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Bayesian Hypothesis Testing Using JASP
Eric-Jan
Wagenmakers
Outline
The Bayesian hypothesis test
The Bayesian t-test
Example: Turning the hands of time
Bayesian Inferencein a Nutshell
In Bayesian inference, uncertainty or degree of belief is quantified by probability.
Prior beliefs are updated by means of the data to yield posterior beliefs.
Bayesian Hypothesis Test
Suppose we have two models, H0 and H1.
After seeing the data, which one is preferable?
The one that has the highest posterior probability!
Bayesian Hypothesis Tests
Bayes Factor Inverse
Bayes Factor Transitivity
Bayes Factor Transitivity
Guidelines for Interpretation of the Bayes Factor
BF Evidence
1 – 3 Anecdotal 3 – 10 Moderate10 – 30 Strong 30 – 100 Very strong >100 Extreme
Visual Interpretation of the Bayes Factor
Visual Interpretation of the Bayes Factor
Visual Interpretation of the Bayes Factor
Advantages of the Bayes Factor
Quantifies evidence instead of forcing an all-or-none decision.
Allows evidence to be monitored as data accumulate.
Able to distinguish between “data support H0” and “data are not diagnostic”.
Disadvantages of the Bayes Factor
Where are the course books for psychologists?
Where is the software?
August 6 & August 7, 2015University of Amsterdam
First Annual JASP WorkshopA Fresh Way to do Bayesian Statistics
jasp-stats.org
August 10 - August 14, 2015University of Amsterdam
Fifth Annual JAGS and WinBUGS WorkshopBayesian Modeling for Cognitive Science
http://bayescourse.socsci.uva.nl/
Outline
The Bayesian hypothesis test
The Bayesian t-test
Example: Turning the hands of time
Bayes Factor for the t Test
Predictive Success for the Null Hypothesis
Predictive Success for the Alternative Hypothesis
Bayes Factor for the t Test
Prob. of Data Under the Null Hypothesis
Prob. of Data Under the Alternative Hypothesis
H0 states that effect size δ = 0.
But how do we specify H1?
Effect size δ under H1
δ = .1
δ = .3
δ = .5
•••
•••
•••
Likelihood ratio
p(data | H0)
p(data | δ = .1)
p(data | H0)
p(data | δ = .3)
p(data | H0)
p(data | δ = .5)
The Bayes factoris the weighted average of the likelihood ratios.The weights are given by the prior plausibility assigned to the effect sizes.
So we need to assign weight to the different values of effect size.
For complicated reasons, a popular default choice is to assume a Cauchy distribution (like a Normal, but with fatter tails):
These weigths reflect the relative plausibility of the effect sizes before seeing the data.
Outline
The Bayesian hypothesis test
The Bayesian t-test
Example: Turning the hands of time
Turning the Wheels of Time
Topolinski and Sparenberg (2012): clockwise movements induce psychological states of temporal progression and an orientation toward the future and novelty.
Concretely: participants who turn kitchen rolls clockwise report more openness to experience.
Turning the Wheels of Time
Turning the Wheels of Time
Let's demonstrate:
– How to run a Bayesian t-test in JASP;
– How to interpret the output;
– How to conduct a sequential analysis;
– How to assess the robustness of the result.
Conclusions
Bayesian hypothesis tests have a number of practical advantages;
These advantages are easily available through JASP;
The example discussed here was simple, but JASP handles more complicated analyses as well!