Why 40 to 60 is better than 50

Recording an accurate maximum and minimum range for a count is better than estimating an exact count.

written Aug 5, 2018 (last updated Oct 28, 2023) • by jonsullivan • Category: Wild Counting

This is one of a series of in-depth dives into the counting concepts used in WildCounts. We take a close look at count approximate, which is what you use when you cannot make an exact count.

I’m amazed at how many counting methods and monitoring webforms require me to enter exact counts. If I see a group of about 50 pigeons flying by, I would like to be able to enter ~50, or 40–60 and not be forced to say that there were exactly 50 birds. This annoys me because it needlessly adds inaccuracy and potential bias to the count data.

Is this really a big deal? Perhaps. Inaccuracy means noise and noise makes it harder to uncover robust patterns and trends. Bias means that some of the patterns and trends revealed might be artefacts of the data collection instead of something real. Inaccuracy can be compensated for by making more counts. Bias makes many more problems.

One clear way that bias can result is if somebody tends to estimate high, and another estimates low, and the first observer is active early in a project and the other observer only later. If forced to give a single count, the first observer would estimated near 60 when the other observer would say 40. This scenario would create a spurious trend in the data, showing a decline where there was none. That’s bad. If only they’d had the opportunity, both observers could have given their counts as 40–60, and there would have been no decline.

Similar bias could occur in a spatially widespread project where the two observers live, and count, a long distance apart from one another. In this case, the conclusion would wrongly be made that the species counted is more common where the second observer lives.

This, and other types of “observer bias”, are traditionally accounted for by having both observers independently count at the same places and times. Their counts can then be compared and calibrated. However, that’s not always possible in widespread and long-term projects. For example, you now and you ten years ago cannot make the same counts at the same time. In these cases, the bias is also entirely avoidable, by just allowing observers to record the minimum-maximum ranges that they’re certain contain the true counts.

Another kind of bias can occur when exact counts are more often made in some habitats or conditions, like open vegetation or sunny weather, and more estimated counts are made in other habitats or conditions, like thick forest, or on dusk. One experimental study found that people tended to overestimate the number of birds singing within 50 m by 17% to 122%. Counts would therefore be overestimated in conditions where a greater proportion of birds were only heard. If people were asked instead to record a conservative minimum-maximum range, this could correctly capture this uncertainty.

An additional, important benefit of recording uncertainty in counts is just that it’s easier to do. I find that it takes extra thought to covert a range or estimated count into the most likely exact count. Like anything, people will get better at this with practice, but it’s an extra layer of difficulty for beginners. I expect that people designing count forms that only allow exact counts are trying to keep things simple. While the counting form might be simpler, this makes doing the counts more difficult.

It is for all these reasons that I include minimum-maximum ranges when I teach students to count birds, butterflies and other mobile species that can be hard to count exactly. Most of the time they can give exact counts but, when they’re not sure, they can honestly record that uncertainty rather than have to guess at an exact count. It works well.

For my real time wild counting with shorthand, I use the tilde (~) to indicate which counts are estimates rather than exact. For my spoken observations, I use the word about before the count. In both cases by default, I use this to mean that I expect the true count to be somewhere between this conservative low count and 1.5 times higher. When I type ~40, and say about forty, that means I expect the true count to be somewhere between 40 and 60. This is easy to do and works well.

So, if you count 40 to 60, don’t say 50. They are not the same. Only give an exact count when that’s what you observed. In all other cases, be sure to record your count honestly, with all its uncertainty.