摘要: The visualization shows a Bayesian two-sample t test, for simplicity the variance is assumed to be known. It illustrates both Bayesian estimation via the posterior distribution for the effect, and Bayesian hypothesis testing via Bayes factor. The frequentist p-value is also shown. The null hypothesis, H0 is that the effect δ = 0, and the alternative H1: δ ≠ 0, just like a two-tailed t test. You can use the sliders to vary the observed effect (Cohen's d), sample size (n per group) and the prior on δ.


圖名

Settings

Observed effect (d = 1)
 
 
 
 
-3
-2
1
0
1
2
3
Sample size (n = 10)
 
 
 
 
1
10
20
30
40
50
75
100
1k
SD of prior (σδ = 0.3)
 
 
 
 
0.1
1
2
3
4
5
prior •likelihood •posterior •-3.0-2.5-2.0-1.5-1.0-0.50.00.51.01.52.02.53.00.00.20.40.60.81.01.295 % CI [0.12, 1.88]95 % HDI [-0.13, 1.08]Effect (d)
0.298Support H₀ (BF₀₁)
3.35Support H₁ (BF₁₀)
0.0253p-value
 

About the visualization

The prior on the effect is a scaled unit-information prior. The black, and red circle on the curves represents the likelihood of 0 under the prior and posterior. Their likelihood ratio is the Savage-Dickey density ratio, which I use here as to compute Bayes factor. The p-value is the traditional p-value for a two-sample t test with known variance (i.e. a Z test). HDI is the posterior highest density interval, which in this case is analogous a credible interval. And CI is the traditional frequentist confidence interval. 

Learn more

Check out Alexander Etz's blog series "Understanding Bayes" for a really good introduction to Bayes factor. Fabian Dablander also wrote a really good post, "Bayesian statistics: why and how", which introduces Bayesian inference in general. If you're interesting in an easy way to perform a Bayesian t test check out JASP, or BayesFactor if you use R.

 

 

轉貼自: R Psychologist


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  • 訪客 - CarolineWebb

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