How to quantify the evidence for the absence of a correlation

• Published in: Behavior research methods Vol. 48; no. 2; pp. 413 - 426
• Main Authors: Wagenmakers, Eric-Jan, Verhagen, Josine, Ly, Alexander
• Format: Journal Article
• Language: English
• Published: New York Springer US 01.06.2016; Springer Nature B.V
• Subjects: Bayes Theorem; Bayesian analysis; Behavioral Science and Psychology; Cognitive Psychology; Correlation analysis; Humans; Psychology; Research methodology; Statistics as Topic - methods; Hypothesis test; Statistical evidence; Bayes factor
• ISSN: 1554-3528; 1554-351X; 1554-3528
• DOI: 10.3758/s13428-015-0593-0

We present a suite of Bayes factor hypothesis tests that allow researchers to grade the decisiveness of the evidence that the data provide for the presence versus the absence of a correlation between two variables. For concreteness, we apply our methods to the recent work of Donnellan et al. ( in press ) who conducted nine replication studies with over 3,000 participants and failed to replicate the phenomenon that lonely people compensate for a lack of social warmth by taking warmer baths or showers. We show how the Bayes factor hypothesis test can quantify evidence in favor of the null hypothesis, and how the prior specification for the correlation coefficient can be used to define a broad range of tests that address complementary questions. Specifically, we show how the prior specification can be adjusted to create a two-sided test, a one-sided test, a sensitivity analysis, and a replication test.