# Reporting the standard error of the mean: a critical analysis of three journals in manual medicine

## TL;DR

This study examines how often researchers in manual medicine incorrectly report the standard error of the mean in three journals, finding a low but notable rate of misuse.

## Contribution

The paper provides the first analysis of SEM reporting accuracy in manual medicine journals, highlighting potential issues in statistical clarity.

## Key findings

- Only 1.4% of articles in three manual medicine journals misreported the standard error of the mean.
- In 2.5% of articles, the ± sign was not clearly defined as representing either standard deviation or standard error of the mean.
- The misuse rate in manual medicine journals was lower than in other biomedical fields.

## Abstract

In the realm of biomedical research articles, authors typically utilize descriptive statistics to outline the characteristics of their study samples. The standard deviation (SD) serves to illustrate variability among the individuals in a sample, whereas the standard error of the mean (SEM) conveys the level of uncertainty associated with the sample mean’s representation of the population mean. It is not unusual for authors of scientific articles to incorrectly utilize the SEM rather than the SD when explaining data variability. This is problematic because the SEM is consistently smaller than the SD, which could cause readers to underestimate variation in the data. In medical journals, inappropriate use has been found in 14–64% of articles. Moreover, in the field of musculoskeletal health and manual medicine, there is a noticeable absence of literature on the appropriate presentation of statistics.

The aim of this study was to map the frequency of inappropriate reporting of SEM in articles published over a three-year period in three prominent journals in manual medicine.

In this critical analysis, all articles in three journals – BMC Chiropractic and Manual Therapies (CMT), Journal of Manipulative and Physiological Therapeutics (JMPT) and Musculoskeletal Science and Practice: An International Journal of Musculoskeletal Physiotherapy (MSP) – published between 2017 and 2019 were analysed based on descriptive statistics that inappropriately or vaguely reported SEMs.

In total, 790 articles were analysed from the three journals, 487 of which were found to report the SEM. Among these articles, we identified a frequency of 1.4% of inadequate SEM use. The investigation also showed that in 2.5% of the cases, authors did not clarify whether the ± sign presented in text, tables or figures expressed SDs or SEMs.

There was a low frequency (1.4%) of inaccurately reported SEMs in scientific journals focusing on manual medicine, which was notably lower than studies conducted in other fields. Additionally, it was noted that in 2.5% of the articles, the ± sign was not adequately defined, which could lead to confusion among readers and hinder the interpretation of the results.