What is the Difference and Similarities between Spearman’s Rank and Product Moment Correlation Coefficient

Correlation coefficient evaluates the degree to which two variables tend to change together. It describes the strength and the direction of the relationship. The values of coefficient correlation ranges from -1.0 to 1.0. If the value is -1.0 it shows a perfect negative correlation, if the value is 1.0 it is a perfect positive correlation and a correlation of 0.0 means there is no linear relationship between the movement of the two variables.

Product Moment Correlation Coefficient 

The Pearson correlation measures the linear relationship between two variables. When thechange in one variable is associated with a proportional change in the other variable, it is a linear correlation. 

Rank-order Correlation Coefficient  

The Spearman correlation evaluates the monotonic relationship between two variables. In a monotonic relationship, the variables tend to change together, but not necessarily at a constant rate. The Spearman correlation coefficient can measure monotonic relationship between two continuous or ordinal variables and it is based on the ranked values for each variable rather than the full set of data.

Difference between Rank-order and Product Correlation Coefficient 

1. The product moment correlation coefficient deals with only linear relationshipsbetween two variables whereas the rank order Coefficient works with only monotonic relationships.

2. Product moment correlation coefficient is more suitable for measurements taken from an interval scale, and the rank order coefficient is more suitable for measurements taken from ordinal scales.

3. Product moment correlation falls under parametric statistics and rank order correlation falls under nonparametric statistics.

4. The product moment coefficient is based on raw data values of the variables while the rank order correlation is based on rank-ordered variables.

Similarities between Rank-order and Product Correlation Coefficient 

1. Both ranges in value from -1.0 to 1.0. 

2. In both cases when the variable of one increases so does the value of another variable for the correlation coefficient to be +1.

3. Both of these coefficients cannot capture any other kind of non-linear relationships other than a scatterplot.