Which hospital (in the wild)?
Say there are two hospitals in your area well call them General Hospital and Specific Hospital. (What?)
Ok. We’ll actually call them A and B. Hospital A starts a marketing campaign and they want to target specific groups of people. They run two ads. The first says, “If you’re under 65 we have a lower death rate than hospital B.” On another channel (probably CBS) they run another ad sayings, “If you’re over 65, we have a lower death rate than hospital B.”
Hospital B goes out and crunches the numbers and they find that, yes, in fact Hospital A is telling the truth. Hospital B then starts it’s marketing campaign with an ad targeted to everyone saying, “Our hospital has a lower death rate than hospital A.” Hospital A crunches the numbers and finds that hospital B is in fact telling the truth.
How can this be? Here is one scenario:
Hosptial A’s stats are:
Under 65: 49 deaths in 100 patients
Over 65: 100 deahts in 300 patients
Hospital B’s stats are:
Under 65: 50 deaths in 100 patients
Over 65: 170 deahts in 500 patients
So this means for people under 65, hosptial A’s death rate is .49 comapred to .5 for hospital B. For Over 65, hospital A’s death rate is .3333 verus hospital B’s death rate of .34. So for each of the two age groups hospital A has the lower death rate. But the overall death rate for hospital A is .3725 and the overall death rate for hospital B is .3666. So hospital B has a lower overall death rate.
Which hospital would you rather visit?