Pearson's Correlation Coefficient

Pearson’s correlation coefficient is also known as Karl Pearson‘s correlation coefficient. Pearson’s correlation coefficient is the method of measuring the correlation. This method was developed by Karl Pearson and is therefore named Pearson’s correlation coefficient. Pearson’s correlation coefficient is known as the best method of measuring the correlation, because it is based on the method of covariance. Pearson’s correlation coefficient gives information about the degree of correlation as well as the direction of the correlation.

Assumptions in calculating the Pearson’s correlation coefficient:

1. Independent of case: In Pearson’s correlation of coefficient, cases should be independent to each other.
2. Distribution: In Pearson’s correlation coefficient, variables of the correlation should be normally distributed.
3. Cause and effect relationship: In Pearson’s correlation coefficient, there should be a cause and effect relationship between the correlation variables.
4. Linear relationship: In Pearson’s correlation coefficient, two variables should be linearly related to each other, or if we plot the value of variables on a scatter diagram, it should yield a straight line.

Properties in Pearson’s correlation coefficient:

The following are the properties of Pearson’s correlation coefficient:

1. Limit of the Pearson correlation coefficient: Karl Pearson’s correlation coefficient value lies between +1 to -1.
2. Pure number: Pearson’s correlation coefficient is a pure number and it is independent of the unit of measurement. For example, if one

variable’s unit of measurement is in inches and the second variable is in quintals, even then, Pearson’s correlation coefficient value does not change.

3. Symmetric: Pearson’s correlation of the coefficient between two variables is symmetric. This means that if we calculate the Pearson’s correlation coefficient between X and Y or Y and X, the value of Pearson’s correlation coefficient will remain the same.

Probable error and Karl Pearson’s correlation coefficient:

Probable error is used to determine the reliability of Pearson’s correlation coefficient. The following formula is used to determine the value of probable error:

• 
• Where:
• P.E = Probable error
• r = Pearson’s correlation coefficient
• N = Number of observations
• If the absolute value of Pearson’s correlation coefficient is greater than 6 times probable error, then the Pearson’s correlation coefficient is taken to be significant. If the absolute value of Pearson’s correlation coefficient is less than 6 times probable error, then the correlation coefficient will be insignificant.

Degree of correlation:

1. Perfect correlation: If Pearson’s correlation coefficient value is near ± 1, then it said to be a perfect correlation.
2. High degree of correlation: If Pearson’s correlation coefficient value lies between ± 0.75 and ± 1, then it is said to be a high degree of correlation.
3. Moderate degree of correlation: If Pearson’s correlation coefficient value lies between ± 0.25 and ± 0.75, then it is said to be moderate degree of correlation.
4. Low degree of correlation: When Pearson’s correlation coefficient value lies between 0 and ± 0.25, then it is said to be a low degree of correlation.
5. No correlation: When Pearson’s correlation coefficient value lies around zero, then there is no correlation.

Karl Pearson’s correlation coefficient and SPSS:

In almost all statistical software, there is an option to calculate the correlation coefficient. In SPSS we can calculate Pearson’s correlation coefficient by following the following steps:

1. Run the SPSS from the Start Menu.
2. Click on the “open data” and select the data.
3. Click on the “analysis” menu. Select “correlate” from the analysis menu.
4. Select “bavariate” from the correlate option. The window that appears is called the bavariate correlation window. Select the correlation variable and drag it into the variable list. Select “Pearson’ correlation coefficient test” from the window. Click on the “ok” button.  In the result window, a correlation table will show the Pearson’s correlation coefficient and associated significance value. The following are the bavariate window and the correlation table:
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