What is “change”? This might at first seem like an oddly philosophical question to encounter in a science blog. The Greek philosopher Heraclitus once described change as the idea that “One cannot step into the same river twice” (paraphrased; Graham 2015). However, this more existential definition for change differs in important ways from the one that scientists use in their research into physical and biological properties of the natural world. Given that the ideas, devices, and data generated by the science and technology industries is enormous, it is critical that we understand these subtle differences in the definitions for change.

But before we can define change, we first need to take a step back. To understand how some measurement (or “variable”) of interest might change over space and time, or relative to a central value, we also need to understand change’s paired half, and that is “variability”. You may be familiar with the concept of an average: average grade in a class, average height of human beings, average daily temperature, etc. An average, or mean, is a single number that we can use to summarize and describe an entire population of individual measurements: multiple test grades, multiple people, multiple days, etc. Yet the individual values within the population can deviate from the mean (Fig. 1). The degree to which individual values differ from the population mean is a measure of variability. Statisticians and scientists need to understand how much variability there is in a population in order to understand differences between groups or how population means might change (Fig. 1).

Many different types of scientists are interested in whether and how means change over space and time – or in other words, how means systematically shift in a consistent pattern. The confusing bit is trying to distinguish these changes in population means from the surrounding variability of individual measurements.

Take for example this next figure (Fig. 2). This graph shows the number of confirmed Zika cases documented worldwide each week during the year 2016. Upon inspection of the figure, we can see that there is some variability in the data – specifically, a large jump in the number of cases at week 20 – but the general trend, or change over time, is positive and roughly linear. In an alternate example (Fig. 3), we can see that the variability matters much more. This figure shows measurements for land surface temperature over the last 150 years. If you were to zoom in on the years 1860-1880, you would see a lot of variability in temperature, but no consistent pattern, no change. Looking at years 1940-1950 alone might show a lot of variability and a decreasing pattern. It is only by looking over the entire time series that we can see that the temperature consistently changes in a positive way.

Through exploration of these real-world examples we can see that, to a scientist, change and variability are really like yin and yang. They are paired halves of the same story. Without a firm understanding of this balance between change and variability, it would be impossible for scientists to accurately identify consistent patterns in their data, or departures from the average or starting values. So the next time you see a graph in the newspaper or in a textbook, think about what the data is showing. How does it change? How does it vary?

References

Graham, Daniel W., “Heraclitus”, The Stanford Encyclopedia of Philosophy (Fall 2015 Edition), Edward N. Zalta (ed.), URL = <https://plato.stanford.edu/archives/fall2015/entries/heraclitus/>.