Significant figures aren’t necessarily significant (especially in tables)

Round to two significant figures is the first of what statistician Andrew Ehrenberg describes as Six Basic Rules in his Rudiments of Numeracy. It contradicts the standard rules about significant figures taught in school, but I agree with Ehrenberg.

Removing the third, fourth, fifth, etc significant figure from a value keeps the focus on what’s important and aids the reader’s mental arithmetic. This is especially important when describing relationships between several numbers. Consider an unrounded example:

The value of X in the first year was 213.8. It rose to a maximum of 357.8 in the second year, before falling to 297.1 in the final year.

Compare with the rounded example:

The value of X in the first year was 210. It rose to a maximum of 360 in the second year, before falling to 300 in the final year.

The changes in this example are 50 to 150, so the third and fourth significant figures don’t matter. That much is obvious. The more subtle change, as noted by Ehrenberg, is that it’s much easier to determine relative changes between the values, which are typically more importantant than the values themselves. Try to mentally determine the increase from year one to year two using the first example. That is, how much bigger is 357.8 compared to 213.8? You’re going to do one of two things… give up or round the two numbers before making your estimate.

Rounding in tables

A table can take the place of a graph, if designed well (Ehrenberg’s sixth basic rule). It isn’t merely a lookup device. One of the features of a good table: appropriate rounding.

Consider the same values rounded to four different levels:

Year Raw x Nearest integer Nearest ten Two sig. fig.
One 6732.82 6732 6730 6700
Two 8142.98 8143 8140 8100
Three 7734.21 7734 7730 7700
Four 7289.05 7289 7290 7300
Five 6874.23 6874 6870 6900

The amount of rounding implies the purpose of the column. For the raw data column, the values are implied to be a reference. Conversely, for the two sig. fig. column, the relationship between the values, how they change over time, is more important. More often than not in science, relationships between values are more important than the values themselves.

But you’re losing information, right?

An argument against rounding is the loss of accuracy. Certainly, it isn’t appropriate in all cases. But treat these cases as exceptions. Only present raw data if there is a specific reason to do so. Otherwise round. Rounding is an inherent part of presenting data in a figure. Why should it be different in a table.

Credit to Ehrenberg

Examples, concepts, and arguments in this post all stem from Ehrenberg’s paper cited at the start. His paper delves much deeper into the presentation of tables, and I recommend reading it. It made me recognise that a table can be much more than a collection of numbers.

Author: Ken Hughes

Post-doctoral research scientist in physical oceanography

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