The Bayesian One-Sample t-Test Supersedes Correlation Analysis as a Test of Validity

Abstract

Abstract: Introduction: The validity of measurement, which refers to how accurately tools measure what they are intended to measure, is essential in science. Researchers rely on statistical approaches to test the validity of their measures. One such approach is correlation analysis. Even though correlation analysis can capture high nonsystematic errors between measures, it can often lead to misleading conclusions when observations are measured with systematic errors. Methods: We used Monte Carlo simulations with 10,000 iterations to generate the data in each simulation. Results: We demonstrate how correlation analysis is commonly used to test for validity and how this method can fail with systematic error. We further propose an alternative to correlation analysis – the Bayesian one-sample t-test – for cases where using a simple statistical test can be justified. We provide additional simulations as well as an application to real data, showcasing the implementation of the Bayesian one-sample t-test and how to use it to address the limitations of correlation analysis. Discussion: We suggest using the Bayesian one-sample t-test to identify both systematic and nonsystematic error and moreover to provide evidence for the null hypothesis of no differences between two measures. Conclusion: As a test of validity, the Bayesian one-sample t-test supersedes correlation analysis.

Keywords

• correlation
• validity
• psychometrics
• Bayesian
• t-test