Page 68 - Intermediate Statistics for Dummies

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Chapter 2: Sorting through Statistical Techniques
For more details on how to calculate margin of error in various statistical
techniques, see Chapter 3.
Interpreting margin of error
Finding the margin of error is one thing — figuring out what it means is a
whole other ball o’ wax. But don’t fear; it’s actually not so bad. 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 per-
centage points (you can find the details of this calculation in Chapter 3). That
result means that you can expect the sample proportion of 65 percent to
change by as much as 3 percentage points either way if you took 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. 47
That’s the best you can say.
Bias not included!
Realizing that the margin of error measures the consistency (precision) of a
statistic only, not its level of bias is extremely important. In other words, a
margin of error can appear on paper to be very small yet actually be way off
target because of bias in the data that was collected. (In the nearby sidebar,
you can see that Gallup discusses margin of error and bias separately.)
Any reported margin of error was 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. If a great deal of
bias exists, you should ignore the results, or take them with a great deal of
skepticism.
Making Conclusions and 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.