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Recalibrating sample size, non-normal distribution

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    DD
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    I used the formula n=(1.96S/delta)sq. to determine sample size for a data collection effort collecting continuous (time) data, having estimated S as 7 (no historical data).
    As the data came in it soon became obvious that the distribution was not normal, but positively skewed; I fitted a Weibull distribution model with shape 0.83, scale 6.64.
    How do I ‘recalibrate’ my estimate of sample size, it seems I don’t need anything like as many samples as I thought, looking at the histogram, but there is now no standard deviation figure from this non-normal distribution to plug into the original formula I used?
    any guidance appreciated.

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