What is Correlation Coefficient and Case Examples in Simple Statistics

Correlation analysis is a term in statistics that is commonly used to study the relationship between variables. Where the purpose of this analysis technique is to get the pattern and the closeness or strength of the relationship between two or more variables which is expressed by the correlation coefficient.

A simple illustration of the use of this analytical technique is when we question whether the variable X has a relationship with the variable Y? Like, do students’ math scores have a relationship with their level of intelligence (IQ)? Or, is there a relationship between rain intensity and fruit ice sales?

To better understand it, this article will describe what a correlation coefficient is, including interpretation, formulas, and examples of its application in simple statistics.


1 What is the Correlation Coefficient?
2 Correlation Coefficient Formula
3 Case Examples of Application of Correlation Coefficient
4 Conclusion

What is Correlation Coefficient?

As mentioned earlier, the correlation coefficient is a value that indicates the strength or absence of a linear relationship between two variables. This correlation is usually denoted by the letter r, whose values ​​are in the range -1 to +1.

An r value close to -1 or +1 indicates a strong relationship between the two variables, while an r value close to 0 indicates a weak relationship.

If the correlation coefficient shows a positive result, then the two variables have a unidirectional relationship. That is, when the variable X is high, the value of the variable Y will be high as well.

Meanwhile, if the correlation coefficient is negative, then the two variables have an opposite relationship. Where if the value of the variable X is high, then the value of the variable Y is actually low or decreasing.

In more detail, to see the interpretation of the correlation between two variables, the following is the calculation criteria quoting from Sarwono: 2006.

0: There is no correlation between the two variables
>0 – 0.25: Very weak correlation
>0.25 – 0.5: Correlation is sufficient
>0.5 – 0.75 : Strong correlation
>0.75 – 0.99: Very strong correlation
1: Correlation perfect positive relationship
-1: The correlation of a perfect relationship is negative

So, overall, the interpretation of the correlation results looks at three things, namely the strength of the relationship between two variables, the significance of the relationship, and the direction of the relationship.

Correlation Coefficient Formula

There are so many formulas that can be used in determining the degree of relationship between variables. However, in this case, we will discuss the Pearson correlation coefficient technique or the product-moment coefficient of correlation introduced by Francis Galton.

Pearson correlation is the most common and easy-to-use method without modifying the data. The close relationship between the two variables is indicated by the interval or ratio data scale. The calculation is obtained by dividing the covariance of the two variables by the product of the standard deviations, as described by the following formula:

Correlation Coefficient: Definition and Case Examples

  • The letter n represents the number of points of the pair (X, Y)
  • X represents the value of the variable X
  • Y represents the value of the variable Y

In linear equations, the variable X is usually called the independent variable, which is the variable used to predict the variable Y. Meanwhile, the variable Y is called the dependent variable, which is the variable whose value is predicted or determined by the value of the variable X.

However, it should be noted that the correlation coefficient results can only be used as an initial indication in the analysis. That is, the correlation value cannot describe the cause and effect relationship between the variables X and Y which is taken into account. Likewise, in the analysis of the relationship between X and Y, it is necessary to have a logical relationship between the two variables.

Example Case Application of Correlation Coefficient

According To The Organic Chemistry Tutor What Correlation Coefficient

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