVqjI\downloaded_packages

LOAD THE PACKAGE

Always reload the package you want to use.

library(ggplot2)
## 
## Attaching package: 'ggplot2'
## The following objects are masked from 'package:psych':
## 
##     %+%, alpha
library(ggpubr)

CREATE THE SCATTERPLOT

ggscatter(dataset, x = "Antivirus", y = "Laptop",
          add = "reg.line",
          conf.int = TRUE,
          cor.coef = TRUE,
          cor.method = "pearson",
          xlab = "Variable Antivirus", ylab = "Variable Laptop")

QUESTION

Is the relationship positive (line pointing up), negative (line pointing down), or is there no relationship (line is flat)?

Ans: The relationship seems to be positive as the line is pointing upwards.

SPEARMAN CORRELATION TEST

PURPOSE

Check if the means of the two groups are different.

cor.test(dataset$Antivirus, dataset$Laptop, method = "pearson")
## 
##  Pearson's product-moment correlation
## 
## data:  dataset$Antivirus and dataset$Laptop
## t = 25.16, df = 120, p-value < 2.2e-16
## alternative hypothesis: true correlation is not equal to 0
## 95 percent confidence interval:
##  0.8830253 0.9412249
## sample estimates:
##       cor 
## 0.9168679

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 Spearman Correlation. The Spearman Correlation is only for abnormally distributed data — not based on outcome significance.

EFFECT SIZE FOR PEARSON CORRELATION

Q1) What is the direction of the effect? A) A correlation of 0.9168679 is positive (+) means as laptop purchases increases, anti-virus license purchases increases.

Q2) What is the size of the effect? A) A correlation of 0.9168679 is a strong relationship

Final Report

A Pearson correlation was conducted to examine the relationship between laptops purchased and anti-virus license purchased (n = 122). There was a statistically significant correlation between laptops (M = 40.02, SD = 12.30) and anti-virus licenses purchased (M = 50.18, SD = 13.36). The correlation was positive and strong, r(122) = 0.92, p < .05. As laptop purchases increases, anti-virus license purchases also increases.