Error bars are the thin lines that extend above and below data points on a graph, showing how much uncertainty or variability exists in the data. They look identical no matter what they represent, but they can mean very different things depending on whether they show standard deviation, standard error, or a confidence interval. Knowing which type you’re looking at changes how you should read the graph.
What Error Bars Actually Show
Every error bar is a visual way of saying “the true value isn’t just this single dot on the graph; it could reasonably fall somewhere within this range.” The bar extends in both directions from a central value, usually the average of a group of measurements. A longer bar means more uncertainty or more spread in the data. A shorter bar means the measurements were tighter or the estimate is more precise.
The critical detail is that error bars fall into two fundamentally different categories, even though they look exactly the same on a graph. Some are descriptive: they tell you how spread out the individual data points are. Others are inferential: they tell you how confident you can be about where the true average lies. Mixing these up is one of the most common mistakes people make when reading graphs.
Standard Deviation Bars
Standard deviation (SD) bars are descriptive. They show how spread out the individual measurements are around the average. If you measured the heights of 50 people and plotted the average with SD bars, those bars would tell you the range where most individual heights fell. About 68% of the data points fall within one standard deviation above and below the average.
SD bars are useful when you want to understand variability in the raw data itself. If one group has long SD bars and another has short ones, it means the first group had much more variation between individual measurements. The size of SD bars does not shrink much as you collect more data, because adding more measurements reveals the true spread of the population rather than reducing it.
Standard Error Bars
Standard error of the mean (SEM) bars are inferential. Instead of describing the spread of individual data points, they estimate how precisely you’ve pinpointed the group’s true average. SEM is always smaller than SD for the same dataset, because it’s calculated by dividing the standard deviation by the square root of the sample size.
This means SEM bars shrink as you collect more data. Measure 10 people and your SEM bars will be relatively wide. Measure 1,000 people and those bars become very narrow, because with more data you’re more confident about where the true average is. This is an important distinction: small SEM bars can make differences between groups look dramatic, but they might just reflect a large sample size rather than a meaningful difference.
Confidence Interval Bars
Confidence interval (CI) bars, usually set at 95%, represent the range where the true population average is likely to fall. The idea is that if you repeated the entire experiment many times, 95% of the confidence intervals you’d calculate would contain the real population average. A 95% confidence interval is roughly equal to two standard errors in each direction from the mean.
CI bars are the most directly useful for judging whether two groups are truly different. If the 95% CI bars of two groups don’t overlap at all, the difference between them is statistically significant. If they overlap a little, the difference might still be significant. If they overlap a lot, you probably can’t conclude the groups are different. This makes CI bars the most intuitive type for readers who want to quickly assess whether a result is meaningful.
Why the Type of Error Bar Matters
Here’s the problem: all three types look identical on a graph. They’re just lines extending from a point. The only way to know which type you’re looking at is to read the figure caption or legend. In published research, error bars have been labeled as any of these:
- Range: the full span from the lowest to the highest value
- Standard deviation: describing how spread out individual values are
- Standard error: estimating precision of the average
- 95% confidence interval: the plausible range for the true average
- Interquartile range: the middle 50% of data points
A graph showing SEM bars will look like it has much tighter, more impressive results than the same data plotted with SD bars. This isn’t deceptive on its own, since both are valid, but it can mislead readers who assume all error bars mean the same thing. If a graph doesn’t specify which type of error bar it uses, you can’t interpret it reliably.
Common Mistakes When Reading Error Bars
The most widespread misreading is treating error bars as hard boundaries. Because the bars are solid visual objects, people tend to think values inside the bar are likely and values outside are unlikely. In reality, the transition is gradual. Values near the edge of an error bar are only slightly less plausible than values near the center, and values just outside the bar are only slightly less plausible than values just inside it.
Another common error is assuming that overlapping error bars always mean “no significant difference” and non-overlapping bars always mean “significant difference.” This rule of thumb works reasonably well for 95% confidence intervals, but it fails for other types. Two groups can have overlapping SEM bars and still be statistically significantly different from each other. Conversely, SD bars can appear to overlap even when the groups are clearly distinct, because SD bars describe individual spread rather than the precision of the average.
Research on how people read graphs has also found that bar charts with error bars cause viewers to overestimate effect sizes. In one study, people looking at bar charts predicted outcomes about 15% larger than people viewing the same data in other formats like violin plots. The visual weight of the bar itself skews perception.
How to Read Error Bars Correctly
First, check the caption or legend. Look for the words “SD,” “SEM,” “SE,” “95% CI,” or “confidence interval.” If the graph doesn’t specify, treat the error bars with caution, because you literally don’t know what they represent.
Next, consider the sample size. If the study measured only 3 to 5 observations per group, even SEM bars will be wide, and the estimates are inherently uncertain. With larger samples (50 or more per group), SEM and CI bars become more reliable indicators of where the true value lies. The sample size also explains why SEM bars can look deceptively small in very large studies, since the precision of the average improves with every additional measurement even if the underlying variability hasn’t changed.
Finally, use the right mental model for the type of bar. SD bars tell you about the spread of individual measurements, so think “this is how variable the data are.” SEM and CI bars tell you about the estimate of the average, so think “this is how confident we are about where the true average falls.” These are fundamentally different questions, and confusing them leads to wrong conclusions about what the data actually show.