# ===================================================
# PEARSON CORRELATION & SPEARMAN CORRELATION OVERVIEW
# ===================================================
# PURPOSE
# Used to test the relationship between two continuous variables.
# ==========
# HYPOTHESES
# ==========
# NULL HYPOTHESIS
# There is no relationship between Variables A and B.
# ALTERNATE HYPOTHESIS
# There is a relationship between Variables A and B.
# DIRECTIONAL ALTERNATE HYPOTHESES
# As Variable A increases, Variable B increases.
# As Variable A increases, Variable B decreases.
# .................................................................
# QUESTION
# What are the null and alternate hypotheses for your research?
# H0:There is no relation between the number of laptops purchased and the number of anti-virus licenses purchased.
# H1:There is a relation between the number of laptops purchased and the number of anti-virus licenses purchased.
# .................................................................
# ======================
# IMPORT EXCEL FILE CODE
# ======================
# PURPOSE OF THIS CODE
# Imports your Excel dataset automatically into R Studio.
# You need to import your dataset every time you want to analyze your data in R Studio.
# INSTALL REQUIRED PACKAGE
# The package only needs to be installed once.
# The code for this task is provided below. Remove the hashtag below to convert the note into code.
# install.packages("readxl")
# LOAD THE PACKAGE
# You must always reload the package you want to use.
# The code for this task is provided below. Remove the hashtag below to convert the note into code.
library(readxl)
# IMPORT THE EXCEL FILE INTO R STUDIO
# Download the Excel file from One Drive and save it to your desktop.
# Right-click the Excel file and click “Copy as path” from the menu.
# In R Studio, replace the example path below with your actual path.
# Replace backslashes \ with forward slashes / or double them //:
# ✘ WRONG "C:\Users\Joseph\Desktop\mydata.xlsx"
# ✔ CORRECT "C:/Users/Joseph/Desktop/mydata.xlsx"
# ✔ CORRECT "C:\\Users\\Joseph\\Desktop\\mydata.xlsx"
# Replace "dataset" with the name of your excel data (without the .xlsx)
# An example of the code for this task is provided below.
# You can edit the code below and remove the hashtag to use the code below.
A5RQ2 <- read_excel("D:\\applied analytics\\A5RQ2.xlsx")
# ======================
# DESCRIPTIVE STATISTICS
# ======================
# Calculate the mean, median, SD, and sample size for each variable.
# INSTALL THE REQUIRED PACKAGE
# Remove the hashtag in front of the code below to install the package once.
# After installing the package, put the hashtag in front of the code again.
# install.packages("psych")
# LOAD THE PACKAGE
# Always reload the package you want to use.
library(psych)
# CALCULATE THE DESCRIPTIVE DATA
# Replace "dataset" with the name of your excel data (without the .xlsx)
# Replace "V1" with the R code name for your first variable.
# Replace "V2" with the R code name for your second variable.
describe(A5RQ2[, 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
# =========================
# VISUALLY DISPLAY THE DATA
# =========================
# CREATE A SCATTERPLOT
# PURPOSE
# A scatterplot visually shows the relationship between two continuous variables.
# INSTALL THE REQUIRED PACKAGES
# Remove the hashtags in front of the code below to install the package once.
# After installing the packages, put the hashtag in front of the code again.
# install.packages("ggplot2")
# install.packages("ggpubr")
# 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
# Replace "dataset" with the name of your excel data (without the .xlsx)
# Replace "V1" with the R code name for your first variable.
# Replace "V2" with the R code name for your second variable.
# Replace "pearson" with "spearman" if you are using the spearman correlation.
ggscatter(A5RQ2, x = "Antivirus", y = "Laptop",
add = "reg.line",
conf.int = TRUE,
cor.coef = TRUE,
cor.method = "pearson",
xlab = "Antivirus", ylab = "Laptop")
# ........................................................
# QUESTION
# Answer the questions below as a comment within the R script:
# Is the relationship positive (line pointing up), negative (line pointing down), or is there no relationship (line is flat)?
# The relationship is positive since the line is pointing up.
# ........................................................
# ===============================================
# CHECK THE NORMALITY OF THE CONTINUOUS VARIABLES
# ===============================================
# OVERVIEW
# 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.
# CREATE A HISTOGRAM FOR EACH CONTINUOUS VARIABLE
# Replace "dataset" with the name of your excel data (without the .xlsx)
# Replace "V1" with the R code name for your first variable.
# Replace "V2" with the R code name for your second variable.
hist(A5RQ2$Antivirus,
main = "Histogram of Antivirus",
xlab = "Value",
ylab = "Frequency",
col = "lightblue",
border = "black",
breaks = 20)
hist(A5RQ2$Laptop,
main = "Histogram of Laptop",
xlab = "Value",
ylab = "Frequency",
col = "lightgreen",
border = "black",
breaks = 20)
# ........................................................
# QUESTION
# Answer the questions below as comments within the R script:
# Q1) Check the SKEWNESS of the VARIABLE 1 histogram. In your opinion, does the histogram look symmetrical, positively skewed, or negatively skewed?
# not symmetrical, it is positively skewed.
# 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?
# In our opinion the histogram of antivirus is too tall.
# Q3) Check the SKEWNESS of the VARIABLE 2 histogram. In your opinion, does the histogram look symmetrical, positively skewed, or negatively skewed?
# The Histogram for Laptops is not symmetrical, it is negatively skewed.
# 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?
# the histogram laptops is a bell 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)?"
# The Shapiro-Wilk test is checking if the variable's data is the same as normal data (null hypothesis) or if it is 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.
# CONDUCT THE SHAPIRO-WILK TEST
# Replace "dataset" with the name of your excel data (without the .xlsx)
# Replace "V1" with the R code name for your first variable.
# Replace "V2" with the R code name for your second variable.
shapiro.test(A5RQ2$Antivirus)
##
## Shapiro-Wilk normality test
##
## data: A5RQ2$Antivirus
## W = 0.99419, p-value = 0.8981
shapiro.test(A5RQ2$Laptop)
##
## Shapiro-Wilk normality test
##
## data: A5RQ2$Laptop
## W = 0.99362, p-value = 0.8559
# .........................................................
# QUESTION
# Answer the questions below as a comment within the R script:
# Was the data normally distributed for Variable 1?
# If the p-value is greater than 0.05 (p > 0.05), the data for that variable is considered to be normally distributed.
# Was the data normally distributed for Variable 2?
# If the p-value is less than 0.05 (p < 0.05), the data is considered to be not normally distributed.
# .........................................................
# If the data is normal for both variables, continue with the Pearson Correlation test.
# If one or both of variables are NOT normal, change to the Spearman Correlation test.
# ================================================
# PEARSON CORRELATION OR SPEARMAN CORRELATION TEST
# ================================================
# PURPOSE
# Check if the means of the two groups are different.
# CONDUCT THE PEARSON CORRELATION OR SPEARMAN CORRELATION
# Replace "dataset" with the name of your excel data (without the .xlsx)
# Replace "V1" with the R code name for your first variable.
# Replace "V2" with the R code name for your second variable.
# Replace "pearson" with "spearman" if you are using the spearman correlation.
cor.test(A5RQ2$Antivirus, A5RQ2$Laptop, method = "pearson")
##
## Pearson's product-moment correlation
##
## data: A5RQ2$Antivirus and A5RQ2$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 & SPEARMAN CORFRELATION
# ===============================================
# If results were statistically significant, then determine how the variables are related and how strong the relationship is.
# 1) REVIEW THE CORRECT CORRELATION TEST
# • For Pearson correlation, find "sample estimates: cor" in your output (when you calculated the Pearson Correlation earlier).
# • For Spearman correlation, find "sample estimates: rho" in your output (when you calculated the Spearman Correlation earlier).
# A Pearson correlation was done to measure the relationship that exists between the number of laptops sold and the number of anti-virus licenses sold(n=122). The correlation between number of antivirus software sold (M = 50.8, SD = 13.36) and number of laptops sold (M = 40.02, SD = 12.30) was statistically not significant. The correlation was also positive and high, r(120) = 0.9168, p <.001.The correlation between the number of purchases of laptops and the amount of antivirus licenses purchased is not related.
# ........................................................