EXAMPLE 6.24 It’s Signifcant But Is It Important?
Suppose that we are testing the hypothesis of no correlation between two variables. With 400 observations, an observed correlation of only is signifcant evidence at the level that the correlation in the population is not zero. Figure 6.17 is an example of 400 (, ) pairs that have an observed correlation of 0.10. For these data, the -value for testing the null hypothesis of no correlation is 0.03. The small -value does not mean that there is a strong association, only that there is evidence of some association.
Figure 6.17: FIGURE 6.17 Scatterplot of observations with an observed correlation of 0.10, Example 6.24. There is not a strong association between the two variables even though there is signifcant evidence that the population correlation is not zero.