SPEARMAN CORRELATION

This analysis is for RESEARCH SCENARIO 1 from assignment 5. It tests to see if there is a relationship between time spent (minutes) in the shop and number of drinks purchased.

Hypotheses

  • H0 (Null Hypothesis): There is no relationship between time spent in the shop and number of drinks purchased.
  • H1 (Alternate Hypothesis): As time spent in the shop increases, the number of drinks purchased increases.

Result paragraph

  • A Spearman correlation was conducted to assess the relationship time spent in the shop and number of drinks purchased (n = 461). There was a statistically significant correlation between time spent in the shop (M = 29.89, SD = 18.63) and number of drinks purchased (M = 3.00, SD = 1.95). The correlation was Positive and strong, ρ(459) = .920, p < .001. As time spent in the shop increases, number of drinks purchased increases.

R code and Analysis

# 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

# install.packages("readxl")

# LOAD THE PACKAGE

library(readxl)

# IMPORT THE EXCEL FILE INTO R STUDIO

dataset <- read_excel("//apporto.com/dfs/SLU/Users/minhoku_slu/Desktop/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(dataset[, 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
# ===============================================
# 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.

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

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

# ........................................................
# Q1) Check the SKEWNESS of the VARIABLE 1 (Minutes) histogram. In your opinion, does the histogram look symmetrical, positively skewed, or negatively skewed?
# Answer 1: The histogram is POSITIVELY SKEWED. The majority of the data is clustered on the left side (shorter times), with a long "tail" of data points stretching out to the right (longer times).


# Q2) Check the KURTOSIS of the VARIABLE 1 (Minutes) histogram. In your opinion, does the histogram look too flat, too tall, or does it have a proper bell curve?
# Answer 2: The histogram looks TOO TALL. It has a very sharp, high peak and is much thinner than a proper bell curve.


# Q3) Check the SKEWNESS of the VARIABLE 2 (Drinks) histogram. In your opinion, does the histogram look symmetrical, positively skewed, or negatively skewed?
# Answer 3: The histogram is POSITIVELY SKEWED. Just like the first histogram, the data is heavily clustered on the left (low number of drinks), with a long tail stretching to the right (high number of drinks).


# Q4) Check the KUROTSIS of the VARIABLE 2 (Drinks) histogram. In your opinion, does the histogram look too flat, too tall, or does it have a proper bell curve?
# Answer 4: The histogram looks TOO TALL. It has an extremely sharp and high peak and does not look like a proper bell curve at all.
# ........................................................

# PURPOSE
# Use a statistical test to check the normality of the continuous variables.

# CONDUCT THE SHAPIRO-WILK TEST

shapiro.test(dataset$Minutes)
## 
##  Shapiro-Wilk normality test
## 
## data:  dataset$Minutes
## W = 0.84706, p-value < 2.2e-16
shapiro.test(dataset$Drinks)
## 
##  Shapiro-Wilk normality test
## 
## data:  dataset$Drinks
## W = 0.85487, p-value < 2.2e-16
# .........................................................
# Was the data normally distributed for Variable 1 (Minutes)?
# No, the data was NOT normally distributed for Variable 1 (Minutes).
# The Shapiro-Wilk test (shapiro.test) result shows a p-value < 2.2e-16 (<0.05).
# Was the data normally distributed for Variable 2?
# No, the data was NOT normally distributed for Variable 2 (Drinks).
# The Shapiro-Wilk test (shapiro.test) result shows a p-value < 2.2e-16 (<0.05).
# .........................................................


# =========================
# 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(dataset, x = "Minutes", y = "Drinks",
          add = "reg.line",
          conf.int = TRUE,
          cor.coef = TRUE,
          cor.method = "spearman",
          xlab = "Variable Minutes", ylab = "Variable Drinks")

# ........................................................

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


# ================================================
# SPEARMAN CORRELATION TEST (not normally distributed)
# ================================================

# PURPOSE
# Check if the means of the two groups are different.

# CONDUCT THE PEARSON CORRELATION OR SPEARMAN CORRELATION

cor.test(dataset$Minutes, dataset$Drinks, method = "spearman")
## Warning in cor.test.default(dataset$Minutes, dataset$Drinks, method =
## "spearman"): Cannot compute exact p-value with ties
## 
##  Spearman's rank correlation rho
## 
## data:  dataset$Minutes and dataset$Drinks
## S = 1305608, p-value < 2.2e-16
## alternative hypothesis: true rho is not equal to 0
## sample estimates:
##       rho 
## 0.9200417
# DETERMINE STATISTICAL SIGNIFICANCE.

# ===============================================
# EFFECT SIZE FOR SPEARMAN CORRRELATION
# ===============================================

# If results were statistically significant, then determine how the variables are related and how strong the relationship is.

# 1) REVIEW THE CORRECT CORRELATION TEST
#    rho = 0.9200417

# ........................................................

# 1) WRITE THE REPORT 
#    Q1) What is the direction of the effect?  
#          A correlation of 0.95 is positive. As X increases, Y increases.
#
#     Q2) What is the size of the effect? 
#         A correlation of 0.95 is a strong relationship.