Uncertainty is a key idea in science. We can rarely have absolute proof in experimental re...

Uncertainty is a key idea in science. We can rarely have absolute proof in experimental results, because our conclusions rest on observations, but we only have a small sample of all possible observations. Because uncertainty is always present, it’s useful to describe how much uncertainty you have, relative to what you know. It might seem ironic, but in science, knowing about uncertainty increases our confidence in our conclusions.

The graph at right is from a landmark field study by D. Tilman, et al. It shows change in biomass within, experimental plots containing varying numbers of native prairie plants after a severe drought. Because more than 200 replicate (repeated test) plots were used, this study was able to give an estimate of uncertainty. This uncertainty is shown with error bars. In this graph, dots show means for groups of test plots; the error bars show the range in which that mean could have fallen, if there had been a slightly different set of test plots.

Let’s examine the error bars in this graph. To begin, as always, make sure you understand what the axes show. This graph is a relatively complex one, so be patient.

Each blue dot represents a group of plots with 5 or fewer species; yellow dots represent plots with more than 5 species. Look at the leftmost dot, plots with only 1 species. Was biomass less or more after the drought?

The error bars show standard error, which you can think of as the range in which the average (the dot) might fall, if you had a slightly different set of plots. (Standard error is just the standard deviation divided by the square root of the number of observations.) For 1-species plots, there’s a small chance that the average could have fallen at the low end of the error bar, or almost as low as about 0.5, or half the pre-drought biomass.