# How Should You Analyze Very Small Samples?

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- This topic has 6 replies, 4 voices, and was last updated 1 year, 10 months ago by Robert Butler.

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- March 21, 2018 at 2:26 am #55964
Hello everyone,

What is your opinion when performing statistical analyses on results from destructive tests, especially when they are extremely small samples (less than 5)? What approach would you recommend and which statistical tests would be of best use?

Thank you for your kind help.

0March 21, 2018 at 7:13 am #202376

Robert ButlerParticipant@rbutler**Include @rbutler in your post and this person will**

be notified via email.The tests designed for exactly that purpose. If you are interested in comparing means then use the t-test and if you are interested in comparing variability then use the F test.

I realize there is lots of stuff out there on the net which insists you have to have gobs of data before you can do anything with either of these tests and there is also lots of stuff that claims you have to have 8 or 10 or 15 or 30 or whatever other number the writer chooses to pick before you can run either of these tests (and there is also the hoary old chestnut concerning a need for normality) but a check of the appendices of any good book on statistics will show you that the minimum number of samples needed to run a t-test is 2 and that for comparison of variance the minimum number of tests per group is also 2. Granted the t value and the F value for significance in both cases is large but that is the way the cookie crumbles.

Most of the work I have done has been in situations where the cost per sample was very high ($5000 and up). The end result has been situation after situation where the max number of allowed samples was between 1 and 5 with most instances being between 1 and 3. In every case I was able to provide information that helped my engineers get where they needed to go with respect to new product development, process improvement, etc.

0March 21, 2018 at 10:05 am #202377

Chris SeiderParticipant@cseider**Include @cseider in your post and this person will**

be notified via email.well put, my friend @rbutler

0March 22, 2018 at 2:55 am #202380Hello @rbutler,

Thank you very much for your kind response. You have been truly helpful.

Best regards.

0March 24, 2018 at 1:02 pm #202386@rbutler If you are doing t or F tests with such small samples as you suggested won’t the confidence intervals be so wide that the Beta error will be so high that difference may not be seen even though it might be there?

0March 26, 2018 at 2:21 pm #202391Before testing small samples:

Make sure that your test system is high accurate by calibration with reference standards.

Make sure that your test system is highly precise.

0March 26, 2018 at 4:10 pm #202392

Robert ButlerParticipant@rbutler**Include @rbutler in your post and this person will**

be notified via email.@Darth – yes, no, maybe. It would be a function of things like sample variation, distance between the sample means, distance between the sample mean and a reference, etc.

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