Paired data: connected points instead of bar charts

Before-and-after data plotted as two bars with error bars is one of the most common ways a figure discards the thing that makes the design valuable.

What the bar chart throws away

Two bars show two group means. A paired design does not measure two groups. It measures the same subjects twice, and the interesting quantity is each subject's change.

Two nearly identical bars can hide the fact that every single participant improved, or that half improved and half declined. Both give the same means. They are completely different findings.

What to plot instead

Connected points. One point per subject at each time, joined by a line. The reader sees the direction and size of every individual change, the consistency of the response, and any subject who moved against the trend.

A paired difference plot. Plot the change itself, one point per subject, with a reference line at zero. This puts the actual quantity you tested on the axis.

Slope charts with a summary overlaid. Individual lines in light grey with the group mean in bold gives both readings in one figure.

Match the plot to the test

If you ran a paired t-test or a Wilcoxon signed-rank test, your analysis used the pairing. A figure that ignores it is inconsistent with your own statistics, and a careful reviewer will notice.

Error bars on paired data

Standard error bars on two bars are computed from between-subject variation, which is not what a paired test uses. If you show an interval, show it on the difference, which is what was actually tested.

When bars are defensible

Large samples where individual lines would be unreadable. Even then, plot the distribution of differences alongside.

In Plotara

Paired and connected points are available as an overlay on box, violin and scatter plots, and the paired t-test and Wilcoxon signed-rank test sit alongside them.