SEM or SD?
One of them describes your animals and one describes your confidence in an average. Collecting more animals shrinks only the second.
It gets asked as though it were a preference, usually late, usually by someone who has already made the figure. Reviewers have opinions. Supervisors have habits. Neither is the answer, because the two are not two ways of drawing the same thing. They are two different quantities, and one of them is under your control in a way the other is not.
The arithmetic, first
Standard deviation describes how spread out your measurements are. Standard error of the mean describes how precisely you have pinned down their average. They are related by one line:
SEM = SD ÷ √n
Which means the error bar you draw depends on how many animals you used, and nothing about that is a claim about the animals.
Here are 151 Adelie penguins. Their flipper lengths average 189.95 mm, and they vary about that by 6.54 mm. The standard error of that average is 0.53 mm.
The same measurements, and the two error bars you could draw on them
Every Adelie in the dataset, then the mean with a standard deviation whisker, then the same mean with a standard error whisker. Nothing differs between the second and third except which quantity is drawn. The SD whisker spans most of the birds. The SEM whisker is smaller than the dot marking the mean.
The SD whisker is 12.3 times the SEM whisker. Same birds, same measurements, same mean. Only the quantity on the whisker changed.
The part that should decide it for you
Take the same birds and pretend you caught fewer of them. Draw three at random, then four, then ten, and so on, and see what each statistic does.
What each statistic does as you collect more
Standard deviation and standard error against sample size, averaged over 4000 random subsamples of the same 151 birds at each size. Standard deviation is flat: the birds vary by about 6.5 mm however many you catch. Standard error falls away with the square root of n, from 3.33 mm at three birds to 0.53 mm at all of them.
The standard deviation line is flat, because it is a fact about penguins and penguins did not change. The standard error line falls away, because it is a fact about your experiment.
So a figure with short error bars is not showing you a cleaner result. It may only be showing you a bigger one. Two labs could measure the same effect with the same variability and publish figures that look completely different in their apparent precision, and the difference would be how many animals they used.
That is not an argument against standard error. It is an argument for saying which one you drew, because a reader who guesses wrong will misjudge the result in a predictable direction.
There is a smaller lesson in that flat line too. At three birds the standard deviation comes out at 5.762 mm rather than 6.54: with a handful of measurements you tend to underestimate the spread as well as overstate the precision.
What each one is for
Cumming, Fidler and Vaux set this out in The Journal of Cell Biology in 2007, and it remains the reference worth reading.
- Standard deviation describes your sample. Use it when the question is how variable the thing you measured actually is.
- Standard error estimates how much the mean would move if you ran the experiment again. It is about the estimate, not the organism.
- A confidence interval answers the question most readers think an error bar is answering, which is the range the true mean plausibly sits in. It is usually the more useful of the inferential two, and it is not much harder to produce.
Their first rule is the one nobody argues with, and it is the one most often broken: say in the legend what the error bars are. A whisker with no definition is not a measurement, it is a decoration.
What to do
- Show the points where you can. With the sample sizes typical in this field, every measurement fits on the page, and then the error bar is a summary of something the reader can already see rather than a substitute for it.
- Name the quantity in the legend, every time, along with n and what n counts.
- Prefer a confidence interval to a standard error if you are making a claim about the mean, because it is the quantity a reader will try to read off anyway.
- Never compare two figures’ error bars across papers without checking both n and both definitions.
This is on the pre-submission checklist as two lines, and A figure is an instrument covers what a bar chart does to a reader before any whisker is added to it.