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Sample Size for Non-Normal Distribution

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  • #50720

    Terry
    Member

    I have a sensor that I need to try to estimate its average output error. Say that an input “x” can be fed into the sensor, and its expected output should be “y.” The values of “x” range from 0 to 1, where the output error is near 0% for values of “x” near 0, and the output error has some growth as “x” increases to 1.
     
    I want to randomly pick “n” “x’s” and feed them into the sensor and calculate the output error from the sensor. I then want to determine the average output error from the sample of “n” output errors. My problem is, how many “n’s” is large enough to be confidence in my measured average output error? My understanding is that if the output errors had been normally distributed, then n=(z*s/E)^2, where z is the z value and E is the acceptable error. But assuming my output errors are not normally distributed, what can I do?

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    #174752

    GB
    Participant

    So, at the end of all that, you need a sampling strategy?
    If so, check this out:
    http://www.variation.com/techlib/as-7.html
    if not, please clarify.

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    #174753

    GB
    Participant

    This is the link I meant to post…and edit feature would be nice…
    http://www.variation.com/as-book.html

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    #174756

    Terry
    Member

    Thank you for your reply. I looked through the links you posted and I don’t think they are what I am looking for. My understanding is that a sampling plan is a method for determining if a lot meets of fails to meet your criteria (binomial). I simply want to determing the average output error (continuous) of a non-normal population by testing a sample of “n” items. For obvious reasons, I want to make “n” as small as possible while still having a reasonably acceptable amount of error in my estimate.

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    #174759

    Darth
    Participant

    If you have accessibility to Minitab you can probably find your answer under the Power and Sample size tab.  When computing any kind of sample size you want to make a judgement on how much difference (precision) you wish to see, how much confidence (alpha error) you want and how much power (beta error) you are willing to accept.  You also need some estimate of variation of your population.  Sometimes you might need to make an adjustment if the population from which you are sampling is small.  If you want to send me some specifics offline, I can take stab at it.  [email protected]

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    #174767

    Michael Mead
    Participant

    What you are looking at is similar to gage error–particularly equipment variation, linearity, and stability,. There are many ways to measure this. Just check a thread here or use a program or the AIAG Measurement Syatem Analysis book.

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    #174782

    Robert Butler
    Participant

      Your statement “The values of “x” range from 0 to 1, where the output error is near 0% for values of “x” near 0, and the output error has some growth as “x” increases to 1.” suggests you have a situation where the mean and the standard deviation are coupled – as the mean increases so does the variability. 
      Under these circumstances you do not want to just take a random sample and compute some estimate of variance because the computation will not accurately reflect your average output error. 
      You will need to take multiple samples at various points over the range of x and plot the means vs the standard deviations. If this plot shows an increasing linear trend you can transform the data by taking the log of the data and then repeat the exercise. If the trend disappears then you can run the calculations on the log values. A computation of test reproducibility based on logs will be a relative test reproducibility. This reports test reproducibility as a percentage of the test measurement property.
      The above is assuming a simple linear trend.  You really need to run tests like this and do some plotting.  Odd looking plots could suggest issues like those mention by Michael Mead – e.g. linearity and stability – and if these are an issue then you will need to do a lot more work before you are in a position to try to provide an assessment of average output error.

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    #174784

    Terry
    Member

    I must say, this comunity of people is absolutely outstanding. Replies are always very fast and helpful.
    Unfortunately, I do not have any access to previous data, and I do not know what the criteria is. All that I need to do is make a spreadsheet that automatically calculates the solution to the problem. Trying to put the problem more concisely: Find the smallest sample size necessary to to have some confidence that the populations output error lies within some error (say +- .005) of the sample output error. Also, I do not know what the distribution of the populations output errors is. Is there any such general solution to this problem?

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