A Bayes factor less than 1 has what implication for the null hypothesis?

A Bayes factor less than 1 has what implication for the null hypothesis?

• A. It supports the alternative hypothesis by suggesting the data are more likely under the alternative.
• B. It indicates equal evidence for both hypotheses.
• C. It shows that the data favor the null hypothesis.
• D. It supports the null hypothesis by suggesting the data are more likely under the null.

Answer: (D)

The key idea is how to read a Bayes factor. A Bayes factor compares how likely the observed data are under two competing hypotheses by forming a ratio of their likelihoods. When we use the common convention BF = P(data | H1) / P(data | H0), a Bayes factor less than 1 means the data are more likely under the null hypothesis than under the alternative. In other words, the evidence provided by the data favors the null hypothesis. The smaller the Bayes factor, the stronger that support (for example, a Bayes factor of 0.5 means the data are twice as likely under the null as under the alternative). Keep in mind that some sources report the reciprocal (BF_01), which would reverse the interpretation, but with the standard BF = P(data|H1)/P(data|H0), a value below 1 indicates support for the null.

The key idea is how to read a Bayes factor. A Bayes factor compares how likely the observed data are under two competing hypotheses by forming a ratio of their likelihoods. When we use the common convention BF = P(data | H1) / P(data | H0), a Bayes factor less than 1 means the data are more likely under the null hypothesis than under the alternative. In other words, the evidence provided by the data favors the null hypothesis. The smaller the Bayes factor, the stronger that support (for example, a Bayes factor of 0.5 means the data are twice as likely under the null as under the alternative).

Keep in mind that some sources report the reciprocal (BF_01), which would reverse the interpretation, but with the standard BF = P(data|H1)/P(data|H0), a value below 1 indicates support for the null.