Bayesian Inference in Psychological Research
Moving Beyond p-values
The Bayes Factor
Unlike frequentist p-values, which only test the probability of data given the null hypothesis, Bayesian inference quantifies the relative evidence for two competing hypotheses. The Bayes Factor () is the ratio of marginal likelihoods: A of 5 means the data are 5 times more likely under the alternative hypothesis than the null.
Frequentist vs. Bayesian Approaches
Frequentist (NHST)
- Treats parameters as fixed, unknown constants.
- Calculates (p-value).
- Cannot quantify evidence in favor of the null hypothesis.
Bayesian
- Treats parameters as random variables with distributions.
- Calculates (posterior).
- Can distinguish between 'absence of evidence' and 'evidence of absence'.
Interpreting the Bayes Factor (Jeffreys' Scale)
Sensitivity Analysis
Priors matter! The Bayes Factor is highly sensitive to the chosen prior distribution for the alternative hypothesis. Always conduct a robustness check by calculating the BF across different prior widths (e.g., varying the Cauchy prior scale from 0.5 to 1.5).
A Bayes Factor () of 0.10 indicates what?
A of 0.10 is equivalent to a of 10 (), which indicates strong evidence for the null hypothesis according to Jeffreys' scale.
Correct answer: Strong evidence for the null hypothesis ().
What term describes the probability distribution representing a researcher's knowledge or belief about a parameter before any data is observed?
The prior distribution encodes beliefs before seeing data. In Bayes' theorem, the prior is updated by the likelihood of the data to yield the posterior distribution.
Correct answer: Prior distribution