'''[[Sample (statistics) | Sample]] size''', usually designated N, is the number of repeated measurements in a statistical [[Sample (statistics) | sample]]. They are used to [[estimate]] a [[parameter]], a descriptive quantity of some [[statistical population | population]]. N determines the [[Accuracy and precision | precision]] of that [[estimate]]. Larger N gives smaller error bounds of estimation. A typical statement is to say that one can be 95% sure the true [[parameter]] is within +or- B of the [[estimate]], where B is an error bound that decreases with increasing N. Such a bounded [[estimate]] is refered to as the [[confidence interval]] for that [[parameter]].

'''[[Sample (statistics) | Sample]] size''', usually designated N, is the number of repeated measurements in a statistical [[Sample (statistics) | sample]]. They are used to [[estimate]] a [[parameter]], a descriptive quantity of some [[statistical population | population]]. N determines the [[Accuracy and precision | precision]] of that [[estimate]]. Larger N gives smaller error bounds of estimation. A typical statement is to say that one can be 95% sure the true [[parameter]] is within +or- B of the [[estimate]], where B is an error bound that decreases with increasing N. Such a bounded [[estimate]] is refered to as the [[confidence interval]] for that [[parameter]].

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For example, the simplest [[rule of thumb]] for estimating any [[parameter]] is the one for a [[Proportionality (mathematics) | proportion]] in a [[statistical population | population]]. It is that the maximum bound, B, of a 95% [[confidence interval]] for an unknown [[Proportionality (mathematics) | proportion]] is 1/sqrt(N). So, N=100 gives B = 10%, N=400 gives B = 5%, N=1000 gives B = ~3%, and N=10000 gives B = 1%. One sees these numbers quoted often in news reports of [[opinion poll]]s and other [[sample survey]]s.

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For example, the simplest rule of thumb for estimating any [[parameter]] is the one for a [[Proportionality (mathematics) | proportion]] in a [[statistical population | population]]. It is that the maximum bound, B, of a 95% [[confidence interval]] for an unknown [[Proportionality (mathematics) | proportion]] is 1/sqrt(N). So, N=100 gives B = 10%, N=400 gives B = 5%, N=1000 gives B = ~3%, and N=10000 gives B = 1%. One sees these numbers quoted often in news reports of [[opinion poll]]s and other [[sample survey]]s.

For sufficient N, usually at least 30, the general 95% [[confidence interval]] for a [[population mean]] or "[[expected value]]" is the [[Sample (statistics) | sample]] [[arithmetic mean | mean]] +or- B, where B = 2sqrt(V/N) and V is the [[variance]] of the sampled variable. Conversely N=4V/B<sup>2</sup>.

For sufficient N, usually at least 30, the general 95% [[confidence interval]] for a [[population mean]] or "[[expected value]]" is the [[Sample (statistics) | sample]] [[arithmetic mean | mean]] +or- B, where B = 2sqrt(V/N) and V is the [[variance]] of the sampled variable. Conversely N=4V/B<sup>2</sup>.

Sample size, usually designated N, is the number of repeated measurements in a statistical sample. They are used to estimate a parameter, a descriptive quantity of some population. N determines the precision of that estimate. Larger N gives smaller error bounds of estimation. A typical statement is to say that one can be 95% sure the true parameter is within +or- B of the estimate, where B is an error bound that decreases with increasing N. Such a bounded estimate is refered to as the confidence interval for that parameter.

For example, the simplest rule of thumb for estimating any parameter is the one for a proportion in a population. It is that the maximum bound, B, of a 95% confidence interval for an unknown proportion is 1/sqrt(N). So, N=100 gives B = 10%, N=400 gives B = 5%, N=1000 gives B = ~3%, and N=10000 gives B = 1%. One sees these numbers quoted often in news reports of opinion polls and other sample surveys.