Table 1: Open in new tab Features and...

	Frequentism-NHST	Bayesianism
Mathematical denotation	$P (data \| hypothesis)$	$P (hypothesis \| data)$
Conceptual explanation	Estimates the probability of observing the data (or more extreme data in repeated similar experiments), under the assumption that H₀ is true	Uses a posterior distribution, derived from a weighted combination of a prior belief and the current data, to provide probability estimates of a hypothesis given the observed data
Introduction of prior data	Impossible	Central aspect to obtain the posterior distribution
Use of current data (likelihood)	Central aspect used to assess the consistency of the data given a specific parameter, value, or hypothesis	Central aspect which quantifies the observed data support for all possible parameter values, serving as a relative measure of evidence
Adherence to the Likelihood Principle	Violates the likelihood principle	Fully respects the likelihood principle
Inference basis	Incorporates P-values, significance levels and sampling distribution	Based entirely on the posterior distribution
Inferential interval	The confidence interval (usually 95%), representing the interval that would contain the parameter of interest in 95% of instances in infinite sample of similar future experiments	The credible interval (usually 95%, or the highest posterior density interval [1]) which represent the interval for where there is 95% (un)certainty that it contains the parameter of interest
Probabilistic quantification of specific hypothesis	Impossible	Directly available from the area under the curve of the posterior distribution

Frequentism-NHST

Bayesianism

Mathematical denotation

P (data | hypothesis)

P (hypothesis | data)

Conceptual explanation

Estimates the probability of observing the data (or more extreme data in repeated similar experiments), under the assumption that H₀ is true

Uses a posterior distribution, derived from a weighted combination of a prior belief and the current data, to provide probability estimates of a hypothesis given the observed data

Introduction of prior data

Impossible

Central aspect to obtain the posterior distribution

Use of current data (likelihood)

Central aspect used to assess the consistency of the data given a specific parameter, value, or hypothesis

Central aspect which quantifies the observed data support for all possible parameter values, serving as a relative measure of evidence

Adherence to the Likelihood Principle

Violates the likelihood principle

Fully respects the likelihood principle

Inference basis

Incorporates P-values, significance levels and sampling distribution

Based entirely on the posterior distribution

Inferential interval

The confidence interval (usually 95%), representing the interval that would contain the parameter of interest in 95% of instances in infinite sample of similar future experiments

The credible interval (usually 95%, or the highest posterior density interval [1]) which represent the interval for where there is 95% (un)certainty that it contains the parameter of interest

Probabilistic quantification of specific hypothesis

Impossible

Directly available from the area under the curve of the posterior distribution

	Frequentism-NHST	Bayesianism
Mathematical denotation	$P (data \| hypothesis)$	$P (hypothesis \| data)$
Conceptual explanation	Estimates the probability of observing the data (or more extreme data in repeated similar experiments), under the assumption that H₀ is true	Uses a posterior distribution, derived from a weighted combination of a prior belief and the current data, to provide probability estimates of a hypothesis given the observed data
Introduction of prior data	Impossible	Central aspect to obtain the posterior distribution
Use of current data (likelihood)	Central aspect used to assess the consistency of the data given a specific parameter, value, or hypothesis	Central aspect which quantifies the observed data support for all possible parameter values, serving as a relative measure of evidence
Adherence to the Likelihood Principle	Violates the likelihood principle	Fully respects the likelihood principle
Inference basis	Incorporates P-values, significance levels and sampling distribution	Based entirely on the posterior distribution
Inferential interval	The confidence interval (usually 95%), representing the interval that would contain the parameter of interest in 95% of instances in infinite sample of similar future experiments	The credible interval (usually 95%, or the highest posterior density interval [1]) which represent the interval for where there is 95% (un)certainty that it contains the parameter of interest
Probabilistic quantification of specific hypothesis	Impossible	Directly available from the area under the curve of the posterior distribution

Table 1:

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Features and differences in frequentism and Bayesianism

	Frequentism-NHST	Bayesianism
Mathematical denotation	$P (data \| hypothesis)$	$P (hypothesis \| data)$
Conceptual explanation	Estimates the probability of observing the data (or more extreme data in repeated similar experiments), under the assumption that H₀ is true	Uses a posterior distribution, derived from a weighted combination of a prior belief and the current data, to provide probability estimates of a hypothesis given the observed data
Introduction of prior data	Impossible	Central aspect to obtain the posterior distribution
Use of current data (likelihood)	Central aspect used to assess the consistency of the data given a specific parameter, value, or hypothesis	Central aspect which quantifies the observed data support for all possible parameter values, serving as a relative measure of evidence
Adherence to the Likelihood Principle	Violates the likelihood principle	Fully respects the likelihood principle
Inference basis	Incorporates P-values, significance levels and sampling distribution	Based entirely on the posterior distribution
Inferential interval	The confidence interval (usually 95%), representing the interval that would contain the parameter of interest in 95% of instances in infinite sample of similar future experiments	The credible interval (usually 95%, or the highest posterior density interval [1]) which represent the interval for where there is 95% (un)certainty that it contains the parameter of interest
Probabilistic quantification of specific hypothesis	Impossible	Directly available from the area under the curve of the posterior distribution

	Frequentism-NHST	Bayesianism
Mathematical denotation	$P (data \| hypothesis)$	$P (hypothesis \| data)$
Conceptual explanation	Estimates the probability of observing the data (or more extreme data in repeated similar experiments), under the assumption that H₀ is true	Uses a posterior distribution, derived from a weighted combination of a prior belief and the current data, to provide probability estimates of a hypothesis given the observed data
Introduction of prior data	Impossible	Central aspect to obtain the posterior distribution
Use of current data (likelihood)	Central aspect used to assess the consistency of the data given a specific parameter, value, or hypothesis	Central aspect which quantifies the observed data support for all possible parameter values, serving as a relative measure of evidence
Adherence to the Likelihood Principle	Violates the likelihood principle	Fully respects the likelihood principle
Inference basis	Incorporates P-values, significance levels and sampling distribution	Based entirely on the posterior distribution
Inferential interval	The confidence interval (usually 95%), representing the interval that would contain the parameter of interest in 95% of instances in infinite sample of similar future experiments	The credible interval (usually 95%, or the highest posterior density interval [1]) which represent the interval for where there is 95% (un)certainty that it contains the parameter of interest
Probabilistic quantification of specific hypothesis	Impossible	Directly available from the area under the curve of the posterior distribution

Partly based on Heuts et al. [1].

H₀: null hypothesis; NHST: null hypothesis significance testing.

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