Pearson’s correlation (r)

Pearson’s correlation (r) check the relationships between two or more variables; there are three types of correlations: simple correlations, multiple correlations, and partial correlations.

• The correlation between two variables is known as simple correlation.
• Multiple correlation is the correlation between three or more variables.
• Partial correlation – Two or more variables are involved, check the correlation between two variables other variables are control/ constant.

A linear and a non-linear correlations exist.

Assumption of the linear correlation

• Random sampling
• Independent measurements or observations
• All variables should be normally distributed.
• Measurements are continuous scale

• The first steps of the correlation analysis is make a scatter plot diagram.
• Dependency of the variables – Measure the strength of a linear relationship. There are two measures for the dependency; covariance and Pearson’s correlation coefficient.

correlation VS covariance –

Correlation	Covariance
Measure the strength of the relationship of two variables.	shows how two variables are dependent on each other
value lie between +1 to – 1, values are standardized	value lie between +infinity to – infinity, values are not standardized
independent on unit	dependent on unit
indicate the direction and strength of the relationship of two variables	indicate the direction of the relationship of two variables

Equations

Decision point  (critical region)

Decision point is determined by the size of the sample, Tables are available to find the decision points (critical region).

• If r is lies within the critical Accepted the H₀
• If r is lies outside the critical region rejected the H₀

Pearson’s correlation in R

#Loading the data file to R console
my_data = read.csv("DATA.csv", header = TRUE)

#Test for normality
shapiro.test(my_data$X)

#Calculating covariance
cov (my_data$X, my_data$Y)

#Conducting the correlation analysis
cor.test (my_data$X, my_data$Y, alternative, method, conf.level)

#my_data$X X variable
#my_data$Y Y variable
#alternative = c("two.sided", "less", "greater")
#method Method of correlation calculation
#c("pearson", "kendall", "spearman")
#conf.level=Confidence level