Correlation Analysis

- Overview

In statistics, correlation (or dependence) is any statistical relationship, whether causal or not, between two random variables or bivariate data. Although in the broadest sense, "correlation" may indicate any type of association, in statistics it usually refers to the degree to which a pair of variables are linearly related.

Correlation analysis calculates the level of change in one variable due to the change in the other. A positive correlation means that both variables increase in relation to each other, while a negative correlation means that as one variable decreases, the other increases. 

The correlation coefficient (r) is a statistical measure of the degree to which changes to the value of one variable predict change to the value of another. Values between 0.7 and 1.0 (−0.7 and −1.0) indicate a strong positive (negative) linear relationship. 

Please refer to the following for more information:

• Wikipedia: Correlation Analysis 

- Correlation

Correlation is a key statistical concept used by researchers to analyze connections in data. It helps us understand the relationship between variables.

In research, we often study the interrelationships between different factors. The connection between two or more variables is called their correlation. Correlation refers to the extent to which variables vary together or together.

It's not enough to just check how a variable increases or decreases independently. Correlation focuses on the simultaneous fluctuations of two or all measured variables. High correlation indicates that variables tend to change in synchrony. Low correlation means that the fluctuations of the variables are not closely related.

Here are some examples of correlation:

• Height and weight: Taller people are usually heavier than shorter people.
• Wheat output, seed quality, and rainfall: The relationship between these three variables can be studied using multiple correlation.
• Illusory correlations: When two variables occur at the same time, and an unproven connection is made based on little evidence. For example, if someone has a bad experience with a lawyer and immediately assumes all lawyers are bad people.

[Jerusalem, Israel]

- Types of Correlation Analysis 

Statistical correlation analysis is a research technique that determines if there is a relationship between two variables or datasets. It measures the strength of the linear relationship between two variables and calculates their association. 

Correlation analysis is used in market research to examine quantitative survey data to identify significant patterns, trends, or connections between the variables. 

Here are some types of correlation analysis:

• Pearson correlation: Measures the strength of the linear relationship between two variables. It has a value between -1 to 1, with a value of -1 meaning a total negative linear correlation, 0 being no correlation, and + 1 meaning a total positive correlation.
• Kendall rank correlation: Estimates a rank-based measure of association. This test may be used if the data do not necessarily come from a bivariate normal distribution.
• Spearman correlation: One of the four types of correlations measured in statistics.
• Point-Biserial correlation: One of the four types of correlations measured in statistics.

- Measures of Correlation

A correlation coefficient is a statistical method that measures the strength and direction of a linear relationship between two continuous variables. It is a number between -1 and 1, and the sign of the coefficient indicates whether the variables change in the same or opposite directions. 

Here are some uses for correlation coefficients:

• Summarizing data
• Comparing results between studies
• Determining the practical significance of a result

An important limitation of the correlation coefficient is that it assumes a linear association. This also means that any linear transformation and any scale transformation of either variable X or Y, or both, will not affect the correlation coefficient.

[More to come ...]