I have a variable (vitamin D levels) that does not follow normal distribution. I wanted to plot its variation throughout a period of time. I used the median. However I wanted to add error bars in this Excel graph. I used standard deviation but I don't know if it is correct. If it is not, what other measure of dispersion should be used?
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6$\begingroup$ Correct or not, that would certainly be unconventional and is likely to be puzzling or surprising to many readers and might be challenged by anyone in authority (peers, examiners, reviewers). Show median and quartiles usually. But there is no reason why apparent lack of normality need stop you looking at the mean too. The mean is a standard parameter for several non-normal distributions e.g. the exponential. What stops you showing mean and median too? $\endgroup$– Nick CoxCommented Dec 14, 2016 at 19:37
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1$\begingroup$ stats.stackexchange.com/questions/190223/… shows one among many possibilities. No rule I would want to respect prohibits showing mean and median too if that is helpful. $\endgroup$– Nick CoxCommented Dec 14, 2016 at 19:40
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$\begingroup$ How to do anything in Excel is off-topic here and in any case I am not a person to advise. $\endgroup$– Nick CoxCommented Dec 14, 2016 at 19:41
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$\begingroup$ If the variables are iid and continuous with a known density the distribution of the sample median can be obtained. Look at Wikipedia's topic "order statistics". If you can make all these assumptions except for known density you can use the bootstrap. $\endgroup$– Michael R. ChernickCommented Dec 14, 2016 at 19:53
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2$\begingroup$ Perhaps you can use Median Absolute Deviations (MAD) for your median column as error bars. Both are non-parametric, and perhaps the best bet. $\endgroup$– Felix BastCommented Aug 28, 2018 at 8:36
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You can use a standard deviation error bar (the distribution and the sample do have standard deviations), but if the distribution is asymmetrical then the resulting graph may not communicate the distribution very well.
Consider instead using a dot plot of the whole sample, or a box and whisker plot or, particularly if you have a large number of data points, a simple histogram of the values in your sample.
answered Dec 14, 2016 at 19:43
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$\begingroup$ Can you elaborate on the first part? I'm not sure if by "you can" you mean "you can make a misleading display if you want" or "you can if you compute it based off of the median" or "you can mix median with standard deviation about the mean and readers will understand it" or "you can if the distribution is symmetrical since mean and median will be about the same" or ... $\endgroup$– xanCommented Dec 16, 2016 at 1:33
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$\begingroup$ The standard deviation calculated from a sample does not relate to the mean or the median. It is an estimator of the standard deviation of the population. Thus there is no impediment to putting SD error bars on a mean or a median. It may not communicate what you want to communicate, but you can do it. $\endgroup$ Commented Dec 16, 2016 at 3:43