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. Author manuscript; available in PMC: 2020 Oct 1.
Published in final edited form as: Neuroinformatics. 2019 Oct;17(4):515–545. doi: 10.1007/s12021-018-9409-6

Table 5:

Interpretation differences between NHST and Bayesian framework

Probability p Effect Interval [L, U]
NHST If H0 is true, the probability of having the current result or more extreme is p (based on what would have occurred under other possible datasets); e.g., P(|T(y)| > tc|easy = difficult) = p, where T(y) is a statistic (e.g., Student’s t) based on data y and tc is a threshold. If the study is exactly repeated an infinite number of times, the percentage of those confidence intervals will cover the true effectis 1 — p; e.g., P(L ≤ easy - difficult ≤ U) = 1 — p, where “easy - difficult” is treated as being fixed while L and U are random.
Bayesian The probability of having the current result being different from zero is p (given the dataset); e.g., P(easy — difficult < L or easy — difficult > U|y) = p, where L and U are lower and upper bounds of the (1 — p)100% quantile interval. The probability that the effect falls in the predictive interval is 1 — p (given the data); e.g., P(L ≤ easy — difficult ≤ U|y) = 1 — p, where “easy - difficult” is considered random while L and U are known conditional on data y.