Page 75 - Statistics for Dummies

How do you interpret a margin of error? Suppose you know that 51% of people
sampled say that they plan to vote for Ms. Calculation in the upcoming election.
Now, projecting these results to the whole voting population, you would have
to add and subtract the margin of error and give a range of possible results in
order to have sufficient confidence that you’re bridging the gap between your
sample and the population. Supposing a margin of error of plus or minus 3 per-
centage points, you would be pretty confident that between 48% (51% – 3%) and
54% (51% + 3%) of the population will vote for Ms. Calculation in the election,
based on the sample results. In this case, Ms. Calculation may get slightly more
or slightly less than the majority of votes and could either win or lose the elec-
tion. This has become a familiar situation in recent years when the media want
to report results on Election Night, but based on early exit polling results, the
election is “too close to call.” For more on the margin of error, see Chapter 12.
The margin of error measures accuracy; it does not measure the amount of
bias that may be present (find a discussion of bias earlier in this chapter).
Results that look numerically scientific and precise don’t mean anything if
they were collected in a biased way. Chapter 4: Tools of the Trade 59
Confidence interval
One of the biggest uses of statistics is to estimate a population parameter
using a sample statistic. In other words, use a number that summarizes a
sample to help you guesstimate the corresponding number that summarizes
the whole population (the definitions of parameter and statistic appear ear-
lier in this chapter). You’re looking for a population parameter in each of the
following questions:
✓ What’s the average household income in America? (Population = all
households in America; parameter = average household income.)
✓ What percentage of all Americans watched the Academy Awards this
year? (Population = all Americans; parameter = percentage who watched
the Academy Awards this year.)
✓ What’s the average life expectancy of a baby born today? (Population =
all babies born today; parameter = average life expectancy.)
✓ How effective is this new drug on adults with Alzheimer’s? (Population =
all people who have Alzheimer’s; parameter = percentage of these people
who see improvement when taking this drug.)
It’s not possible to find these parameters exactly; they each require an
estimate based on a sample. You start by taking a random sample from a
population (say a sample of 1,000 households in America) and then finding
the corresponding statistic from that sample (the sample’s mean household
income). Because you know that sample results vary from sample to sample,
you need to add a “plus or minus something” to your sample results if you
want to draw conclusions about the whole population (all households in

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