Spearman's Correlation Coefficient

Spearman's correlation coefficient is a number that tells us how strongly related our ranked items are.

Positive Correlation would be if our coefficient is near the number 1. This means that our items are ranked the same. The scatterplot for positive correlation is composed of points going up and to the right on the graph. The closer they are to a line with slope of 1, the stronger the correlation is; meaning the closer the coefficient will be to the number 1. The more spaced out the points are from that line, the weaker the correlation is; meaning the coefficient will be closer to zero but still positive.

Negative Correlation would be if our coefficient is near the number -1. This means that our items are ranked opposite. The scatterplot for negative correlation is composed of points going down and to the right on the graph. The closer they are to a line with slope -1, the stronger the corelation is; meaning the closer the coefficient will be to the number -1. The more spaced out the points are from that line, the weaker the correlation is; meaning the coefficient will be closer to zero but still negative.

No Correlation would be if our coefficient is the number 0. This means we cannot determine one of the rankings from the other ranking, it is random. The scatterplot for no correlation is composed of points that are randomly on the graph; really spaced out all over.

Spearman's Correlation Coefficient Formula:
r = (6*sum of differences squared) / (number of items ranked *( number of items ranked squared -1))