Fig 1.
Many different datasets can lead to the same bar graph.
The full data may suggest different conclusions from the summary statistics. The means and SEs for the four example datasets shown in Panels B–E are all within 0.5 units of the means and SEs shown in the bar graph (Panel A). p-values were calculated in R (version 3.0.3) using an unpaired t-test, an unpaired t-test with Welch’s correction for unequal variances, or a Wilcoxon rank sum test. In Panel B, the distribution in both groups appears symmetric. Although the data suggest a small difference between groups, there is substantial overlap between groups. In Panel C, the apparent difference between groups is driven by an outlier. Panel D suggests a possible bimodal distribution. Additional data are needed to confirm that the distribution is bimodal and to determine whether this effect is explained by a covariate. In Panel E, the smaller range of values in group two may simply be due to the fact that there are only three observations. Additional data for group two would be needed to determine whether the groups are actually different.
Fig 2.
Additional problems with using bar graphs to show paired data.
The bar graph (mean ± SE) suggests that the groups are independent and provides no information about whether changes are consistent across individuals (Panel A). The scatterplots shown in the Panels B–D clearly demonstrate that the data are paired. Each scatterplot reveals very different patterns of change, even though the means and SEs differ by less than 0.3 units. The lower scatterplots showing the differences between measurements allow readers to quickly assess the direction, magnitude, and distribution of the changes. The solid lines show the median difference. In Panel B, values for every subject are higher in the second condition. In Panel C, there are no consistent differences between the two conditions. Panel D suggests that there may be distinct subgroups of “responders” and “nonresponders.”
Fig 3.
Bar graphs and scatterplots convey very different information.
While scatterplots prompt the reader to critically evaluate the statistical tests and the authors’ interpretation of the data, bar graphs discourage the reader from thinking about these issues. Placental endothelin 1 (EDN1) mRNA data for four different groups of participants is presented in bar graphs showing mean ± SE (Panel A), or mean ± SD (Panel B), and in a univariate scatterplot (Panel C). Panel A (mean ± SE) suggests that the second group has higher values than the remaining groups; however, Panel B (mean ± SD) reveals that there is considerable overlap between groups. Showing SE rather than SD magnifies the apparent visual differences between groups, and this is exacerbated by the fact that SE obscures any effect of unequal sample size. The scatterplot (Panel C) clearly shows that the sample sizes are small, group one has a much larger variance than the other groups, and there is an outlier in group three. These problems are not apparent in the bar graphs shown in Panels A and B.