11.2 Determining the correlation coefficient

The strength of a correlation can be estimated using the correlation coefficient. It is sometimes called Pearson’s correlation coefficient after its Karl Pearson. This coefficient is denoted by r and is a measure of linear association. The correlation coefficient (r) can vary between –1 and 1.

An r of 1 indicates a perfect positive correlation; that is, all the data points fall on a straight line and y increases as x increases.An r of –1 indicates a perfect negative correlation; that is, all the data points fall on a straight line and y decreases as x increases.

An r of 0 indicates there is no correlation; that is, points appear to be random in their association between x and y, and even if we know the values of one variable we cannot conclude anything about the values of the other variable.

So, strength of correlation can be estimated by r. The closer r is to either –1 or 1 the stronger the correlation. That is, the absolute value of the correlation coefficient gives us the relationship strength. The larger the number, the stronger the relationship. It is worth noting that a perfect correlation (r = +1 or r = –1) is generally not seen in biological systems and mostly occurs in theoretical models only.

For a general ‘rule of thumb’ for interpreting and describing correlation coefficients:

• .90 to 1.00 (–.90 to –1.00) is a very strong positive (negative) correlation
• .70 to .90 (−.70 to −.90) is a strong positive (negative) correlation
• .50 to .70 (−.50 to −.70) is a moderate positive (negative) correlation
• .30 to .50 (−.30 to −.50) is a low or weak positive (negative) correlation
• .00 to .30 (.00 to −.30) is a negligible or very weak positive (negative) correlation.