NUMBAT OER - Open Educational Resources

3.3 Comparing average and variability for several datasets

Both error plots and box plots can be used to compare different samples or populations. A chart can include several error plots or box plots, and these allow the user to make an instant comparison between the averages and variabilities of different datasets. The degree of overlap between variabilties is an important initial indicator of the likelihood that differences in means or medians are meaningful (Fig. 7), an assessment that can then be tested more rigorously using the appropriate test.

Overlap in error bars

Figure 7. Different levels of overlap in error bars: (a) large amount of overlap, that includes the mean values, (b) small amount of overlap, that does not include the mean values, (c) no overlap

If making comparison between several parametric datasets, it is important that the variability is similar in all. If the most variable has a variance measure that is more than ten times the variance of the least variable, statistical comparison of the means is invalid, and a box plot might be a more appropriate way to display the data (Fig. 8).

Two box plots

Figure 8. An example of the use of box plots to compare two samples, in this case illustrating differences in bone density between men and women