Datasheet
17
Chapter 1: Evaluating Data in the Real World
Although not likely, those errors are possible. They lurk in every study that
involves inferential statistics. Statisticians have named them Type I and
Type II.
If you reject H
0
and you shouldn’t, that’s a Type I error. In the coin example,
that’s rejecting the hypothesis that the coin is fair, when in reality it is a fair
coin.
If you don’t reject H
0
and you should have, that’s a Type II error. That hap-
pens if you don’t reject the hypothesis that the coin is fair, and in reality it’s
biased.
How do you know if you’ve made either type of error? You don’t — at least
not right after you make your decision to reject or not reject H
0
. (If it’s pos-
sible to know, you wouldn’t make the error in the first place!) All you can do
is gather more data and see if the additional data are consistent with your
decision.
If you think of H
0
as a tendency to maintain the status quo and not interpret
anything as being out of the ordinary (no matter how it looks), a Type II error
means you missed out on something big. Looked at in that way, Type II errors
form the basis of many historical ironies.
Here’s what I mean: In the 1950s, a particular TV show gave talented young
entertainers a few minutes to perform on stage and a chance to compete for a
prize. The audience voted to determine the winner. The producers held audi-
tions around the country to find people for the show. Many years after the
show went off the air, the producer was interviewed. The interviewer asked
him if he had ever turned down anyone at an audition that he shouldn’t have.
“Well,” said the producer, “once a young singer auditioned for us and he
seemed really odd.”
“In what way?” asked the interviewer.
“In a couple of ways,” said the producer. “He sang really loud, gyrated his
body and his legs when he played the guitar, and he had these long side-
burns. We figured this kid would never make it in show business, so we
thanked him for showing up, but we sent him on his way.”
“Wait a minute, are you telling me you turned down . . .”
“That’s right. We actually said ‘no’ . . . to Elvis Presley!”
Now that’s a Type II error.
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