MONSTERPET and PETPLUMP are two different brandsof pet food. Each is guaranteed to make your animal growlarger. The following study involves 11 cats and 11 dogs.

4 cats eat Monsterpet. 3 of them double in size; 1 remains puny.7 cats eat Petplump. 5 of them double in size; 2 remain puny.7 dogs eat Monsterpet. 2 of them double in size; 5 remain puny.4 dogs eat Petplump. 1 of them doubles in size; 3 remain puny.

MONSTERPET PETPLUMP

Success rate=3/4=75%

Success rate=5/7=71%

Success rate=1/4=25%

Success rate=2/7=28%

MONSTERPET PETPLUMP

Total success rate

=5/11=45% Total success rate

=6/11=54%

Overall, PETLUMP outperforms MONSTERPET54% grow with Petplump while 45% grow with Monsterpet

• Perhaps we can unravel this paradox.• Notice that with both brands of food, the cats respond much

more than the dogs:• Seventy some percent of cats grow with each product.• Twenty some percent of dogs grow with each product.

But a higher percentage of cats grow with Monsterpet:

75% compared to 71%

And a higher percentage of dogs grow with Monsterpet:

28% compared to 25%

MONSTERPET PETPLUMP

Because there are more cats onthe Petplump side, the overall percentages for Petplump are higher

This puny creature would not deter a burglar.

But feed her Monsterpet and see results

MEOW

We are going to rework this example, turning the animalsinto people participating in a drug trial.

Monsterpet becomes drug A Petplump becomes drug B

The animals who responded favorably to the petfoods by growing large will become people who were cured by the drug.

The small animals who did not respond become people who were not cured.

DRUG A DRUG B

Cure rate = 5/11 = 45% Cure rate = 6/11 = 54%

Drug B appears to be more effective.

Now, suppose the people who used to be catsshare a genetic trait that predisposes them to respondmore favorably to treatment. Suppose this trait is invisible.

Drug A really works better for both groups of people - those with the trait and those without the trait.

But, because more of the people with the trait are assignedto the sample being treated with B, it makes B look better.

DRUG A DRUG B3/4=75%cure rate

5/7=71%cure rate

2/7=28%cure rate

1/4=25%cure rate