Abstract
Error bars often show confidence intervals or standard error of the mean. Confidence intervals are calculated so that over a lifetime of plotting, for example, 95% confidence intervals around sample means, the population means will be outside of those intervals 5% of the time. If this sounds like the meaning of α, it is because confidence intervals are calculated by performing null hypothesis tests backwards. Consequently, confidence intervals (and standard error bars) can be used to test null hypotheses in our heads. It is generally a myth, however, that if error bars do not overlap, the difference is statistically “significant.” A great option is to make that myth reality and show comparative confidence intervals: if the bars just touch, p is equal to α. Families of comparative confidence intervals can be plotted as boxes and whiskers to illustrate p with some precision. The intervals can also be corrected for multiple comparisons.
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