Title: Strength of association - How strong is strong?
Course: UGQuants (SSPS) > Section: Correlation and Regression

Strength of association - How strong is strong?

In producing statistics such as 'r' we are faced with the question: 'how strong is strong?' The first and most important answer is that the relationship between a pair of variables with a higher correlation coefficient is stronger than that between a pair of variables with a lower coefficient and it is usually such comparisons that we are interested in making.  For example we might want to claim that there is a stronger relationship between the number of hospital beds and life expectancy in countries with low GDP than in countries with high GDP.

The median GDP per capita score in our WDI dataset, for example, is $2522. We can group together all the countries with GDPs per capita of less than this figure and create a second group out of all the countries with GDPs per capital greater than this figure.  If we calculate the Pearson’s r for hospital beds and life expectancy for these two groups, we find get a figure of .368 for the countries in our datset with below average GPD pc and a figure of .275 for the countries in our dataset with above average GDP pc. In other words, there is a stronger relationship between hospital beds and life expectancy for poorer countries than in richer countries..

A second, more general type of answer can be given using Rowntree's classification guidance, which gives us a very general, rule of thumb description of coefficient strengths.

Number coefficient size

(positive or negative)
Verbal description
0.0 - 0.2 | Very weak, negligible
0.2 - 0.4 | Weak
0.4 - 0.7 | Moderate
0.7 - 0.9 | Strong
0.9 - 1.0 | Very strong

Perfect relationships are extremely rare in social science. Often we may be interested in relationships that are weak or moderate, rather than confining our interest to those with very high correlations.  This reflects the reality of carrying out research on individual humans or societies