Bayesian Versus orthodox statistics: which side are you on? - summary of an article by Dienes, 2011
Critical thinking
Article: Dienes, Z, 2011
Bayesian Versus orthodox statistics: which side are you on?
doi: 10.1177/1745691611406920
The contrast: orthodox versus Bayesian statistics
The orthodox logic of statistics, starts from the assumption that probabilities are long-run relative frequencies.
A long-run relative frequency requires an indefinitely large series of events that constitutes the collective probability of some property (q) occurring is then the proportion of events in the collective with property q.
- The probability applies to the whole collective, not to any one person.
- One person may belong to two different collectives that have different probabilities
- Long run relative frequencies do not apply to the truth of individual theories because theories are not collectives. They are just true or false.
- Thus, when using this approach to probability, the null hypothesis of no population difference between two particular conditions cannot be assigned a probability.
- Given both a theory and a decision procedure, one can determine a long-run relative frequency with which certain data might be obtained. We can symbolize this as P(data| theory and decision procedure).
The logic of Neyman Pearson (orthodox) statistics is to adopt decision procedures with known long-term error rates and then control those errors at acceptable levels.
- Alpha: the error rate for false positives, the significance level
- Beta: the error rate for false negatives
Thus, setting significance and power controls long-run error rates.
- An error rate can be calculated from the tail area of test statistics.
- An error rate can be adjusted for factors that affect long-run error rates
- These error rates apply to decision procedures, not to individual experiments.
- An individual experiment is a one-time event, so does not constitute a long-run set of events
- A decision procedure can in principle be considered to apply over a indefinite long-run number of experiments.
The probabilities of data given theory and theory given data
The probability of a theory being true given data can be symbolized as P(theory|data).
This is what orthodox statistics tell us.
One cannot infer one conditional probability just by knowing its inverse. (So P(data|theory) is unknown).
Bayesian statistics starts from the premise that we can assign degrees of plausibility to theories, and what we want our
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