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Part IV: Guesstimating and Hypothesizing with Confidence
in the United States could get to within about 3% of what the whole popula-
tion would have said, if they had all been asked.
Using the formula for margin of error for a sample proportion, you can look at
how the margin of error changes dramatically for samples of different sizes.
Suppose in the presidential approval poll that n was 500 instead of 1,000. (Recall
that = 0.52 for this example.) Therefore the margin of error for 95% confidence
is
When n = 1,000 in the same example, the margin of error (for 95% confidence)
, which is equal to 3.10%. If n
is
is increased to 1,500, the margin of error (with the same level of confidence)
becomes
, or 2.53%. Finally, when
,
n = 2,000, the margin of error is , which is equivalent to 4.38%.
or 2.19%.
Looking at these different results, you can see that larger sample sizes
decrease the MOE, but after a certain point, you have a diminished return.
Each time you survey one more person, the cost of your survey increases,
and going from a sample size of, say, 1,500 to a sample size of 2,000 decreases
your margin of error by only 0.34% (one third of one percent!) — from 0.0253
to 0.0219. The extra cost and trouble to get that small decrease in the MOE
may not be worthwhile. Bigger isn’t always that much better!
But what may really surprise you is that bigger can actually be worse! I
explain this surprising fact in the following section.
Keeping margin of error in perspective
The margin of error is a measure of how close you expect your sample
results to represent the entire population being studied. (Or at least it gives
an upper limit for the amount of error you should have.) Because you’re
basing your conclusions about the population on your one sample, you have
to account for how much those sample results could vary just due to chance.
Another view of margin of error is that it represents the maximum expected
distance between the sample results and the actual population results (if
you’d been able to obtain them through a census). Of course if you had the
absolute truth about the population, you wouldn’t be trying to do a survey,
would you?

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