Table 1 Differences between Bayesian and Frequentist/Fisherian approaches to investigative inference

Incorporates past knowledge

Ignores past knowledge

Result based on strength of the evidence

Result typically (but not necessarily) based on assumption of no effect or assumption of a statement counterfactual to one’s question

The parameters describing the relationships within the data are treated as random within some distribution. (e.g., in Markov chain Monte Carlo methods, the data is treated as constant, but the relationships taking the researcher from the data to a prediction are randomly iterated to optimize the model for each data value and determine how parameter values vary)

The data are treated as random so that the likelihood of obtaining it under the null can be assessed

Follows “inverse logic”, moving from effect to estimation of cause

Typically uses null logic: rejection of no effect to infer effect

Probability is a measure of evidence, belief, or willingness to gamble based on all available information

Probability is relative frequency over time.

“The probability of H, given the evidence, is x%”

“If its contrary were true, then the chances of H (or a more extreme statement of H) would be less than x%”

New information must compete with old, making the process of discovery more conservative and necessarily cumulative

The assumption of no difference is always false. Given a large enough sample size, any difference will be found statistically significant.

Determining the measure of one’s priors can be difficult, and Bayesian methods can be perceived as unscientific, especially in legal circles

Does not produce estimates of the form typically desired (e.g., “a 77% chance”), and results logically pertain to the data itself, not to the prediction of new cases