Although most researchers have seen and used error bars, misconceptions persist about how error bars relate to statistical significance. In light of the fact that error bars are meant to help us assess the significance of the difference between two values, this observation is disheartening and worrisome. Here we illustrate error bar differences with examples based on a simplified situation in which the values are means of independent unrelated samples of the same size and drawn from normal populations with the same spread.
We calculate the significance of the difference in the sample means using the two-sample t -test and report it as the familiar P value. We will discuss P values and the t -test in more detail in a subsequent column. The importance of distinguishing the error bar type is illustrated in Figure 1 , in which the three common types of error bars—standard deviation s.
In Figure 1a , we simulated the samples so that each error bar type has the same length, chosen to make them exactly abut. Although these three data pairs and their error bars are visually identical, each represents a different data scenario with a different P value.
In this latter scenario, each of the three pairs of points represents the same pair of samples, but the bars have different lengths because they indicate different statistical properties of the same data. And because each bar is a different length, you are likely to interpret each one quite differently. In general, a gap between bars does not ensure significance, nor does overlap rule it out—it depends on the type of bar. Chances are you were surprised to learn this unintuitive result.
When s. The first step in avoiding misinterpretation is to be clear about which measure of uncertainty is being represented by the error bar.
In , error bars appeared in Nature Methods in about two-thirds of the figure panels in which they could be expected scatter and bar plots. The type of error bars was nearly evenly split between s. CIs are a more intuitive measure of uncertainty and are popular in the medical literature. Error bars based on s. They can also be used to draw attention to very large or small population spreads. Because s.
What should a reader conclude from the very large and overlapping s. That although the means differ, and this can be detected with a sufficiently large sample size, there is considerable overlap in the data from the two populations.
Unlike s. Intuitively, s. We cannot overstate the importance of recognizing the difference between s. The third type of error bar you are likely to encounter is that based on the CI. This is an interval estimate that indicates the reliability of a measurement 3. The size of the s.
The two are related by the t -statistic, and in large samples the s. Because CI position and size vary with each sample, this chance is actually lower. By chance, two of the intervals red do not capture the mean.
Journal of Climate vol. Payton et al. Overlapping confidence intervals or standard error intervals: what do they mean in terms of statistical significance?. J Insect Sci vol. Analyze, graph and present your scientific work easily with GraphPad Prism.
No coding required. Home Support. Resist that temptation Lanzante, ! Here is a simpler rule: If two SEM error bars do overlap, and the sample sizes are equal or nearly equal, then you know that the P value is much greater than 0.
Explore the Knowledgebase. Try for Free. Type of error bar. It is quite possible - especially in mixed models - that means can have similar standard errors, but comparisons among the means have radically different standard errors.
Sign up to join this community. The best answers are voted up and rise to the top. Stack Overflow for Teams — Collaborate and share knowledge with a private group. Create a free Team What is Teams? Learn more. Standard error bars overlap but significance - estimated marginal means versus observed means Ask Question. Asked 7 years, 2 months ago. Active 7 years, 2 months ago.
Viewed 4k times. My question is: is the difference between estimated marginal means and observed means due to having a random factor in my model, or what is the reason for the discrepancy? Thank you! Improve this question. Add a comment. Active Oldest Votes.
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