Ronny Gunnarsson. Significant figures [in Science Network TV]. Available at: https://science-network.tv/significant-figures/. Accessed December 3, 2022.

Suggested pre-reading |
What this web page adds |
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This web-page describes how to properly round up figures when you want to present your results. Reading this will give you an understanding of rounding up figures properly. It is all about understanding the concept of precision. |

Sometimes you see the advice to round up figures and present them with the same number of decimals. However, this is not a good advice because it does not take into account that figures need to be presented with a varying number of decimals to reflect the underlying precision of the figures. Using the same number of decimals will present some figures less precise than they are while others are presented as being more precise than they are. We have two types of figures to consider in a research project; raw data and calculated data.

Table of Contents (with links)

# Presenting your own results

## Significant figures when presenting raw data

If an observation is exact such as number of participants or number of children in a family then the exact number should be given. However, a lot of retained raw data are measurements producing a figure that is not exact. It is an estimate. Example can be height, weight, cholesterol levels in blood etc. Figures that are estimates should be given with a precision that reflects the accuracy of the measurement. Raw data can be presented with many significant figures if you are measuring using a method with very high accuracy. However, you should present the raw data with few significant figures if your method of measuring / estimating is unreliable . This is elegantly explained in the (rather funny) video “Why are Significant Figures Important?” by Tyler DeWitt:

## Significant figures when presenting calculated data

Significant figures are also of interest as soon as you present any type of descriptive statistics or inferential statistics. How do I know what number of significant figures are appropriate? The number of significant figures that should be used when presenting research results (such as mean, standard deviation, odds ratios, p-values, etc) is given by the size of the sample you have. As a rule of thumb the appropriate number of significant figures can be obtained by taking the base 10 logarithm of the sample size and rounding to the nearest integer. The base 10 logarithm for a sample size of 100 is 2, for 1,000 is 3, for 10,000 is 4, for 100,000 is 5 and so forth.

Please note that if your raw data are very unreliable and only valid with one significant figure (unusual) it means that your calculated output should also be presented with only one significant figure. However, a lot of significant figures will make your manuscript more difficult to read and in most situations there is no need to present more than 3 significant figures even if your sample size is large enough to allow more significant figures. Some examples of proper rounding of figures:

Result of a calculation / analysis | Two significant figures | Three significant figures |
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148.6772 | 150 | 149 |

14.86335 | 15 | 14.9 |

1.35756 | 1.4 | 1.36 |

0.0653442 | 0.065 | 0.0653 |

0.0000021463 | 2.1 x 10^{-6} | 2.15 x 10^{-6} |

## Consequences when writing a manuscript

The above means that you should vary the number of decimals when writing a manuscript. Please see the following examples.

- Percentages presented in table 1 in Nordeman et al 2017 and in table 1 in Tenenbaum et al 2017 .
- P-values presented in table 4 in Tenenbaum et al 2017 .
- Point estimate and confidence intervals for odds ratio as well as p-values in table 3 in Sundvall et al 2014 .

# Systematic literature reviews

A systematic literature review does not aim to simply copy conclusions from previous authors. It aim to evaluate previous studies and if possible making new conclusions. It is common that authors of included studies use many more significant figures than their observations support. In this case don’t repeat their mistake. Reduce the number of significant figures to reflect what their observations actually support if previous authors of included publications provide more significant figures than their observations support.

However, don’t invent more significant figures (unless you have access to raw data so you can calculate yourself), if observations in previous publications support more significant figures than they provide. In many situations there is no reason to provide more than three significant figures even if the number of observations or precision of measurements would support that.

# More about proper rounding of figures

Further details about how to round figures is explained in the video “How to Count and Round Significant Figures” by MahanChem:

# References

Ronny Gunnarsson. Significant figures [in Science Network TV]. Available at: https://science-network.tv/significant-figures/. Accessed December 3, 2022.