The article explores using a new approach called peri-null hypotheses in Bayes factor tests. Instead of assuming a point-null hypothesis is completely false, they consider a narrow range around it. The peri-null Bayes factor is the original Bayes factor multiplied by a correction term. For small sample sizes, the correction term doesn't change much, but for large samples, it can significantly affect the results. The peri-null Bayes factor becomes inconsistent and approaches a limit based on the prior distribution. The researchers discuss how to create consistent peri-null Bayes factor tests.