Inappropriate use of statistics can seriously undermine the validity of
published medical research. This paper aims to make recommendations to authors
on the use and presentation of statistics in submissions to the
*Psychiatric Bulletin*. We derive our recommendations from a review of
the quality of statistical reporting in 50 consecutive ‘original’
papers published in the *Psychiatric Bulletin*. However simple the
methodology of a study, adequate emphasis needs to be given to the correct and
appropriate use and presentation of statistics in scientific papers.

Appropriate use of statistics is crucial in medical research. Use of
inappropriate statistical methods and/or faulty interpretation of results can
alter research findings significantly. Studies of statistical errors in
published medical research have found statistical error rates in the region of
30-75% (Pocock *et al*,
1987; McGuigan,
1995). McGuigan
(1995) looked at the use of
statistics in papers published in the *British Journal of Psychiatry*
over a 1-year period and found that nearly 40% of papers contained statistical
errors. More worryingly, he found that these rates were very similar to those
noted in an earlier study by White
(1979), and concluded that
there was no evidence of a change in the statistical error rate over that
period (1977-1993).

Authors, reviewers and editors all have crucial roles to play, at different
stages of a paper's pre-publication ‘journey’, in ensuring the
statistical quality and rigour of published papers. The aim of this paper is
to provide recommendations to prospective authors in their use of statistics
in papers submitted to the *Psychiatric Bulletin*. In order to best
tailor this guidance to potential contributors to the *Psychiatric
Bulletin*, we based it on the findings of an analysis of the statistical
reporting in 50 papers published in the *Psychiatric Bulletin* in 2003.
As detailed guidelines for authors on the use of statistics in medical
research are easily available (see Box 1), rather than reinvent the wheel, we
have attempted to tailor our recommendations to address the simple statistics
that are relevant and appropriate to papers in the *Psychiatric
Bulletin*.

## Method

The *Psychiatric Bulletin* was hand searched for 50 consecutive ‘
original’ papers published in 2003 (starting with the January
2003 issue). Papers published in this section (i.e. ‘original
papers’) were included in the study as they were most likely to have
used and presented statistical analyses than papers published in other
sections in the journal. We looked at each paper to identify statistical
errors, that is, errors in the use and presentation of statistics. For the
purpose of this paper, we took ‘statistical error’ to mean any of
the following: inappropriate choice of statistical methods, incorrect use of
statistical tests, faulty interpretation of results and errors in presentation
of statistics as used by Hand & Sham
(1995).

**Box 1. Useful references for statistical guidelines for authors**

*BMJ*advice on statistical methods (http://resources.bmj.com/bmj/authors/special-methods)Balilar, J. C. & Mosteller, F. (1988) Guidelines for statistical reporting in articles for medical journals.

*Annals of Internal Medicine*,**108**, 266-273.Wilkinson, L. & Task Force on Statistical Inference, APA Board of Scientific Affairs (1999) Statistical methods in psychology journals: guidelines and explanations.

*American Psychologist*,**54**, 594-604.International Committee of Medical Journal Editors website (http://www.icmje.org/icmje.pdf)

See instructions for authors section in major psychiatric journals.

## Results

Tables 1, 2, 3 show the types of study design, statistical procedures used and the number of papers using different statistical methods respectively.

### Examples of errors in use and presentation of statistics

Here we present some examples of errors in use and presentation of statistics in the papers looked at. These included

no mention in the Method section as to what statistical methods were used

mean value reported but standard deviation not given

*t*-test used but did not mention which one (i.e. one-sample*t*-test or two independent samples*t*-test or two paired samples*t*-test)reported ‘no significant difference’ but no

*P*value quoted*P*values quoted but no tests mentionedanalysis of variance (ANOVA) used but degrees of freedom (d.f.) not stated

mean value reported as ‘mean ±’ with no clarification of what ± means (i.e. standard deviation or standard error).

A large majority of the studies (82%) were questionnaire surveys or case
note-based studies. Only 5 out of 50 original studies involved direct patient
contact (see Table 1). The
simplicity of the study designs and methodology reflected the type of
statistical tests used in these studies: mostly descriptive statistics and
simple tests of significance (see Tables
2 and
3). The most commonly used
tests were the χ^{2}-test (16 papers) and the *t*-test (9
papers). This is consistent with research findings from psychiatric and
non-psychiatric medical literature (Elster,
1994; Rigby *et al*,
2004). Reed *et al*
(2003) studied the use of
statistics in six medical journals and noted that χ^{2}-test and
*t*-test were the most commonly used tests. They went on to argue that
clinicians could satisfactorily interpret 70% of medical literature if they
understood descriptive statistics, chi-squared test and *t*-test.
Although this statement may be an over-simplification, the underlying message
may be particularly relevant to authors and readers of the *Psychiatric
Bulletin*.

## Recommendations to authors in their use and presentation of statistics

Based on the results described above, we make some simple recommendations
on the appropriate use and presentation of statistics for authors submitting
papers to the *Psychiatric Bulletin*. We suggest that these
recommendations be read in conjunction with more detailed guidelines published
elsewhere (see Box 1).

### General

Mention/explain the statistical methods used in the Method section of your paper (as a separate paragraph if appropriate)

Mention the statistical software used in analysing the data

Draw only justifiable conclusions from the results

Avoid overuse of statistical abbreviations

If uncommon statistical tests are used, provide reference

If a statistician has helped with the study, it is good practice to acknowledge their contribution as appropriate.

### Presentation of results

Avoid duplication of data in text and table/graph

No value reported should have more than 2 decimal places

Where possible, exact

*P*values should be quoted rather than merely stating ‘a significant result was found’ or ‘*P*<0.05’If the statistical software output shows that the

*P*value is equal to 0.000, then report that the*P*value is smaller than 0.001 or*P*<0.001Whenever the mean value is reported it is good practice to also report with it the standard deviation or the standard error, and clarify which measure is being reported. For example, mean12.3 (s.d.=2.6).

### Use of statistics

If using descriptive statistics, report values appropriately (i.e. for continuous data report mean and standard deviation and for discrete data quote median and interquartile range or range)

If using the χ

^{2}-test, it should be justified. Note that if the expected cell frequency is less than 5 in 20% or more of the cells, then the χ^{2}-test is not validWhenever the

*t*-test is used, the type should be mentioned (i.e. independent samples*t*-test or paired samples*t*-test (if using the independent samples*t*-test, it should also be mentioned whether equality of variance or inequality of variance was used)Use of parametric tests such as the

*t*-test and ANOVA should be justified (i.e. the data follow normal distribution)Use appropriate statistical analyses to answer the research question under study.

Authors should ‘describe statistical methods with enough detail to enable a knowledgeable reader with access to the original data to verify the reported results’ (http://www.icmje.org/icmje.pdf).

## Conclusions

Inappropriate use of statistics can seriously undermine the validity of published medical research. However simple the methodology of a study, adequate emphasis needs to be given to the correct and appropriate use and presentation of statistics in scientific papers.

- © 2007 Royal College of Psychiatrists