Page 50 - Statistics II for Dummies

34 Part I: Tackling Data Analysis and Model-Building Basics

The margin of error is affected by two elements:

✓ The sample size
✓ The amount of diversity in the population (also known as the population
standard deviation)

You can read more about these elements in Chapter 3, but here’s the big pic-
ture: As your sample size increases, you have more data to work with, and
your results become more precise. As a result, the margin of error goes down.

On the other hand, a high amount of diversity in your population reduces
your level of precision because the diversity makes it harder to get a handle
on what’s going on. As a result, the margin of error increases. (To offset this
problem, just increase the sample size to get your precision back.)
To interpret the margin of error, just think of it as the amount of play you
allow in your results to cover most of the other samples you could have taken.
Suppose you’re trying to estimate the proportion of people in the population
who support a certain issue, and you want to be 95 percent confident in your
results. You sample 1,002 individuals and find that 65 percent support the
issue. The margin of error for this survey turns out to be plus or minus 3
percentage points (you can find the details of this calculation in Chapter 3).
That result means that you could expect the sample proportion of 65 percent
to change by as much as 3 percentage points either way if you were to take
a different sample of 1,002 individuals. In other words, you believe the
actual population proportion is somewhere between 65 – 3 = 62 percent
and 65 + 3 = 68 percent. That’s the best you can say.

Any reported margin of error is calculated on the basis of having zero bias
in the data. However, this assumption is rarely true. Before interpreting any
margin of error, check first to be sure that the sampling process and the
data-collection process don’t contain any obvious sources of bias. Ignore
results that are based on biased data, or at least take them with a great deal
of skepticism.

For more details on how to calculate margin of error in various statistical
techniques, turn to Chapter 3.

Knowing Your Limitations

The most important goal of any data analyst is to remain focused on the big
picture — the question that you or someone else is asking — and make sure
that the data analysis used is appropriate and comprehensive enough to
answer that question correctly and fairly.

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