# ===================================================
# PEARSON CORRELATION & SPEARMAN CORRELATION OVERVIEW
# ===================================================
# PURPOSE
# Used to test the relationship between two continuous variables.
# ==========
# HYPOTHESES
# ==========
# .................................................................
# QUESTION
# What are the null and alternate hypotheses for your research?
# H0: There is no relation between time spent and number of drinks purchased.
# H1: There is a relation between time spent and number of drinks purchased.
# .................................................................
# ======================
# IMPORT EXCEL FILE CODE
# ======================
#install.packages("readxl")
# LOAD THE PACKAGE
library(readxl)
# IMPORT THE EXCEL FILE INTO R STUDIO
A5RQ1 <- read_excel("C:\\Users\\leena\\Desktop\\SLU\\Sem 3 Fall 1\\Week 5\\A5RQ1.xlsx")
# ======================
# DESCRIPTIVE STATISTICS
# ======================
# Calculate the mean, median, SD, and sample size for each variable.
# INSTALL THE REQUIRED PACKAGE
#install.packages("psych")
# LOAD THE PACKAGE
library(psych)
# CALCULATE THE DESCRIPTIVE DATA
describe(A5RQ1[, c("Minutes", "Drinks")])
## vars n mean sd median trimmed mad min max range skew kurtosis
## Minutes 1 461 29.89 18.63 24.4 26.99 15.12 10 154.2 144.2 1.79 5.20
## Drinks 2 461 3.00 1.95 3.0 2.75 1.48 0 17.0 17.0 1.78 6.46
## se
## Minutes 0.87
## Drinks 0.09
# =========================
# VISUALLY DISPLAY THE DATA
# =========================
# CREATE A SCATTERPLOT
# PURPOSE
# A scatterplot visually shows the relationship between two continuous variables.
# INSTALL THE REQUIRED PACKAGES
#install.packages("ggplot2")
#install.packages("ggpubr")
# LOAD THE PACKAGE
library(ggplot2)
##
## Attaching package: 'ggplot2'
## The following objects are masked from 'package:psych':
##
## %+%, alpha
library(ggpubr)
# CREATE THE SCATTERPLOT
ggscatter(A5RQ1, x = "Minutes", y = "Drinks",
add = "reg.line",
conf.int = TRUE,
cor.coef = TRUE,
cor.method = "spearman",
xlab = "Variable V1", ylab = "Variable V2")
# ........................................................
# 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)?
# Ans: 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(A5RQ1$Minutes,
main = "Histogram of V1",
xlab = "Value",
ylab = "Frequency",
col = "lightblue",
border = "black",
breaks = 20)
hist(A5RQ1$Drinks,
main = "Histogram of V2",
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?
# Ans: The Variable 1 is 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?
# Ans: In our opinion the Kurosis of the variable 1 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?
# Ans:The Variable 2 is not symmetrical, it is positively 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?
# Ans: In our opinion the Kurosis of the variable 2 is too tall.
# ........................................................
# 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.
# CONDUCT THE SHAPIRO-WILK TEST
shapiro.test(A5RQ1$Minutes)
##
## Shapiro-Wilk normality test
##
## data: A5RQ1$Minutes
## W = 0.84706, p-value < 2.2e-16
shapiro.test(A5RQ1$Drinks)
##
## Shapiro-Wilk normality test
##
## data: A5RQ1$Drinks
## W = 0.85487, p-value < 2.2e-16
# .........................................................
# QUESTION
# Answer the questions below as a comment within the R script:
# Was the data normally distributed for Variable 1?
# No, the data is not normally distributed for Variable 1.
# Was the data normally distributed for Variable 2?
# No, the data is not normally distributed for Variable 2.
# .........................................................
#
# Since the data for both variables are NOT normal, we conducted the Spearman Correlation test.
# ================================================
# PEARSON CORRELATION OR SPEARMAN CORRELATION TEST
# ================================================
# PURPOSE
# Check if the means of the two groups are different.
cor.test(A5RQ1$Minutes, A5RQ1$Drinks, method = "spearman")
## Warning in cor.test.default(A5RQ1$Minutes, A5RQ1$Drinks, method = "spearman"):
## Cannot compute exact p-value with ties
##
## Spearman's rank correlation rho
##
## data: A5RQ1$Minutes and A5RQ1$Drinks
## S = 1305608, p-value < 2.2e-16
## alternative hypothesis: true rho is not equal to 0
## sample estimates:
## rho
## 0.9200417
# 1) REVIEW THE CORRECT CORRELATION TEST
# ===============================================
# EFFECT SIZE FOR 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
# The rho value is 0.9200417, Which says that the data is statistically dependent, So if the number of hours spent in cafe increases the number of drinks also increases.