Contents - Index

Pearson's and Spearman's correlation coefficients

Theory

Correlation summarizes the strength of relationship between two variables, but it is important to remember that correlation is not causation. Several different correlation coefficients can be calculated. The two most commonly used are Pearson's correlation coefficient and Spearman's rank correlation coefficient. Pearson's correlation coefficient requires both variables to be measured on an interval or ratio scale, and the calculation is based on the actual values. Spearman's rank correlation coefficient requires data that are at least ordinal and the calculation, which is the same as for Pearson's correlation, is carried out on the ranks of the data. Each variable is ranked separately by putting the values of the variable in order and numbering them: the lowest value is given rank 1, the next lowest is given rank 2 and so on. If two data values for the variable are the same they are given averaged ranks, so if they would have been ranked 14 and 15 then they both receive rank 14.5.

Spearman's rank correlation coefficient is used as a measure of linear relationship between two sets of ranked data, i.e. it measures how tightly the ranked data clusters around a straight line. Spearman's rank correlation coefficient, like all other correlation coefficient, will take a value between -1 and +1. A positive correlation is one in which the ranks of both variables increase together. A negative correlation is one in which the ranks of one variable increase as the ranks of the other variable decrease. A correlation of +1 or -1 will arise if the relationship between the two variables is exactly linear. A correlation close to zero means there is no linear relationship between the ranks.

How to

Open the Correlation tab among the analyses tabs in the top of the main window, and press either the Pearsons correlation or the Spearmans correlation button to execute the analysis.

The results are presented in a table where the correlation coefficient between each column (gene) pair is given. The diagonal values are colored yellow and are always 1, since a variable is always fully correlated with itself. The other cells are by default colored so that if the absolute value is over 0.8, the cell is pink and if the absolute value is over 0.5, the cell is cyan. This coloring can be changed by selecting Cut-off in the Coloring menu. The absolute values in the table will be used if the ABS(Value) check box is ticked. If you want to have several colors, start with the lowest cut off value working your way to higher values.

References

Altman D.G (1991). Practical Statistics for Medical Research. Chapman & Hall, London, pp 285-288.