Page 64 - Statistics II for Dummies

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Part I: Tackling Data Analysis and Model-Building Basics
Type I and Type II errors sit on opposite ends of a seesaw — as one goes up,
the other goes down. Try to meet in the middle by choosing 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.

The power of a hypothesis test

Type II errors, which I explain in the preceding section, show the downside
of a hypothesis test. But statisticians, despite what many may think, actu-
ally try to look on the bright side once in a while; so instead of looking at the
chance of missing a difference from Ho that actually is there, they 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 1 – 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 bigwigs, mind you); you also find out how to quantify power
by using a power curve.

Throwing a power curve
The specific calculations for the power of a hypothesis test are beyond the
scope of this book (so you can take a sigh of relief), but computer programs
and graphs are available online to show you what the power is for different
hypothesis tests and various sample sizes (just type “power curve for the
[blah blah blah] test” into an Internet search engine).

These graphs are called power curves for a hypothesis test. A power curve
is a special kind of graph that gives you an idea of how much of a difference
from Ho you can detect with the sample size that you have. Because the
precision of your test statistic increases as your sample size increases,
sample size is directly related to power. But it also depends on how much
of a difference from Ho you’re trying to detect. For example, if a package
delivery company claims that its packages arrive in 2 days or less, do you
want to blow the whistle if it’s actually 2.1 days? Or wait until it’s 3 days? You
need a much larger sample size to detect the 2.1-days situation versus the
3-days situation just because of the precision level needed.

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