Page 205 - Statistics for Dummies

2.58 – 1.96 = 0.62 (see Table 12-1). Most people don’t think adding and sub-
tracting this much more of a MOE is worthwhile, just to be 4% more confident
(99% versus 95%) in the results obtained.
You can never be completely certain that your sample results do reflect the
population, even with the margin of error included. Even if you’re 95% confi-
dent in your results, that actually means that if you repeat the sampling pro-
cess over and over, 5% of the time the sample won’t represent the population
well, simply due to chance (not because of problems with the sampling pro-
cess or anything else). In these cases, you would miss the mark. So all results
need to be viewed with that in mind.
Determining the Impact of Sample Size
The two most important ideas regarding sample size and margin of error are
the following: Chapter 12: Leaving Room for a Margin of Error 189
✓ Sample size and margin of error have an inverse relationship.
✓ After a point, increasing n beyond what you already have gives you
a diminished return.
This section illustrates both concepts.
Sample size and margin of error
The relationship between margin of error and sample size is simple: As the
sample size increases, the margin of error decreases. This relationship is
called an inverse because the two move in opposite directions. If you think
about it, it makes sense that the more information you have, the more accu-
rate your results are going to get (in other words, the smaller your margin
of error will get). (That assumes, of course, that the data were collected and
handled properly.)

In the previous section, you see that the impact of a larger confidence level
is a larger MOE. But if you increase the sample size, you can offset the larger
MOE and bring it down to a reasonable size! Find out more about this concept
in Chapter 13.

Bigger isn’t always (that much) better!

In the example of the poll involving the approval rating of the president (see
the earlier section “Calculating margin of error for a sample proportion”), the
results of a sample of only 1,000 people from well over 310,000,000 residents

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