Many people think they are pretty good at basic
statistics and probability theory. So give this one some thought
...Imagine there are two drugs, A and B,
that might help cure a problem you have and you are given the following
information. 1100 people took drug A and it helped 505 of them. And 1100 people
took drug B and it helped 195 of them. I put this in the table below along with
the percentage of people where each drug was a success. Assume you can't take
both drugs and that neither drug has any ill effect, risk, or cost from taking
it. Drug | Successful | Failed | percentage success
A | 505 | 595 | 46%
B | 195 | 905 | 18%
Which drug would you choose to take given this
information?Now let me provide a little
extra information. In the study above, it turns out that for drug A, there were
100 males and it worked for 5 of them and for drug B there were 1000 males and
it worked for 100 of them. From this information, and a little subtraction, I
have filled out the two tables below.
For
malesDrug | Successful | Failed | percentage success
A | 5 | 95 | 5%
B | 100 | 900 | 10%
For
femalesDrug | Successful | Failed | percentage success
A | 500 | 500 | 50%
B | 95 | 5 | 95%
From the percentage success, it looks like for
humans, drug A is successful about twice as often as drug B. However, for males
drug B is successful about twice as often and for females, drug B is successful
about twice as often.
So which drug
would you take? And how good is basic probability theory?
The really disturbing information thing
here was there was nothing special about the male/female separator. It might be
that if you looked at the data based on any other separator such as over/under
18 years old you would get something like this.
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