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Thread: minimum number of data points for calculating standard error

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    minimum number of data points for calculating standard error




    Hi
    Is it valid to use only 3 data points to calculate standard error. I have seen many papers with mean and standard error calculated for a variable like pH of water sample recorded in triplicate only. That is only three observations. For example: pH = 7, 8 and 9. Is standard error valid for this case. Please help.

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    Re: minimum number of data points for calculating standard error

    I don't think there is a formal rule for this - technically you could do it with two points. There are many problems with only three data points, however. First, you confidence intervals will be huge, second your power will be horrible, third you can't generalize easy from 3 points, and 4th many methods are only asymptotically correct.

    So while you could do it, you almost certainly should not.
    "Very few theories have been abandoned because they were found to be invalid on the basis of empirical evidence...." Spanos, 1995

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    Re: minimum number of data points for calculating standard error

    Thankyou! Can I use standard deviation as alternative.

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    Re: minimum number of data points for calculating standard error

    Can I use standard deviation.

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    Re: minimum number of data points for calculating standard error

    No they are effectively the same thing in this context. That is the problems are the same.

    Why do you want to calculate a standard error with only 3 data points. That is what is the purpose, and why do you only have 3 data points - that is pretty rare with real world data.
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    Re: minimum number of data points for calculating standard error

    One thing a contributor pointed out. If you have a population of 3 or 4....then using 3 for SE makes some sense. Its jut pretty unlikely with real world data you will have populations that small I would think. And for large populations a few cases has the problems I mentioned.
    "Very few theories have been abandoned because they were found to be invalid on the basis of empirical evidence...." Spanos, 1995

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    Re: minimum number of data points for calculating standard error


    In the case of pH or most other water quality parameters subject to temporal variation, it makes little sense to me estimating error with only 3 samples.
    But that wasn't the point was it? i am just coming into this from a practical pov.
    The earth is round: P<0.05

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