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I'm trying to figure out a starting point for conducting statistical analysis on chemical composition of different bars of metal. I have data from about 150 different bars made over the course of a year. Because these bars are final product, I can only take samples from the top and bottom. Currently, we take three random samples from the top and three random samples from the bottom of each bar. The data is averaged to obtain a representative composition for the whole bar.

  • The number of samples we are currently taking was chosen at random. If possible, I would like to reduce the number of samples being taken. Is there a way to determine the amount of risk of the error incurred in reducing the sample size?

Also, due to the nature of this product, it is expected that the chemistry of one bar will not be similar to the chemistry of another bar. Additionally, due to the minimum detection value of the equipment, I have left censored data so my sampling distribution isn't normal.

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  • $\begingroup$ The variance is proportional to 1/n where n is the sample size. So the sampling error increases as the sample size decreases. $\endgroup$
    – Michael R. Chernick
    Feb 14, 2017 at 4:36
  • $\begingroup$ Just because you have censored data does not mean your distribution is not normal (although, physical properties that are strictly positive are often at best approximately normal, so probably it really is not normal). Since it is not really clear what you are trying to do in the analysis you plan to do, it is hard to give advice, but given that you already have some data, could you simulate some more data with a suitable distribution based on what you have seen and see what the effect of having less data would be on whatever analysis you plan to do? $\endgroup$
    – Björn
    Feb 14, 2017 at 7:49

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You have data from 150 bars, and from these data you have calculated some statistic (maybe the proportion of bars whose composition is outside some acceptable range).

You want to know how much extra error you would suffer if you only sampled 100 bars. You can find this out by repeatedly selecting at random 100 bars from your data and computing the statistic. Plot the distribution of the results. Is the interdecile range acceptable?

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  • $\begingroup$ I think the question was not about how to estimate the size of the error but rather how change in sample affects error. This is given by the standard error of the mean. $\endgroup$
    – Michael R. Chernick
    Jan 19, 2018 at 22:38

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