Summary
The standard error reflects the precision of a mean and is often displayed as error bars.
In depth
SE = SD / √n. Error bars show variability or uncertainty; 95 percent confidence interval is about ±2 SE. Non-overlapping error bars suggest (not prove) a real difference.
State what error bars represent in a figure legend. Overlapping SE bars don't guarantee no difference; test statistically.
Example: 95 percent confidence intervals give a range likely to contain the true mean.
The standard error of the mean (SEM) is the standard deviation divided by the square root of the sample size (SD / sqrt n). It estimates how precisely the sample mean estimates the true population mean, and shrinks as the sample gets larger.
Error bars on graphs show variation or uncertainty: they can show SD, SEM or 95 percent confidence intervals, so the figure legend must say which. Roughly, if the 95 percent confidence intervals of two means do not overlap, the difference is likely to be significant; overlapping SEM bars do not guarantee non-significance.
Example: means of 5.2 plus or minus 0.3 SEM and 6.1 plus or minus 0.3 might differ significantly.
Common mistake: confusing SD and SEM.
Frequently asked questions
What is Standard Error and Error Bars?
The standard error reflects the precision of a mean and is often displayed as error bars.
Which area of biology covers Standard Error and Error Bars, and how advanced is it?
Standard Error and Error Bars is one of the 51 topics in Lab Methods & Biostatistics. It is rated Intermediate, so it suits learners who already know the core vocabulary. Related topics in this area include t-Test, Standard Deviation, Statistical Power.
Can you give an example of Standard Error and Error Bars?
A bar graph with SE bars for treatment means.
What should I learn before Standard Error and Error Bars?
Work through the Beginner topics in Lab Methods & Biostatistics first, such as Scientific Method, Hypothesis, Variables, then return to Standard Error and Error Bars. Intermediate topics assume the Beginner vocabulary.
What topics are related to Standard Error and Error Bars?
The closest topics to Standard Error and Error Bars are t-Test, Standard Deviation, Statistical Power, Null Hypothesis. Comparing them side by side is a good way to see how the ideas connect.
How can I check that I understand Standard Error and Error Bars?
Read the summary and the in-depth section, then use the quick check on the interactive lesson for Standard Error and Error Bars. To practise the whole of Lab Methods & Biostatistics, use the Lab Methods & Biostatistics quiz.
How is Standard Error and Error Bars different from t-Test?
Standard Error and Error Bars: The standard error reflects the precision of a mean and is often displayed as error bars. t-Test: A test for significant differences between the means of two groups. Read both side by side and note what each one explains.
What is a common mistake about Standard Error and Error Bars?
Confusing SD and SEM.
How should I study Standard Error and Error Bars step by step?
First, read the summary and write the definition in your own words. Second, read the in-depth section and note any example. Third, compare it with t-Test and explain the difference aloud. Finally, take the Lab Methods & Biostatistics quiz and come back to this page for any question you miss.