Showing SD is good to indicate the variability of the values, but only when the distribution of the values is approximately normal (otherwise the graphical representation of the SD will likely be misinterpreted). If the distribution is not normal, it is better to indicate the variability of the values by interquartile ranges (or some other quantile ranges). This works well when the sample sizes are relatively large (>10 or so). If the sample sizes are smaller, it is usually the best to show the data itself instead of summaries.

The SE is an estimate of the uncertainty of an estimate. If this is interesting, then show it. However, a proper confidence interval would be preferrable over SE.

The SE is often seen but usually misused in graphical representations. Usually, the interesting quantity is not a mean value of the groups but rather a mean difference between groups. Most peaople show the mean values per group and let it to the reader to judge the mean difference from the diagram (often an ugly barplot). The statistical significance of this mean difference has to be evaluated with respect to its standard error (the SE of the mean difference, not of the group means!). However, often are only the SEs of the group means shown and the reader has again to guess how these will translate to the SE of the mean difference (this can be difficult, especially when the data in the groups are correlated or the actual comparison includes an adjustment for other covariables).

A good way to show the mean differences is to plot these mean differences together with their confidence intervals. An example is shown n the attached link.

So my advice is to first think what should be visualized: the data or the mean differences (between groups). If you want to show the data, then do show the data (in a scatterplot or as a boxplot, if the sample sizes are large). If you want to show differences between groups, then do show them, together with their 95% confidence intervals.

https://onlinecourses.science.psu.edu/stat200/sites/onlinecourses.science.psu.edu.stat200/files/lesson09/TukeyCIs.png

A great paper to read to understand what should be used:

http://www.med.uottawa.ca/Research/PostdoctoralFellows/assets/documents/error%20bars.pdf

Probably neither. If you want the precision of the estimate, use the confidence interval. If you use either SD or SE, I wouldn't use the +- symbol, because that suggests a range of some sort, and neither SD or SE give you that. It's probably the CI you want.

I am for confidence interval if data are normal, and for interquartile range in other case. Note that if data come from an ANOVA the assumption is homogeneity of variance, to allow to estimate a pooled error. If you assume homogeneity of variance, the confidence interval (and standard error, and standard deviation) will be the same for all means and bars from single means are misleading. As an example, if some bar is 5 times longer than another, it is a indication of not homogeneity of variances so is very useful, but you cant apply classical ANOVA!

the reply of Jochen Wilhelm is excellent... Unluckily only few researcher uses a correct way to represent variability. Sometime referees asked me to change correct representation of data and their variability to a wrong one...

I stopped to fight on this.

The SE is a measure of the precision of the sample mean. It allows us to estimate how much sample means will vary from the SD of this sampling distribution. The SE can be calculated to indicate the degree of uncertainty due to sampling variation.

We are usually interested not in the mean of this particular sample, but the population from which the sample comes.

for me, it is better to show SD, because it is good to indicate the variability of the population from which the sample was draw.

I think it depends on the design of the study. if you have one sample size and you are interested to find out the variability of the sample the SD is appropriate but if your sample is sample which is sum of samples through multiple measurements over different times then you need the mean of means of samples, therefore the SE is better option here.

.. sorry for another consideration.. if you have a manipulative experiment that follow an experimental scheme (e.g. a randomized block experiment, or a balanced factorial experiment) where an ANOVA is done, the standard deviation, the standard error and the confidence bounds are the same for all means due to the assumption of homogeneity of variance and consequently from the use of a pooled variance to compute the error variance and the P values. But I see error bars of different size in this case too. What is the sense to suppose that each population from where are taken the samples had a different variance when you use a pooled variance in your analysis ? in this case I think that the correct approach is not to put the error bars but to write the estimate of the mean "error" in the paper or the very old approach to put in the graph the value of LSD. I think that error bars of different length in an ANOVA experiment could be showed only if you use explicitely a model that fit the variances too (e.g. mixed models based on REML and not on the moments methods as the conventional ANOVA)

Darren C Greenwood I think that claiming that CI's have anything to do with precision could be very misleading to most people

Article The Fallacy of Placing Confidence in Confidence Intervals

There is no necessary connection between the precision of an estimate and the size of a confidence interval

https://www.statease.com/docs/v11/contents/analysis/standard-error-plot/

Depends on your kind of study but I use SD most times.

SE

Both are comparable depending on what exactly you want to achieve.

Is it important to describe the figure in text based on error bars after showing it on a figure? or it is self-explanatory?

What you show figures must be clearly explained at some place. This might be the methods section (if all the figures are similar, to avoid replication) and/or the figure legends (if there is only one figure, or if the figure/s is/are different to the rest).

In biomedical journals, Standard Error of Mean (SEM) and Standard Deviation (SD) are used interchangeably to express the variability. However, they measure different parameters. SEM quantifies uncertainty in estimate of the mean whereas SD indicates dispersion of the data from mean.

In other words, SD characterizes typical distance of an observation from distribution center or middle value. If observations are more disperse, then there will be more variability. Thus, a low SD signifies less variability while high SD indicates more spread out of data.

On the other hand, SEM by itself does not convey much useful information. Its main function is to help construct confidence intervals (CI). CI is the range of values that is believed to encompass the actual (“true”) population value. This true population value usually is not known, but can be estimated from an appropriately selected sample. Wider CIs indicate lesser precision, while narrower ones indicate greater precision.

In conclusion, SD quantifies the variability, whereas SEM quantifies uncertainty in estimate of the mean. As readers are generally interested in knowing the variability within sample and not proximity of mean to the population mean, data should be precisely summarized with SD and not with SEM.

In general, the use of the SEM should be limited to inferential statistics where the author explicitly wants to inform the reader about the precision of the study, and how well the sample truly represents the entire population.

Kindly refer to these citations for additional information:

1. What to use to express the variability of data: Standard deviation or standard error of mean? https://doi.org/10.4103/2229-3485.100662

2. Empowering statistical methods for cellular and molecular biologists. https://doi.org/10.1091/mbc.E15-02-0076

3. Error bars in experimental biology. https://doi.org/10.1083/jcb.200611141

This video shows how to add error bars in Origin graph easily. #aminulcheminnovation #AminulSir #Aminulchem

https://youtu.be/8Lof155mngg

This video shows how to plot publication quality bar chart or graph easily using originpro. #aminulcheminnovation #AminulSir #Aminulchem

https://youtu.be/HilkkzTQjT8

For normally distributed data, showing SE can help to visually see if two sets of data are statistically different. That is why there is a benefit to illustrating the results with SE, especially if you are in the middle of an experiment and want a fast interpretation of the results.

What's the point of encouraging readers to try judging if a mean difference is statistically significant different from zero by comparing error bars? Every relevant comparison is typically indicated the p-value or some indicator ("stars"), see [1] for an example. If it is the point to judge mean differences then show them directly, ideally with their confidence intervals that may even be adjusted for multiple testing if required (see "forest plot" and "catepillar plot" for examples).

[1] Article Enriched environment and stress exposure influence splenic B...