5. Correlation

5. Correlation

• To study the interdependence or covariation of 2 variables
• Positive Correlations
  • If large (small) values of one variable are associated with the large (small) values of other variable
• Negative Correlations
  • If large (small) values of one variable are associated with small (large) values of other variable
• Interpretation of result:
  • If value is 1, then there is perfect uphill (positive) linear relationship between the 2 variables
  • If value is −1, then there is a perfect downhill (negative) linear relationship between the 2 variables
  • If value is between 0.7 and 1, then there is strong uphill (positive) linear relationship between the 2 variables
  • If value is between -0.7 and −1, then there is strong downhill (negative) linear relationship between the 2 variables
  • If value is 0, then there is no linear relationship between the 2 variables

5.1. Correlation in Excel

• Data -> Data Analysis -> Correlation

OR

• =CORREL(A2:A6,B2:B6) etc.

5.2. Correlation in R-Programming

• To compute Pearson’s product moment correlation coefficient:
  • x <- c(1,2,3,4,5)
  • y <- c(2,4,6,8,10)
  • cor(x, y) = 1
• To plot scatter diagram:
  • plot(x, y)

5.3. Scatter Diagram

• The graphical method which gives rough idea about the existence and degree of correlation between 2 variables

5.4. cor.testin R

• R command cor.test is used to test the significance of Pearson’s correlation coefficient using t-test as well as the significance of Spearman’s correlation coefficient
• The value of Pearson sample correlation is 0.6496543. H0 is rejected as p-value is less than 0.05

• Spearman’s sample correlation
  • The value of Spearman’s sample correlation coefficient is 0.4181818. In this case, H0 is accepted as p-value is larger than nominal value

5.5. Shapiro-Wilk normality test

• For the output of Shapiro-Wilk normality test, the normality of distribution of X is rejected. Therefore, the assumption of normality of bivariate parent population is not justifiable.
• Therefore, one has to go by the conclusion of nonparametric test procedure based on Spearman’s rank correlation coefficient.