See Writing about data and statistics for more information on how to choose the right statistics and present them accurately.
International standards and resources
See Guidelines for reporting statistics in journals published by the American Physiological Society(Opens in a new tab/window) for useful advice on presenting statistics in journal articles.
Australian conventions and resources
The Australian Bureau of Statistics provides explanations of statistical concepts and terms(Opens in a new tab/window), and a glossary of terms(Opens in a new tab/window).
Terms to watch out for:
Statistical functions
If statistical functions are abbreviated as single letters, use either Greek or roman letters. Use italics for roman letters, but not for Greek letters or superscripts. The following table provides examples.
| Symbol | Definition |
|---|---|
| P | probability (e.g. P ≤ 0.05) |
| F | variance ratio (F-test) |
| N | number of subjects in a total sample |
| n | number of subjects in a limited portion of the total sample |
| R | coefficient of multiple correlation |
| r | coefficient of correlation |
| ρ | coefficient of correlation (population) |
| χ2 | chi-squared |
| Q | Cochran chi-square (Note: Cochran is spelt without an e, unlike Cochrane Collaboration, which has an e.) |
| I2 | heterogeneity coefficient (not in italics) |
Statistical significance
Statistical significance is widely considered to have been achieved when the probability of a result occurring by chance is equal to or less than 5% (P ≤ 0.05). Higher levels of significance are P ≤ 0.01 (less than 1%) and P ≤ 0.001 (less than 0.1%).
These levels of significance are also sometimes referred to as significant at the 5%, 1% and 0.1% levels, respectively, but it is much better to give the P values as indicated above.
P values greater than 0.05 are generally considered to be ‘not significant’. However, in some disciplines, a different cut-off may be used (e.g. 0.1, or 10%).
Since P is a measure of probability, its value must lie between 0 and 1. Some statistical software programs report the exact value of P, and may round a very small value (e.g. 0.00001) to 0.000. This should be reported as P ≤ 0.001.
Sometimes the ‘equals’ is omitted, and the value is given as P < 0.01; strictly speaking, the symbol should be ‘≤’.
Do not use wording such as A was greater than B; however, the difference was not statistically significant. If the difference was not statistically significant, A cannot be said to be greater than B.
It is usually best to quote a precise P value. This permits readers to assess a statistical result individually. For example, the P values associated with the main results of your study might be P = 0.057 and P = 0.57. Although you could report both these as P > 0.05 or P = NS (not significant), you can only report that the 2 results differ if you provide the precise values.
In tables or figures, levels of statistical significance are often denoted by a system of symbols. For clarity, these should be defined under the table or figure in terms of P values:
* P ≤ 0.05
** P ≤ 0.01
*** P ≤ 0.001
However, P values are just one aspect of quantitative statistical information. A discussion of variability and uncertainty may also benefit from presenting standard deviations and confidence intervals.
Presentation of uncertainty
Report variability using standard deviation (SD) rather than standard error (SE). Do not use ‘±’ for SD:
110 mmHg (SD 10) not 110 mmHg (SD ±10)
The most appropriate measure of uncertainty is the confidence interval (CI). This gives an indication of how tightly the results from our experimental sample are expected to predict the ‘real’ value in the wider population. In general, the 95% confidence level is used.
If the 95% CI for the difference between 2 values (e.g. before versus after, treated versus untreated) includes zero (0), the change is not statistically significant (at the P ≤ 0.05 level).
If the relevant terms have not already been defined, data can be presented as follows:
The risk ratio (RR) was 0.14 (95% confidence interval [CI] 0.08 to 0.24)
If the terms have already been defined, use one of the following formats:
MD 1.11 hours (95% CI 0.98 to 1.20)
The risk was not increased (RR 1.02; 95% CI 0.87 to 1.19)
Do not use an en dash to denote a span of values for the CI because this could be confused with a minus sign:
… with a mean value of 4.23 (95% CI –2.13 to 6.33) not (95% CI –2.13–6.33)
For more information on writing about risk, see Writing about risk.
Level of precision in reporting statistics
Statistics should be reported at the same level of precision as the measurements (not at a higher level). For example, the mean age of participants in a study (in years) should be reported to a maximum of 1 decimal place. Reporting the mean to 2 or 3 decimal places could imply that ages were determined at the level of days, or even hours, rather than just years.
Percentages should also be reported using a sensible level of precision. If the number of people in a sample is below 100, reporting that 15.32%, or even 15.3%, of them were affected by a treatment is not reasonable; the percentage should be given as a whole number (15%).