EXAMPLE 6.23
It’s significant but is it important? Suppose that we are testing the null hypothesis of no correlation between two variables. With 400 observations, an observed correlation of only r = 0.1 is significant evidence at the α = 0.05 level that the correlation in the population is not zero. Figure 6.15 is an example of 400 (x, y) pairs that have an observed correlation of 0.10. The low significance level does not mean that there is a strong association, only that there is strong evidence of some association. The proportion of the variability in one of the variables explained by the other is r2 = 0.01, or 1%.
Figure 6.15 Scatterplot of n = 400 observations with an observed correlation of 0.10, Example 6.23. There is not a strong association between the two variables even though there is significant evidence (P < 0.05) that the population correlation is not zero.