## Correlation Analysis Definition

This analysis is a statistical technique that is used to determine the correlation strength and direction of relationship between variables of interest.

It is important to note that correlation analysis is only conducted when the **variables** involved are **continuous** in nature.

A continuous variable is a variable that takes on infinitely number of values. Example of such variables include age, height, weight and price amongst others.

Many researchers think that correlation analysis determines cause and effect which is not true.

Correlation analysis can either be computed manually or using statistical softwares such as R Studio, R Gui, Microsoft Excel, SPSS, SAS, STATA and Minitab amongst others.

The correlation between variables is captured using a value referred to as a Pearson coefficient which is calculated using the formula shown below

Where:

- N = number of pairs of scores/observations
- ∑xy = sum of the product of paired scores
- ∑x = sum of x scores
- ∑y = sum of y scores
- ∑x² = sum of squared x scores
- ∑y2 = sum of squared y scores.

## Types of Correlation

There are different types of correlation. They depend on the direction of the relationship. The three main types are positive, negative and zero correlation.

**Correlation in Research Methodology**

In research methodology, correlation analysis is the type of analysis conducted to determine the magnitude and direction of the relationship between variables. Pearson is the most commonly used. In research methodology, the interpretation of the analysis is usually done using the coefficient and the P value. They are 3 stages to solve a correlation problem

- Stage 1: Determination of the relation, if yes, measure it
- Stage 2: Significance of the correlation
- Stage 3: Establishing the cause and effect of relationship, if any.

**Correlation and Covariance**

People often misunderstand correlation for covariance which are two distinct measures. While correlation is a measure of association between variables, covariance is the measure of how one variable varies with another. However, the two are very much related. This close relationship is as shown below

To calculate the variance of a given variable say X is done using the formula, where E is the expectation (mean)

E (XX) – E(X) E(X)

Now to calculate the covariance between two variables X and Y is similar to the variance in that

Cov (X, Y) = E (XY)-E (X) E(Y)

Now, the correlation between the two variables can be calculated as

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