Considerations on linear correlation analysis

The paper “Auditory processing screening: contributions of the combined use of questionnaire and auditory tasks”, recently published in the 23^rd volume of this journal⁽¹⁾, brings significant contribution on the search of valid and reliable auditory processing screening procedures, a recurrent topic in international consensus on the matter^(2,3). Nevertheless, the paper has two important mistakes regarding linear correlation analysis that might lead to incorrect interpretation of research’s results and related statistical concepts.

In the paper’s “Results” section, table 3 presents 78 correlation analyses between the score of Scale of Auditory Behaviors questionnaire and the hit percentage of tests that make up the Auditory Processing Simplified Assessment.

The first mistake consists in the fact that correlation coefficient (r), obtained through Pearson’s correlation test, is inappropriately represented in the form of percentage.

The equation that determines r limits its value to real numbers contained between 1 and -1. Positive and negative signs indicate, respectively, directly or inversely proportional correlations, while absolute value indicates correlation’s strength, with higher values denoting stronger correlations⁽⁴⁾.

The representation of r by means of percentage might lead the reader to incorrect interpretations of the results, the most common being the idea that percentage represents variance proportion of one variable that can be explained by other variable⁽⁵⁾. This interpretation, however, is possible only if one squares r, obtaining coefficient of determination (r²)⁽⁶⁾.

Thus, it is recommended that r values must be reported in real numbers contained between -1 and 1, limiting its interpretation to correlation power, and the use of percentage must be reserved to r² representation⁽⁷⁾.

The second mistake refers to the lack of correction for multiple comparisons of p values corresponding to each r.

It is known that, the more hypotheses tested simultaneously, the higher the probability of incurring into type I error (rejecting null hypothesis when it is true). This means that performing multiple correlation analyses increases the risk of finding statistically significant correlations by chance. Thus, interpretation of the results of a study and its conclusion can be altered if the effects of multiple comparisons are ignored⁽⁸⁾.

Many methods of correction for multiple comparisons can be used, like Bonferroni’s method, which consists in dividing the originally proposed p value by the number of comparisons to be made⁽⁹⁾. In this study, the application of this method would lead to consider statistical significance only for p values ≤ 0,00064, consequently changing the interpretation of the results presented.

Statistics is a science based on concepts that are sometimes abstract and, for this reason, can be easily mistaken by readers and researchers alike. Yet, given the importance of this science for the construction of new knowledge and clinical decision, elucidation of misconceptions is necessary so that scientific knowledge can progress on solid bases.

• Study carried out at Programa de Pós-graduação em Ciências da Reabilitação, Departamento de Fisioterapia, Fonoaudiologia e Terapia Ocupacional, Faculdade de Medicina, Universidade de São Paulo – USP – São Paulo (SP), Brasil.
• Funding: None.

REFERÊNCIAS

• ¹
  Souza IMP, Carvalho ND, Plotegher SDCB, Colella-Santos MF, Amaral MIR. Triagem do processamento auditivo central: contribuições do uso combinado de questionário e tarefas auditivas. Audiol Commun Res. 2018 Dez;23(3):1-8. http://dx.doi.org/10.1590/2317-6431-2018-2021
  » http://dx.doi.org/10.1590/2317-6431-2018-2021
• ²
  American Academy of Audiology Clinical Practice Guidelines. Diagnosis, treatment and management of children and adults with central auditory processing disorder [Internet]. Reston: American Academy of Audiology; 2010 [cited 2019 Feb 1]. Available from: https://audiology-web.s3.amazonaws.com/migrated/CAPD%20Guidelines%208-2010.pdf_539952af956c79.73897613.pdf
  » https://audiology-web.s3.amazonaws.com/migrated/CAPD%20Guidelines%208-2010.pdf_539952af956c79.73897613.pdf
• ³
  BSA: British Society of Audiology. Position Statement and Practice Guidance. Auditory Processing Disorder (APD) [Internet]. Bathgate: BSA; 2018 [cited 2019 Feb 1]. Available from: https://www.thebsa.org.uk/wp-content/uploads/2018/02/Position-Statement-and-Practice-Guidance-APD-2018.pdf
  » https://www.thebsa.org.uk/wp-content/uploads/2018/02/Position-Statement-and-Practice-Guidance-APD-2018.pdf
• ⁴
  Zou KH, Tuncali K, Silverman SG. Correlation and simple linear regression. Radiology. 2003 Jun;227(3):617-22. http://dx.doi.org/10.1148/radiol.2273011499 PMid:12773666.
  » http://dx.doi.org/10.1148/radiol.2273011499
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  Higgins J. The radical statistician: unleashing the power of applied statistics in the real world. 5th ed. The Higgins Group: Sacramento; 2010. 374 p.
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  Goodwin LD, Leech NL. Understanding correlation: factors that affect the size of r. J Exp Educ. 2006;74(3):251-66. http://dx.doi.org/10.3200/JEXE.74.3.249-266
  » http://dx.doi.org/10.3200/JEXE.74.3.249-266
• ⁷
  Field A. Discovering statistics using IBM SPSS Statistics. 5th ed. London: SAGE Publications; 2017. 1070 p.
• ⁸
  Chen SY, Feng Z, Yi X. A general introduction to adjustment for multiple comparisons. J Thorac Dis. 2017 Jun;9(6):1725-9. http://dx.doi.org/10.21037/jtd.2017.05.34 PMid:28740688.
  » http://dx.doi.org/10.21037/jtd.2017.05.34
• ⁹
  Curtin F, Schulz P. Multiple correlations and Bonferroni’s correction. Biol Psychiatry. 1998 Out;44(8):775-7. http://dx.doi.org/10.1016/S0006-3223(98)00043-2 PMid:9798082.
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Publication Dates

• Publication in this collection
  12 Sept 2019
• Date of issue
  2019

History

• Received
  05 Feb 2019
• Accepted
  17 June 2019