objections to example given ambiguous and false The probability of taking data more than two standard deviations from the mean is roughly 05 Six measurements were taken so the probability that one should be so far from the mean is 05 6 3 I have several objections to this statement the first sentence above is true in the case of data from a normal distribution for which the true mean and true variance are known In general it is not true Furthermore in the example given the observed estimated values of these parameters are used One can t just replace true values of the parameters with the estimated values and expect whatever probabilistic statement one s trying to make to remain true and not necessarily even roughly true as stated especially for a sample of size 6 Furthermore even IF the data are from a normal distribution and IF one does happen to know the parameters true values or good estimates thereof the probabilistic statement made the second sentence above is ambiguous and false the probability that one should be so far from the mean in the exact sense is in fact zero since the normal distribution has no point masses If the event whose probability is meant to be calculated is exactly one should be so far or further from the mean then that value is actually not 0 3 as claimed Or the probability that at least one should be so far or further from the mean is actually not 0 3 as claimed I would fix the article myself but first I d like to hear what others think about all this 30 June 2005 22 46 UTC