Page 66 - Intermediate Statistics for Dummies

06_045206 ch02.qxd 2/1/07 9:43 AM Page 45
Chapter 2: Sorting through Statistical Techniques
A statistic can be precise with or without bias, and vice versa. The best situa-
tion is when your results are both precise (consistent) as well as unbiased
(on target). That goal is what statisticians always strive for. How often does
it happen? You can have a lot of control of the precision part by simply taking
a larger sample. However, the goal of completely unbiased results is rarely
achieved, but that doesn’t stop statisticians from trying. And you do have
ways to minimize it (keep reading).
Measuring precision with margin of error
You can measure precision by the margin of error. The margin of error is the
amount that you expect your statistical results to change from one sample
to the next. While you always hope, and may even assume, that statistical
results shouldn’t change much with another sample, that’s not always the
case. It’s like a commercial that tries to sell a weight-loss product by showing
a person who lost 50 pounds in a single weekend; then in small letters at the
bottom of the screen, you see the words “results will vary.” Before you report 45
or try to interpret any statistical results, you need to have some measure-
ment of how much those results are expected to vary from sample to sample.
The following sections show how to calculate the precision of your statistic
and how to come up with a margin of error.
Calculating precision
The exact formulas for margin of error differ depending on the type of data
that you’re analyzing; however, they all contain two major components:
Confidence coefficient
Standard error of the statistic
The general structure of a formula for margin of error is the following, where
standard error is the standard deviation of the population divided by the
square root of the sample size (you can see all the details on margin of error
in Chapter 3):
Margin of error = ± Confidence coefficient Standard error
*
The big idea is that the confidence coefficient tells you the number of stan-
dard errors you’re willing to add and subtract in order to have a certain level
of confidence in your results. If you want to be more confident in your results,
you add or subtract more standard errors. If you don’t have to be as confi-
dent, you don’t have to add or subtract as many standard errors. Typically,
you add and subtract about two standard errors if you want to be 95 percent
confident and three standard errors if you want to be more than 99 percent
confident. This rule of thumb follows a statistical result called the Empirical
Rule, also known as the 68-95-99.7 Rule.