Types of Correlation

There are mainly four types of correlation analysis:

  • Positive correlation
  • Negative correlation
  • No Correlation

Positive Correlation

positive correlation

This is the type where an increase in one variable coincides with an increase in another variable. In this example both exam score and score move to the same positive direction

Negative Correlation

Negative correlation

In this case, variables move in opposite directions. As one variable increases, the other variable decreases. In this example, more missed classes is related to a lower exam score.

No Correlation

No correlation

In this case there is no visible relationship between the variables.

These are the major types of correlation analysis. Various methods are used to compute types of correlation.

Methods of Computing Correlation Coefficient

  • Kendall rank correlation
  • Pearson correlation.
  • Point-Biserial
  • Spearman’s correlation

Pearson Correlation

This is the most commonly used. It is used to measure the degree of the relationship between linearly related variables. It is often abbreviated as r. For example, it could be used to measure the degree of the relationship between height and weight among teenagers. It is important to note that Pearson method is said to be significant if a sample size greater than 10 is used.

Some of the assumptions made are:

  • Variables involved should be approximately normally distributed
  • Variables should be continuous.
  • The variables should be linear(Linearity), that is, the variables should have a linear relationship
  • Homoscedasticity – data is equally distributed about the regression line.

Point-Biserial

Point-biserial is the same as Pearson. The only difference is that in the point-biserial one of the variables is dichotomous. A dichotomous variable is a variable that has two levels such as gender which has male and female. The two even share the same formula of computation

Kendall Rank correlation

This is a non-parametric statistical test that is used to examine the strength of dependence between variables. The formula used to calculate the value of Kendall rank is as shown below

Where:

nc = number of concordant (Ordered in the same way)

nd = number of discordant (Ordered differently)

n(n-1) = Total number of pairings with ab

Spearman Rank Correlation

This is also a non-parametric test which does not make any assumption about the distribution of data. Spearman is used to evaluate the degree of association between variables that are ordinal in nature. The following formula is used to calculate the Spearman’s rank coefficient

spearman rank correlation formula

Where:

di = difference between the ranks of corresponding variables

n = number of observations

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