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PEARSON CORRELATION & SPEARMAN CORRELATION OVERVIEW

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PURPOSE

Used to test the relationship between two continuous variables.

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HYPOTHESES

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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.

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QUESTION

What are the null and alternate hypotheses for your research?

H0:

H1:

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IMPORT EXCEL FILE CODE

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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:.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.

dataset <- read_excel("C:\\Users\\DELL\\Downloads\\A5RQ1 (1).xlsx")

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DESCRIPTIVE STATISTICS

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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(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

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CHECK THE NORMALITY OF THE CONTINUOUS VARIABLES

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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(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)

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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?

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?

Q3) Check the SKEWNESS of the VARIABLE 2 histogram. In your opinion, does the histogram look symmetrical, positively skewed, or 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?

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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.

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(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

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QUESTION

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

Was the data normally distributed for Variable 1?

Was the data normally distributed for Variable 2?

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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.

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VISUALLY DISPLAY THE DATA

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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(dataset, x = "Minutes", y = "Drinks",
          add = "reg.line",
          conf.int = TRUE,
          cor.coef = TRUE,
          cor.method = "Spearman",
          xlab = "Variable Minutes", ylab = "Variable Drinks")
## Warning: Computation failed in `stat_cor()`.
## Caused by error in `match.arg()`:
## ! 'arg' should be one of "pearson", "kendall", "spearman"

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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 (line pointing up)

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PEARSON CORRELATION OR SPEARMAN CORRELATION TEST

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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(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

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.

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EFFECT SIZE FOR PEARSON & SPEARMAN CORRRELATION

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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).

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1) WRITE THE REPORT

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

Q1) What is the direction of the effect?

“Direction” explains the relationship between the variables.

A positive (+) correlation means as Variable X increases, Variable Y increases.

A negative (-) correlation means as Variable X increases, Variable Y decreases.

#Q1 Answer: A correlation of 0.9200417 is positive this means that the more time customers spend in the café, the more drinks they tend to purchase.

Q2) What is the size of the effect?

Ranges from 0 (no relationship) to 1.00 (perfect relationship).

“Size” explains how much the variables are connected to each other.

± 0.00 to 0.09 = no relationship

± 0.10 to 0.29 = weak

± 0.30 to 0.49 = moderate

± 0.50 to 1.00 = strong

#Q2 Answer:A correlation of 0.9200417 indicates a very strong connection.

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>> WRITTEN REPORT FOR PEARSON CORRELATION <<

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Write a paragraph summarizing your findings.

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1) REVIEW YOUR OUTPUT

Collect the information below from your output:

1) The name of the inferential test used (Pearson Correlation)

2) The names of the two variables you analyzed (their proper names, not their R code names).

3) The total sample size (labeled as “n”).

4) Whether the inferential test results were statistically significant (p < .05) or not (p > .05)

5) The mean and SD for each variable (rounded to two places after the decimal)

6) The direction and size of the correlation.

7) Degrees of freedom (labeled as “df”)

8) r-value (labeled as “sample estimate: cor” in output)

9) EXACT p-value to three decimals. NOTE: If p > .05, just report p > .05 If p < .001, just report p < .001

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2) WRITE YOUR FINAL REPORT

An example report is provided below. You should copy the paragraph and just edit/ replace words with your information.

This is not considered plagiarizing because science has a specific format for reporting information.

EXAMPLE

A Pearson correlation was conducted to examine the relationship between

job satisfaction and employee performance (n = 300).

There was a statistically significant correlation between

job satisfaction (M = 8.21, SD = 0.2) and employee performance (M = 4.2, SD = 0.02).

The correlation was positive and strong, r(298) = 0.65, p < .05.

As job satisfaction increases, employee performance also increases.

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>> WRITTEN REPORT FOR SPEARMAN CORRELATION <<

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Write a paragraph summarizing your findings.

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1) REVIEW YOUR OUTPUT

Collect the information below from your output:

1) The name of the inferential test used (Spearman Correlation)

2) The names of the two variables you analyzed (their proper names, not their R code names).

3) The total sample size (labeled as “n”).

4) Whether the inferential test results were statistically significant (p < .05) or not (p > .05)

5) The mean and SD for each variable (rounded to two places after the decimal)

6) The direction and size of the correlation.

7) rho-value (labeled as “sample estimate: rho” in output, and labeled as ρ in paragraph)

8) EXACT p-value to three decimals. NOTE: If p > .05, just report p > .05 If p < .001, just report p < .001

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2) WRITE YOUR FINAL REPORT

# A Spearman test was used to determine whether the duration of a customer’s visit was related to how many drinks they ordered . The analysis revealed a significant and highly positive association between visit length  and drink count . With a rho value of 0.9200417 and p < .001, the findings suggest that customers who remain in the café for longer periods typically purchase a greater number of drinks.