Illuminating Statistical Analysis Using Scenarios and Simulations

39Judging Correlation Differences

Statistical Scenario—Correlation Differences

Is there a difference in the predictability of male versus female weights based on heights?

Null hypothesis: There is no difference between the population correlation of males' heights and weights and the population correlation of females' heights and weights.

With our actual height and weight data, the male sample correlation is 0.65 and the female sample correlation is 0.77, for a difference of −0.12. This difference suggests the possibility that females' weights are more predictable, but we need to determine how likely it is that such a difference in sample correlations could simply arise by chance.

In the following simulation, we'll assume the null hypothesis is true, with the same population correlation for males and females. For the population correlation we'll use the average of 0.65 and 0.77, which is 0.71.¹ Each of 10,000 surveyors gathers height and weight data for 60 random males and 60 random females, calculates the male and the female sample correlations, and then calculates the correlation difference of males minus females.² We want to see how many of the 10,000 differences are less than or equal to −0.12. To make it two-tail, we'll also consider differences greater than or equal to +0.12. This will show us how likely it is to get sample correlation differences as extreme as −0.12 or +0.12 when the null hypothesis is actually true. Figure 39.1 is the simulation results histogram. ...