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Thread: Relationship Between Increasing Mean and Standard Deviation

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    Relationship Between Increasing Mean and Standard Deviation




    Greetings, we sampled some fungal populations from an agricultural field. Our sample size is 24, and we sampled six plots. We noticed the standard deviation of our samples increases along with the mean, which we did not expect. What might this suggest about our data, and does anyone have ideas for how we might follow up on this? Thanks

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    Re: Relationship Between Increasing Mean and Standard Deviation

    I'm not sure why you would find it surprising that s.d. goes up as mean goes up. Imagine an extreme case, where your sample mean is 100 times larger than the previous one, but the s.d was the same. That would indicate extremely low variation, which is rare in the real world. So your results seem normal to me (I'm not an expert).

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    Re: Relationship Between Increasing Mean and Standard Deviation

    If I have exam results graded on a scale of 0 to 10 and the standard deviation is 3 and the mean a 6, then if I would have graded the results on a scale of 0 to 100 the standard deviation would be 30 and the mean 60. Sometimes the coefficient of variation is used to compare two standard deviations. It is simply the standard deviation divided by the mean.

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    Re: Relationship Between Increasing Mean and Standard Deviation

    Quote Originally Posted by stat4640 View Post
    Greetings, we sampled some fungal populations from an agricultural field. Our sample size is 24, and we sampled six plots. We noticed the standard deviation of our samples increases along with the mean, which we did not expect. What might this suggest about our data, and does anyone have ideas for how we might follow up on this? Thanks
    What is the topic and the research question here, and
    what did you actually measure as dependent variable?
    Moreover, it is not quite clear to me what you mean by
    six plots. Did you measure your DV at 6 different time
    points?

    With kind regards

    K.

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    Re: Relationship Between Increasing Mean and Standard Deviation

    Quote Originally Posted by stat4640 View Post
    We noticed the standard deviation of our samples increases along with the mean, which we did not expect. What might this suggest about our data, and does anyone have ideas for how we might follow up on this? Thanks
    Hi,
    this could be something as simple as a measurement instrument with a constant procentual error. Is your coefficient of variation constant?

    regards

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    Re: Relationship Between Increasing Mean and Standard Deviation

    I agree with Karabiner, in that your original post was not clear. Can you describe what you did in more detail to ensure you get appropriate replies.


    Thanks!
    Stop cowardice, ban guns!

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    Re: Relationship Between Increasing Mean and Standard Deviation

    Quote Originally Posted by stat4640 View Post
    Greetings, we sampled some fungal populations from an agricultural field. Our sample size is 24, and we sampled six plots. We noticed the standard deviation of our samples increases along with the mean, which we did not expect. What might this suggest about our data, and does anyone have ideas for how we might follow up on this? Thanks
    What did you measure? If you are measuring some type of count data, such as the population size, you would model it with a Poisson distribution where the variance = the mean. This would fit what you are seeing.

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    Re: Relationship Between Increasing Mean and Standard Deviation

    Quote Originally Posted by Miner View Post
    What did you measure? If you are measuring some type of count data, such as the population size, you would model it with a Poisson distribution where the variance = the mean. This would fit what you are seeing.
    Or a negative binomial, where the variance does not have to be exactly equal to the mean. Or a gamma distribution where the coefficient of variation (cv) is constant (cv=sigma/mean). The lognormal distribution also has the property of an increasing standard deviation when the mean increases.

    It would be more interesting if stat4640 showed us the original data.

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    Re: Relationship Between Increasing Mean and Standard Deviation


    It is common for variance to increase with the mean in practice with say financial data. This is a common cause of non-constant variance (heteroscedacity).
    "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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