# Jonas Ranstam's website

### 7. The statistics section

2022-02-18

A statistics section is necessary for most manuscripts to explain the methodology used to estimate effects and test hypotheses. The ICMJE guideline for manuscript preparation is to "Describe statistical methods with enough detail to enable a knowledgeable reader with access to the original data to judge its appropriateness for the study and to verify the reported results". In practice, three awkward problems often occur.

First, most statistics sections start by explaining how variables are presented, e.g. "data are presented as means and standard deviation (SD)", which later is repeated when the results are presented. Is the information really necessary in the statistics section, or does it just reflect an inability to distinguish between descriptive measures and inferential methods?

Another commonly occurring problem is that it is described how it has been assessed whether or not variables are normally distributed. In most cases, however, the variables' distributions are unimportant. Mean values are studied, and, as stated by the central limit theorem, when the sample size is reasonable large (say 30 or more), the distribution of the means from random samples will be approximately normally distributed. Furthermore, a variable's distribution cannot be "assessed" using information from a sample. A significance test of the distribution can be performed, but statistical nonsignificance does not imply that the variable is a normal distribution. It just means that the sample size has been insufficient to refute the hypothesis that the variable is normally distribution.

The third problem is describing that the variables have been "compared" using significance tests such as Student's t-test and the chi-squared test. Statistical tests, however, are performed for evaluating inferential uncertainty, not for comparing observed characteristics in a sample of subjects. Again, the described presentation reveals an embarrassing lack of methodological insights.

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