Illuminating Statistical Analysis Using Scenarios and Simulations

40Correlation with Mixed Data Types

Statistical Scenario—Correlation Between a Binomial and a Scaled Variable

We can also use the correlation approach we have been using to assess the relationship between a 0 or 1 valued binomial, such as sex, and a scaled variable, such as height.

For sex and height, calculations give us of −0.67 and an extremely small -value of 10⁻¹⁶. We reject the null hypothesis of no relationship between sex and height. Also, since males have been designated by 0 and females by 1, the negative correlation means that females are generally shorter than males: Higher values for sex are associated with lower values for height. Given the teeny-tiny -value, you can probably rest assured that males tend to be taller than females.

Shown in Figure 40.1 is the (weird looking) scatterplot with the A, B, C, and D regions. All the males' heights are bunched up at and all the females' heights are bunched up at . You can see that the majority of males are above the overall ...