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Assuming we have a sample (some observables) from a population of unknown distribution, can I assume that the right way to estimate the sample size (for estimating means, medians, etc.) is using the formula:

$$n = 4s^2 / d^2$$

where $s$ is the sample standard deviation, $d$ is the margin of error (precision), and $n$ is the sample size? ... or is there some implicit assumption that the population itself must be Normal in order for this to be valid?

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  • $\begingroup$ That formula you quote is not suitable for estimating sample size in respect of medians. It's specifically designed for means, since its based on the standard error of the mean. It isn't restricted to normality as long as the sample size is large enough for the distribution of the sample mean to be sufficiently well-approximated by the normal (and when that is depends on the distribution as well as your individual criteria for how close you need your approximation). For medians you'd need a different constant than 4, and that constant would depend on the distribution. ... ctd $\endgroup$
    – Glen_b
    Sep 18, 2013 at 22:46
  • $\begingroup$ It really comes down to (i) what population quantity you're estimating, (ii) what estimator you're using for it, and (iii) the properties of that estimator (which in most cases differs from distribution to distribution). In many cases there will be a formula somewhat like the one you have (many estimators will be asymptotically normal with some standard error, for example), but different in detail. $\endgroup$
    – Glen_b
    Sep 19, 2013 at 2:50

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