The Quick Count and Election Observation

THE QUICK COUNT AND ELECTION OBSERVATION
The size of the variance determines the precise shape of the actual distribution.
The key point for quick count purposes is that any dataset that conforms
to the normal distribution curve has exactly the same standard properties.
These are: 68.3 percent of all observed values will fall within one standard
deviation of the mean, 95.4 percent of all results will fall within two standard
deviations of the mean and 99.7 percent of all results will fall within three standard
deviations of the mean. Not all datasets will conform to this exact pattern.
If there is a lot of variance within the data, the curve will be relatively flat. If
there is little variation, the curve will appear more peaked.
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The distance from the mean, expressed as standard deviations, can also be
referred to as Z scores or critical values. Most standard statistics textbooks contain
a table of Z values for the normal distribution and analysts do not have
to calculate Z values each time they confront a data set. Significantly, if data
have a 95 percent confidence interval (95 percent of all sample means will
include the population mean), then it is clear that the results will fall within
1.96 standard deviations of the mean. Similarly, a 99 percent confidence level
indicates that 99 percent of all results (for which the sample mean will include
the population mean) fall within 2.58 standard deviations from the mean. In
these cases, the values 1.96 and 2.58 represent the critical values, or Z values,
for the confidence levels 95 percent and 99 percent, respectively.
Calculating the margin of error requires relying on the standard deviation and
Z values. The standard deviation and Z values, in turn, involve measures of
central tendency, measures of dispersion and confidence levels. As Figure 5-3
shows, margins of error vary with confidence levels and with sample sizes. In
general, the higher the confidence level, the higher the margin of error. The
larger the sample size, the lower the margin of error. Decisions about what
margin of error can be tolerated with a quick count will directly impact calculations
to determine the required minimum sample size.
Decisions about what
margin of error can be
tolerated with a quick
count will directly
impact calculations to
determine the required
minimum sample size.
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FIGURE 5-3:
MARGINS OF ERROR
AND SAMPLE SIZES
Margin of Error
10
8
6
4
2
95% confidence level
99% confidence level
0
100 250 500 750 1,000 1,500 2,000 3,000 5,000 10,000
Sample Size (individual voters)