Datasheet

16
Part I: Statistics and Excel: A Marriage Made in Heaven
With the hypotheses in place, toss the coin 100 times and note the number
of heads and tails. If the results are something like 90 heads and 10 tails, it’s
a good idea to reject H
0
. If the results are around 50 heads and 50 tails, don’t
reject H
0
.
Similar ideas apply to the reading-speed example I gave earlier. One sample
of children receives reading instruction under a new method designed to
increase reading speed, the other learns via a traditional method. Measure
the children’s reading speeds before and after instruction, and tabulate the
improvement for each child. The null hypothesis, H
0
, is that one method
isn’t different from the other. If the improvements are greater with the new
method than with the traditional method — so much greater that it’s unlikely
that the methods aren’t different from one another — reject H
0
. If they’re not,
don’t reject H
0
.
Notice that I didn’t say “accept H
0
.” The way the logic works, you never accept
a hypothesis. You either reject H
0
or don’t reject H
0
.
Notice also that in the coin-tossing example I said around 50 heads and 50
tails. What does “around” mean? Also, I said if it’s 90-10, reject H
0
. What about
85-15? 80-20? 70-30? Exactly how much different from 50-50 does the split
have to be for you reject H
0
? In the reading-speed example, how much greater
does the improvement have to be to reject H
0
?
I won’t answer these questions now. Statisticians have formulated decision
rules for situations like this, and we’ll explore those rules throughout the
book.
Two types of error
Whenever you evaluate the data from a study and decide to reject H
0
or to
not reject H
0
, you can never be absolutely sure. You never really know what
the true state of the world is. In the context of the coin-tossing example, that
means you never know for certain if the coin is fair or not. All you can do is
make a decision based on the sample data you gather. If you want to be cer-
tain about the coin, you’d have to have the data for the entire population of
tosses — which means you’d have to keep tossing the coin until the end
of time.
Because you’re never certain about your decisions, it’s possible to make an
error regardless of what you decide. As I mentioned before, the coin could be
fair and you just happen to get 99 heads in 100 tosses. That’s not likely, and
that’s why you reject H
0
. It’s also possible that the coin is biased, and yet you
just happen to toss 50 heads in 100 tosses. Again, that’s not likely and you
don’t reject H
0
in that case.
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