Page 67 - Intermediate Statistics for Dummies

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Part I: Data Analysis and Model-Building Basics
The standard error is the average amount of movement in the statistic you’re
using. It’s a function of two quantities:
Sample size: Sample size is perhaps the most important factor in con-
trolling margin of error. The sample size is in the denominator of the
standard error, meaning that as your sample size increases, the standard
error goes down, and that’s why the margin of error goes down.
This result makes sense, because having a larger sample means having
more information in your analysis, which should lead to greater precision.
As the sample size decreases, the margin of error goes up, because you
have less information to work with and that makes for less-precise results.
Standard deviation in the population: Standard deviation is close to the
average distance from the mean. If the population you took your sample
from has a large amount of variability, the standard deviation is large,
and the margin of error for your statistic goes up (because standard
deviation is in the numerator of the margin of error). If the population is
more homogeneous, your sample results are more homogeneous as well,
and the margin of error goes down (because the standard error gets
smaller).
Up close and personal: Survey results
The Gallup Organization states its survey results as the size of the sample. As you can guess, pre-
in a universal, statistically correct format. Using cision is related to the sample size, as seen in the
a specific example from a recent survey it con- section “Calculating precision.”
ducted, you can see the language it uses to The second sentence of the quote refers to the
report its results:
precision measurement: How much did Gallup
“These results are based on telephone inter- expect these sample results to vary? The fact
views with a randomly selected national that Gallup is 95 percent confident means that if
sample of 1,002 adults, aged 18 years and this process were repeated a large number of
older, conducted June 9–11, 2006. For results times, in 5 percent of the cases the results would
based on this sample, one can say with 95% be wrong, just by chance. This inconsistency
confidence that the maximum error attribut- occurs if the sample selected for the analysis
able to sampling and other random effects is doesn’t represent the population — not due to
±3 percentage points. In addition to sampling biased reasons, but due to chance alone (more
error, question wording and practical diffi- on this in Chapter 3).
culties in conducting surveys can introduce
(Check out the section “Bias not included” to get
error or bias into the findings of public opin-
the info on why the third sentence is included in
ion polls.”
this quote.)
The first sentence of the quote refers to how the
Gallup Organization collected the data, as well