Page 71 - Intermediate Statistics for Dummies

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Part I: Data Analysis and Model-Building Basics
It all comes down in the end to testing hypotheses to see whether certain
models fit, and if they do, to using confidence intervals to estimate certain
values in the population or to make predictions based on the model that you
built.
This chapter reviews the basic concepts of confidence intervals and hypothe-
sis tests, including the probabilities of making errors by chance. I also dis-
cuss how statisticians measure the ability of a statistical procedure to do a
good job — of detecting a real difference in the populations, for example.
Hang on — you’re in for quite a ride.
Estimating Parameters by Using
Confidence Intervals
Confidence intervals are a statistician’s way of covering themselves when it
comes to estimating a population parameter. For example, instead of just
giving a one-number guess as to what the average household income is in the
United States, a statistician would give a range of likely values for this
number. Statisticians do this for two reasons:
All good statisticians know sample results vary from sample to sample,
so a one-number estimate isn’t any good.
Statisticians have developed some awfully nice formulas you can use to
give a range of likely values, so why not use them?
In this section, you get the general formula for a confidence interval, includ-
ing the margin of error, and a good look at the common approach to building
confidence intervals. I also discuss interpretation and the chance of making
an error.
Getting the basics: The general form
of a confidence interval
The big idea of a confidence interval is coming up with a range of likely
values for a population parameter. The confidence level represents the
chance that if you repeated your sample-taking over and over, you’d get a
range of likely values that actually contains the actual population parameter.
In other words, it’s the long-term chance of being correct.