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I'm currently researching the variability of sizes of potatoes when all of the potatoes in question have been harvested from a single field. One question keeps coming up in my statistical analyses: Under normal circumstances, are the sizes of potatoes - within a single field - normally distributed? (Please feel free to define the weasel words "normal circumstances" in the most helpful way you can imagine.)

Human height is often given as one of those classic examples of a normally distributed phenomenon. The little that I know about plant biology suggests that the central limit theorem applies just as much to potatoes as to the human body: the lengths of potato tubers and the lengths of human bones should have similarly-shaped distributions. But is that correct?


A bit of context to my original question: what I'm trying to do is to take the mean and standard deviation of my data and then, using the 68-95-99 rule, construct a series of confidence intervals, which I can then test or refine by looking at other data sets. Obviously, no real data set is going to conform perfectly to a model; I just need to know that, in principle, potato sizes are normally distributed enough that my method for drawing up confidence intervals isn't hopelessly misguided.

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    $\begingroup$ There seems to be some misunderstanding of the central limit theorem (CLT). CLT emphatically does NOT say that all variables in nature are normally distributed. Rather, it says that the sample means are normally distributed (approximately) when sample size is large. $\endgroup$ – Adhish Aug 29 '20 at 17:59
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    $\begingroup$ The only way to find out whether the sizes of potatoes or human beings are normally distributed is empirical measurement. $\endgroup$ – Adhish Aug 29 '20 at 18:03
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    $\begingroup$ @Adhish 'The only way to find out whether the sizes of potatoes or human beings are normally distributed is empirical measurement.' I was hoping that someone would point me to some empirical research on the topic. That's why I asked the question. $\endgroup$ – Tom Hosker Aug 29 '20 at 18:33
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    $\begingroup$ If you have data from your potatoes of one field, can't you answer empirically what the size distribution is from your own data? $\endgroup$ – Bryan Krause Aug 29 '20 at 19:32
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    $\begingroup$ @Adhish as far as I know, since height is the average of many QTLs it is normally distributed since it becomes a distribution of the means of these genes. I use this alot so I'd like to be corrected on this if I'm wrong $\endgroup$ – Hachiloni Aug 29 '20 at 20:58
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According to Evaluation of the Effect of Density on Potato Yield and Tuber Size Distribution potato tuber size was estimated using a normal distribution but they are not normally distributed

They found that a Weibull distribution with specific parameters estimated better than a normal distribution.

In fact you should not expect a normal distribution because there are no potatoes of negative size As such you expect a gamma distribution. The Weibull distribution is in the same family of distributions.

But in many cases the normal distribution is used since the probability of a negative number is negligigble.

Does this mean that potato sizes are still the result of many factors? It would seem so

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    $\begingroup$ The link to "this article" for me yields "access denied". Perhaps a bit more explicit citation would be good. $\endgroup$ – mgkrebbs Aug 30 '20 at 0:07
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    $\begingroup$ StackExchange answers should stand on their own; other references are great and are even required in many cases here at Biology.SE, but people need to be able to read your answer and understand it by itself, too. $\endgroup$ – Bryan Krause Aug 30 '20 at 5:16
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    $\begingroup$ i added more explanatory text with a reference. $\endgroup$ – shigeta Aug 30 '20 at 20:27
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    $\begingroup$ As a side note: I'm not convinced by your claim that 'you should not expect a normal distribution because there are no potatoes of negative size'. There are plenty of normally distributed phenomena which never take negative values. Am I misunderstanding something here? $\endgroup$ – Tom Hosker Aug 31 '20 at 13:26
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    $\begingroup$ If you are looking for the CI of the mean and you sample n >30 you can assume the mean is normally distributed per CLT which is different from the distribution of the potatoes. I added another link explaining why the normal distribution is used for only positive vallues. In short, the probability of a negative is so low that it is ignored $\endgroup$ – Hachiloni Aug 31 '20 at 21:26

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