Remarks on the use of Pearson’s and Spearman’s correlation coefficients in assessing relationships in ophthalmic data

Background: A correlation coefficient is a measure of a relationship between any two quantitative and categorical variables. The coefficient describes the degree of relationship between two variables. Associated variables change in tandem – a change in one variable, and the second changes in the same or opposite direction. Correlation is a commonly used statistical procedure. Medical studies use this test widely to explore diagnosis, prognosis and predicting normative parameters for reference measurements. This test is not uncommon in the ophthalmic field, and many studies in the literature used this statistical procedure. However, in some studies, the interpretation of this test was incorrect, possibly because of the test being partially misunderstood. Aim: This study aims to review articles that used those statistic tests to provide an overview of correlation coefficient tests, their indications and interpretations. Correlation analyses and interpretations in ophthalmic data studies are also discussed. Methods: The preferred reporting items for systematic reviews and meta-analyses guidelines were followed and correlation studies that explored ophthalmic data were searched, investigated and reviewed. This review covered a span over the period published between 1990–2020. Results: This critical review included 64 papers. The papers were directed to investigate many variables, for example, visual acuity, contrast sensitivity, dry eye, myopia, retina and low vision. Some of those papers found significant results while the others did not report any. Their reporting and interpretation of the correlation coefficient varied widely. Conclusion: The studies reviewed suggested that there is a need for reporting, in every single study, the normality of the data, r -value, p -value and the extent of the shared variance between investigated outcomes. Lastly, the clinical implications of those studies findings are recommended to be stated clearly.