**If in doubt and if possible, consult a statistician at the stage of experimental or survey design.**This will ensure that the data collected can be correctly analysed by accepted statistical methods.

# Reporting statistical results

Article first published online: 2 MAR 2011

DOI: 10.1111/j.1095-8649.2011.02914.x

© 2011 The Author. Journal of Fish Biology © 2011 The Fisheries Society of the British Isles

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#### How to Cite

Wootton, R. J. and Craig, J. F. (2011), Reporting statistical results. Journal of Fish Biology, 78: 697–699. doi: 10.1111/j.1095-8649.2011.02914.x

#### Publication History

- Issue published online: 2 MAR 2011
- Article first published online: 2 MAR 2011

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This editorial draws attention to an initiative of The Physiological Society, which has commissioned a series of articles on best practice in statistical reporting in life science journals. The articles are published in the two journals of The Physiological Society, *Journal of Physiology* and *Experimental Physiology*. Other journals including the *British Journal of Pharmacology* and *Advances in Physiology Education* are joining this project. In an earlier initiative, The American Physiological Society published guidelines for the reporting of statistical results (Curran-Everett & Benos, 2004, 2007). These guidelines have partly influenced the section on reporting statistical results in the latest version of *Instructions for Authors* for the *Journal of Fish Biology*. In Curran-Everett & Benos (2004), 10 guidelines are provided and these are listed below with some commentary.

- 1
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**Chose a critical significance level**Conventionally, an*α*appropriate to aims of the research.*α <*0·05 is used to define significance level, but there may be circumstances when*α <*0·1 or <0·01 are more appropriate. - 3
**Name the statistical methods used, citing the textbooks or review papers that are the sources of the methods.**Separately, identify the commercial software used for the analyses and quote the URL. - 4
**Use an accepted method to control for multiple comparisons.**If there is only a single dependent variable, the best solution is to use pre-planned orthogonal contrasts. The use of methods of multiple comparisons such as Tukey's HSD test, however, may be acceptable (Quinn & Keough, 2002). If there are several dependent variables measured on the same replicate individuals, the situation is more complicated. A common solution is to apply a Bonferroni correction, but the use of false discovery rate is increasing (Curran-Everett, 2000). - 5
**Report variability in a sample using the standard deviation (****s.d****.) rather than a standard error (****s.e****.).**The s.d. describes the variability of the observed data, whereas the s.e. describes the theoretical dispersion of sample means about the population mean. - 6
**Use confidence intervals (CIs) to describe the uncertainty about the true value of a population parameter.**The 95% CI is typically used, but in some circumstances, a 99% CI may be more appropriate. The CI may be reported in the text, tables or graphics. The 95% CI about a population parameter allows the claim that with 95% confidence, the true population parameter lies in the defined interval. In contrast, even with a relatively high number of replicates, the s.e. of the mean only gives about a 68% CI. Confidence intervals should be provided for sample statistics such as means and regression coefficients. - 7
**Report a precise probability (**Most computer software packages now give precise*P*) value.*P*-values. Such precise values are useful for researchers carrying out meta-analyses. This guideline, however, is more contentious. The precise*P*-value reported by a computer package assumes that the data analysed conform precisely to all the assumptions of the statistical method used. This may not be the case with biological data and then it is better to report a*P*-range,*e.g.*0·05*> P >*0·01. The problem can be circumvented by providing the statistical method, the value of the test statistic, degrees of freedom (d.f.) and the*P*-value range (*e.g.*ANOVA:*F*_{n1,n2}=*x*; 0·05*> P >*0·01). If a reader wishes to determine the precise*P*-value (hence making a strong assumption about the data), the value can be obtained from the test statistic and associated d.f. The information in this form is also valuable for a reviewer, allowing a check that the use of the test statistic is correct. - 8
**The number of digits used when reporting a quantity should reflect the accuracy of the original measurements and be commensurate with scientific relevance of the measurements.**Computer packages frequently give an excessive number of digits when presenting results and the number of digits should be adjusted carefully before being included in a report. Note that for the*Journal of Fish Biology*means and their errors must have the same number of decimal places. - 9
**In the ‘Abstract’ of a manuscript provide confidence intervals and precise***P***-values for each result reported.**This guideline is not followed by the*Journal of Fish Biology*. - 10
**Use the numerical bounds of the confidence interval and the**In general, there needs to be a shift of attention from the level of significance to the magnitude of the effect declared significant (Nakagawa & Cuthill, 2007). For example, pay particular attention to the*P*-value to interpret the main results.*r*^{2}-value in regression analyses. Is the significant regression accounting for a high proportion of the variance in the dependent variable?

In parallel with these guidelines, a series of useful articles on statistical methods have been published by Curran-Everett in *Advances in Physiology Education* and can be downloaded as PDF files. A discussion of data exploration in the context of statistical analyses is also a valuable resource (Zuur *et al.*, 2010).

R. J. Wootton, Assistant Editor J. F. Craig, Editor-in-Chief

### References

- 2000). Multiple comparisons: philosophies and illustrations. American Journal of Physiology Regulatory Integrative Comparative Physiology 279, R1–R8. (
- 2004). Guidelines for reporting statistics in journals published by the American Physiological Society. Physiological Genomics 18, 249–251. & (
- 2007). Guidelines for reporting statistics in journals published by the American Physiological Society: the sequel. Advances in Physiology Education 31, 295–298. & (
- 2007). Effect size, confidence interval and statistical significance: a practical guide for biologists. Biological Reviews 82, 591–605. & (
- 2002).
*Experimental Design and Data Analysis for Biologists*. Cambridge: Cambridge University Press. & ( - 2010). A protocol for data exploration to avoid common statistical problems. Methods in Ecology & Evolution 1, 3–14. , & (