How to Estimate Correct Sample Sizes

Those readers who do not want to be frustrated by the possibility that their past decisions might be based on a number of measurements which was not theoretically correct should skip this section. 

Obviously tests and decisions drawn from them are dependent on the estimated (calculated) parameters. It is worth mentioning that they also depend on the number, n, of measurements or replicates. In addition we know that we do not have one risk alone. Therefore we have to accept that the sensitivity of tests is determined by the proper choice of n, it increases with increasing n. It is, however, not usually possible to increase n without additional costs. On the other hand one can often say, e.g. from experience or from legal requirement which difference between two means may be tolerated and which difference must be assured. Taking into account this and both tolerable risks of wrong decisions, associated with type I and type II errors, one can compute the necessary number of replicates in advance (see textbooks on statistics or ZWANZIGER et al. [1986])  

Assume that a waterworks is able to maintain water quality without problems if the actual Zn concentration is within a tolerance Ax = 10 qg L 1 around /r0 = 190 pg L 1. Is it acceptable to continue monitoring water quality by drawing n = 10 samples at each test interval Because we further assume that incorrect decisions about Zn have no dramatic effects we 

Hence we decide that n = 10 samples will be sufficient. 

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