Page 83 - Intermediate Statistics for Dummies

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Part I: Data Analysis and Model-Building Basics
Actual value of the parameter: A Type II error is also related to how big
the problem is that you’re trying to uncover. For example, suppose a com-
pany claims that the average delivery time for packages is 3.5 days. If the
actual average delivery time is 5 days, you won’t have a very hard time
detecting that with your sample (even a small sample). Evidence will
mount up fast for rejecting Ho, which is exactly what you’re supposed to
do in this situation. But if the actual average delivery time is 4.0 days, you
have to do more work to actually detect the problem. Note that you never
do know the actual value of a parameter, but you want to protect yourself
against the different possibilities, which is why you consider them.
To reduce the chance of a Type II error, take a larger sample size. A greater
sample size makes it easier to reject Ho, but increases the chance of a Type I
error. Type I and Type II errors sit on opposite ends of a seesaw — as one
goes up, the other goes down. To try to meet in the middle, choose a large
sample size (the bigger, the better; see Figures 3-1 and 3-2) and a small α level
(0.05 or less) for your hypothesis test.
Getting empowered by the
power of a hypothesis test
Type II errors (see preceding section) show the downside of a hypothesis
test. Statisticians, despite what many may think, actually try to look on the
bright side once in a while, and this case is one of those times. Instead of
looking at the chance of missing a difference from Ho that actually is there,
you can look at the chance of detecting a difference that really is there. This
detection is called the power of a hypothesis test.
The power of a hypothesis test is one minus the probability of making a
Type II error. So power is a number between 0 and 1 that represents the
chance that you rejected Ho when Ho was false. (You can even sing about it
“If Ho is false and you know it, clap your hands. . . .”) Remember that power
(just like Type II errors) depends on two elements: the sample size and the
actual value of the parameter (see the preceding section for a description of
these elements).
In the following sections, you discover what power means in statistics (not
being one of the big wigs, mind you); you also find out how to quantify power
by using a power curve.