Skowhegan Area High School
 Topics Introduction Spearman's Rank Correlation Coefficient Scatterplot Matrix Rank Correlation Matrix Pearson's Correlation Coefficient Influential Point Lurking Variable Cause and Effect Least Squares Regression ("r" and residuals)

Patterns of Association

Spearman's Rank Correlation Coefficient

Charles Spearman was a British statistician who invented a simple formula to measure the strength of linear assosciation between two rankings, or how close the data fit to a line. Spearman's Rank Correlation Coefficient can be denoted by

His equation is as follows;

The means the sum of the differences squared, the n is the number of objects you are ranking. Here is an example:

 Car Deven's Rank Biff's Rank Difference of Rank Squared Difference Corvette 4 5 1 1 Viper 1 1 0 0 Lamborghini 2 2 0 0 Porsche 5 3 2 4 Firebird 3 4 1 1
n=5 (number of objects ranked)                                                            (Sum of difference^2)    (6)

Now we can substitute in our values from our equation above:    =    = .7
So =.7  Big deal, what does it mean? The  value is basically on a scale of -1 to 1, the closer to -1 the less
alike the rankings are, the closer to 1, the more alike the rankings are. As you can see Deven and Biff's ranking of cars
were fairly close.