When I first saw inequalities (1) and (2) below, I quantified them as:
$\color{red}{\text{1.1. married people < all smokers}}$
$\color{red}{\text{2.1. and married smokers < all married people}}$
.
My guesses are wrong because I'm comparing quantities, but the author below compares fractions. But why are my guesses wrong?
> When you’re comparing two binary variables, correlation takes on a
particularly simple form. To say that marital status and smoking status are
negatively correlated, for example, is simply to say that married people are
less likely than the average person to smoke. Or, to put it another way,
smokers are less likely than the average person to be married. It’s worth
taking a moment to persuade yourself that those two things are indeed the
same! The first statement can be written as an inequality
>$\color{limegreen}{\text{married smokers / all married people < all smokers / all people}}$ Why doesn't `$\tag{1}$` work?
>and the second as
>$\color{limegreen}{\text{married smokers / all smokers < all married people / all people}}$ Why doesn't `$\tag{2}$` work?
> If you multiply both sides of each inequality by the common denominator
(all people) × (all smokers) you can see that the two statements are different
ways of saying the same thing:
>(married smokers) × (all people) < (all smokers) × (all
married people) Why doesn't `$\tag{3}$` work?
> In the same way, if smoking and marriage were positively correlated, it
would mean that married people were more likely than average to smoke and
smokers more likely than average to be married.
Ellenberg, *How Not to Be Wrong* (2014), pages 347-8.
Chgg Clou
·
2021-06-04T04:43:32Z (over 3 years ago)