3
$\begingroup$

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?

$\endgroup$
  • 5
    $\begingroup$ 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 Cox Dec 14 '16 at 19:37
  • 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 Cox Dec 14 '16 at 19:40
  • $\begingroup$ How to do anything in Excel is off-topic here and in any case I am not a person to advise. $\endgroup$ – Nick Cox Dec 14 '16 at 19:41
  • $\begingroup$ 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. Chernick Dec 14 '16 at 19:53
  • 1
    $\begingroup$ 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 Bast Aug 28 '18 at 8:36
3
$\begingroup$

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.

| cite | improve this answer | |
$\endgroup$
  • $\begingroup$ 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 ... $\endgroup$ – xan Dec 16 '16 at 1:33
  • $\begingroup$ 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. $\endgroup$ – Michael Lew Dec 16 '16 at 3:43

Your Answer

By clicking “Post Your Answer”, you agree to our terms of service, privacy policy and cookie policy

Not the answer you're looking for? Browse other questions tagged or ask your own question.