Statistics for Non-Statisticians by Birger Madsen

Author:Birger Madsen
Language: eng
Format: epub, pdf
Publisher: Springer Berlin Heidelberg, Berlin, Heidelberg

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It is clear from the figure that as long as p is not too close to 0 or 1 (for example, if p is somewhere in the interval from 0.2 = 20% to 0.8 = 80%), the statistical uncertainty is roughly the same as when p = 0.5.

In other words:

The relative statistical uncertainty is u/p; this number gets larger, the smaller p is, see Fig. 5.5 which is still based on a sample size of n = 100

Fig. 5.5Relative statistical uncertainty

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When the relative frequency approaches 0, the relative statistical uncertainty can get infinitely large.

This can be translated to the opinion polls: The largest political parties, which come close to 50%, have the largest statistical uncertainty. In contrast, the smallest political parties have the largest relative statistical uncertainty.

It appears from the formula that the statistical uncertainty u is inversely proportional to the square root of the sample size n. For example, if the sample gets four times larger, the statistical uncertainty is halved. Conversely, if the sample gets four times smaller, the statistical uncertainty is doubled.

This is illustrated in Fig. 5.6, which shows the statistical uncertainty vs. n, where p = 0.5. In other words, this is the maximum statistical uncertainty for a given sample size

Fig. 5.6Statistical uncertainty vs. n

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