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> # This file is part of the standard setup for testthat.
> # It is recommended that you do not modify it.
> #
> # Where should you do additional test configuration?
> # Learn more about the roles of various files in:
> # * https://r-pkgs.org/testing-design.html#sec-tests-files-overview
> # * https://testthat.r-lib.org/articles/special-files.html
> 
> library(testthat)
> library(bayesics)
> 
> test_check("bayesics")

---
Bayes factor in favor of the full vs. null model: 4.81e+55;
      =>Level of evidence: Decisive



--- Summary of factor level means ---
# A tibble: 10 x 5
   Variable      `Post Mean`  Lower  Upper `Prob Dir`
   <chr>               <dbl>  <dbl>  <dbl>      <dbl>
 1 Mean : x1 : a      -0.911 -1.11  -0.716      1.000
 2 Mean : x1 : b      -1.09  -1.31  -0.882      1    
 3 Mean : x1 : c      -0.915 -1.09  -0.737      1    
 4 Mean : x1 : d       0.905  0.707  1.10       1.000
 5 Mean : x1 : e       1.05   0.854  1.25       1    
 6 Var : x1 : a        0.992  0.750  1.31      NA    
 7 Var : x1 : b        1.17   0.884  1.54      NA    
 8 Var : x1 : c        0.829  0.627  1.09      NA    
 9 Var : x1 : d        1.03   0.776  1.36      NA    
10 Var : x1 : e        1.01   0.764  1.33      NA    




--- Summary of pairwise differences ---
# A tibble: 10 x 9
   Comparison `Post Mean`  Lower   Upper `Prob Dir` `ROPE (0.1)`    EPR
   <chr>            <dbl>  <dbl>   <dbl>      <dbl>        <dbl>  <dbl>
 1 a-b            0.182   -0.103  0.465       0.894        0.270 0.549 
 2 a-c            0.00419 -0.261  0.268       0.506        0.525 0.501 
 3 a-d           -1.82    -2.09  -1.54        1            0     0.101 
 4 a-e           -1.96    -2.24  -1.69        1            0     0.0836
 5 b-c           -0.178   -0.452  0.0985      0.900        0.261 0.450 
 6 b-d           -2.00    -2.28  -1.71        1            0     0.0893
 7 b-e           -2.14    -2.43  -1.85        1            0     0.0740
 8 c-d           -1.82    -2.09  -1.55        1            0     0.0913
 9 c-e           -1.97    -2.23  -1.70        1            0     0.0744
10 d-e           -0.145   -0.428  0.135       0.844        0.340 0.460 
# i 2 more variables: `EPR Lower` <dbl>, `EPR Upper` <dbl>


   *Note: EPR (Exceedence in Pairs Rate) for a Comparison of g-h = Pr(Y_(gi) > Y_(hi)|parameters) 
---
Bayes factor in favor of the full vs. null model: 5.79e+65;
      =>Level of evidence: Decisive



--- Summary of factor level means ---
# A tibble: 6 x 5
  Variable      `Post Mean`  Lower  Upper `Prob Dir`
  <chr>               <dbl>  <dbl>  <dbl>      <dbl>
1 Mean : x1 : a      -0.911 -1.11  -0.717          1
2 Mean : x1 : b      -1.09  -1.29  -0.899          1
3 Mean : x1 : c      -0.915 -1.11  -0.721          1
4 Mean : x1 : d       0.905  0.711  1.10           1
5 Mean : x1 : e       1.05   0.856  1.24           1
6 Var                 0.989  0.874  1.12          NA




--- Summary of pairwise differences ---
# A tibble: 10 x 9
   Comparison `Post Mean`   Lower   Upper `Prob Dir` `ROPE (0.1)`    EPR
   <chr>            <dbl>   <dbl>   <dbl>      <dbl>        <dbl>  <dbl>
 1 a-b            0.182   -0.0926  0.453       0.903        0.254 0.551 
 2 a-c            0.00419 -0.272   0.279       0.512        0.527 0.501 
 3 a-d           -1.82    -2.09   -1.54        1            0     0.0990
 4 a-e           -1.96    -2.24   -1.69        1            0     0.0825
 5 b-c           -0.178   -0.450   0.0973      0.898        0.262 0.450 
 6 b-d           -2.00    -2.27   -1.73        1            0     0.0784
 7 b-e           -2.14    -2.42   -1.87        1            0     0.0647
 8 c-d           -1.82    -2.10   -1.55        1            0     0.0986
 9 c-e           -1.97    -2.24   -1.69        1            0     0.0822
10 d-e           -0.145   -0.422   0.131       0.850        0.339 0.460 
# i 2 more variables: `EPR Lower` <dbl>, `EPR Upper` <dbl>


   *Note: EPR (Exceedence in Pairs Rate) for a Comparison of g-h = Pr(Y_(gi) > Y_(hi)|parameters) 



--- Summary of factor level means ---
# A tibble: 10 x 5
   Variable      `Post Mean`  Lower  Upper `Prob Dir`
   <chr>               <dbl>  <dbl>  <dbl>      <dbl>
 1 Mean : x1 : a      -0.926 -1.12  -0.731      1.000
 2 Mean : x1 : b      -1.11  -1.32  -0.898      1    
 3 Mean : x1 : c      -0.930 -1.11  -0.753      1    
 4 Mean : x1 : d       0.900  0.700  1.10       1.000
 5 Mean : x1 : e       1.05   0.847  1.24       1    
 6 Var : x1 : a        0.980  0.740  1.30      NA    
 7 Var : x1 : b        1.16   0.873  1.53      NA    
 8 Var : x1 : c        0.815  0.616  1.08      NA    
 9 Var : x1 : d        1.03   0.781  1.37      NA    
10 Var : x1 : e        1.02   0.769  1.35      NA    




--- Summary of pairwise differences ---
# A tibble: 10 x 9
   Comparison `Post Mean`  Lower   Upper `Prob Dir` `ROPE (0.1)`    EPR
   <chr>            <dbl>  <dbl>   <dbl>      <dbl>        <dbl>  <dbl>
 1 a-b            0.183   -0.101  0.467       0.895        0.267 0.550 
 2 a-c            0.00421 -0.260  0.266       0.507        0.523 0.501 
 3 a-d           -1.83    -2.11  -1.55        1            0     0.0997
 4 a-e           -1.97    -2.25  -1.69        1            0     0.0823
 5 b-c           -0.179   -0.454  0.0971      0.901        0.257 0.449 
 6 b-d           -2.01    -2.30  -1.72        1            0     0.0880
 7 b-e           -2.15    -2.44  -1.86        1            0     0.0728
 8 c-d           -1.83    -2.10  -1.56        1            0     0.0899
 9 c-e           -1.98    -2.24  -1.71        1            0     0.0731
10 d-e           -0.146   -0.431  0.137       0.843        0.340 0.460 
# i 2 more variables: `EPR Lower` <dbl>, `EPR Upper` <dbl>


   *Note: EPR (Exceedence in Pairs Rate) for a Comparison of g-h = Pr(Y_(gi) > Y_(hi)|parameters) 



--- Summary of factor level means ---
# A tibble: 6 x 5
  Variable      `Post Mean`  Lower  Upper `Prob Dir`
  <chr>               <dbl>  <dbl>  <dbl>      <dbl>
1 Mean : x1 : a      -0.926 -1.12  -0.732          1
2 Mean : x1 : b      -1.11  -1.30  -0.915          1
3 Mean : x1 : c      -0.930 -1.12  -0.736          1
4 Mean : x1 : d       0.900  0.706  1.09           1
5 Mean : x1 : e       1.05   0.852  1.24           1
6 Var                 0.977  0.863  1.11          NA




--- Summary of pairwise differences ---
# A tibble: 10 x 9
   Comparison `Post Mean`   Lower   Upper `Prob Dir` `ROPE (0.1)`    EPR
   <chr>            <dbl>   <dbl>   <dbl>      <dbl>        <dbl>  <dbl>
 1 a-b            0.183   -0.0907  0.452       0.905        0.251 0.552 
 2 a-c            0.00421 -0.271   0.278       0.512        0.526 0.501 
 3 a-d           -1.83    -2.10   -1.55        1            0     0.0964
 4 a-e           -1.97    -2.25   -1.70        1            0     0.0801
 5 b-c           -0.179   -0.449   0.0954      0.900        0.258 0.449 
 6 b-d           -2.01    -2.28   -1.74        1            0     0.0761
 7 b-e           -2.15    -2.43   -1.88        1            0     0.0625
 8 c-d           -1.83    -2.11   -1.56        1            0     0.0961
 9 c-e           -1.98    -2.25   -1.70        1            0     0.0798
10 d-e           -0.146   -0.421   0.130       0.852        0.335 0.459 
# i 2 more variables: `EPR Lower` <dbl>, `EPR Upper` <dbl>


   *Note: EPR (Exceedence in Pairs Rate) for a Comparison of g-h = Pr(Y_(gi) > Y_(hi)|parameters) Bayesian p-values measure GOF via 
Pr(T(y_obs) - T(y_pred) > 0 | y_obs).
Thus values close to 0.5 are ideal.  Be concerned if values are near 0 or 1.
These Bayesian p-values correspond to quantiles of the distribution of y.
Partial dependence plots typically require long run times.  Plan accordingly.
Missing other covariate values in 'exemplar_covariates.'  Using medoid observation instead.
Missing other covariate values in 'exemplar_covariates.'  Using medoid observation instead.
Missing other covariate values in 'exemplar_covariates.'  Using medoid observation instead.
Missing other covariate values in 'exemplar_covariates.'  Using medoid observation instead.
Cell sizes were too small for large sample approximation.
Instead, setting uniform prior on Pr(exposure|outcome) and making exact finite sample inference.

----------

Case-control analysis using Bayesian techniques

----------

Data: 
            Cases Controls
At risk         8        1
Not at risk    47       26


Posterior mean of the odds ratio: 5.16; Population 2 = 

95% credible interval: (0.64, 22.6)

Probability that the odds ratio is in the ROPE, defined to be (0.889,1.12) = 0.0515


----------

Cell sizes were too small for large sample approximation.
Instead, setting uniform prior on Pr(exposure|outcome) and making exact finite sample inference.

----------

Case-control analysis using Bayesian techniques

----------

Data: 
            Cases Controls
At risk         8        1
Not at risk    47       26


Posterior mean of the odds ratio: 5.16; Population 2 = 

95% credible interval: (0.64, 22.6)

Probability that the odds ratio is in the ROPE, defined to be (0.889,1.12) = 0.0515


----------

Cell sizes were too small for large sample approximation.
Instead, setting uniform prior on Pr(exposure|outcome) and making exact finite sample inference.

----------

Case-control analysis using Bayesian techniques

----------

Data: 
            Cases Controls
At risk         8        1
Not at risk    47       26


Posterior mean of the odds ratio: 5.16; Population 2 = 

95% credible interval: (0.64, 22.6)

Probability that the odds ratio is in the ROPE, defined to be (0.889,1.12) = 0.0515


----------


----------

Case-control analysis using Bayesian techniques

----------

Data: 
            Cases Controls
At risk        13        6
Not at risk    52       31


Prior used on log odds ratio: N(0,1.17)

Posterior mean of the odds ratio: 1.39; Population 2 = 

Posterior median of the odds ratio: 1.23; Population 2 = 

95% credible interval: (0.47, 3.25)

Probability that the odds ratio is in the ROPE, defined to be (0.889,1.12) = 0.173


----------

Cell sizes were too small for large sample approximation.
Instead, setting uniform prior on Pr(exposure|outcome) and making exact finite sample inference.

----------

Case-control analysis using Bayesian techniques

----------

Data: 
            Cases Controls
At risk         8        1
Not at risk    47       26


Posterior mean of the odds ratio: 5.16; Population 2 = 

95% credible interval: (0.64, 22.6)

Probability that the odds ratio is in the ROPE, defined to be (0.952,1.05) = 0.0215


----------


----------

Case-control analysis using Bayesian techniques

----------

Data: 
            Cases Controls
At risk        13        6
Not at risk    52       31


Prior used on log odds ratio: N(0,1.17)

Posterior mean of the odds ratio: 1.39; Population 2 = 

Posterior median of the odds ratio: 1.23; Population 2 = 

95% credible interval: (0.47, 3.25)

Probability that the odds ratio is in the ROPE, defined to be (0.952,1.05) = 0.072


----------


----------

Case-control analysis using Bayesian techniques

----------

Data: 
            Cases Controls
At risk        13        6
Not at risk    52       31


Prior used on log odds ratio: N(0,1.17)

Posterior mean of the odds ratio: 1.39; Population 2 = 

Posterior median of the odds ratio: 1.23; Population 2 = 

95% credible interval: (0.47, 3.25)

Probability that the odds ratio is in the ROPE, defined to be (0.952,1.05) = 0.072


----------


----------

Case-control analysis using Bayesian techniques

----------

Data: 
            Cases Controls
At risk        13        6
Not at risk    52       31


Prior used on log odds ratio: N(10,1.17)

Posterior mean of the odds ratio: 8.12; Population 2 = 

Posterior median of the odds ratio: 7.19; Population 2 = 

95% credible interval: (2.73, 18.9)

Probability that the odds ratio is in the ROPE, defined to be (0.952,1.05) = 0.0000271


----------


----------

Case-control analysis using Bayesian techniques

----------

Data: 
            Cases Controls
At risk        13        6
Not at risk    52       31


Prior used on log odds ratio: N(0,0.01)

Posterior mean of the odds ratio: 1; Population 2 = 

Posterior median of the odds ratio: 1; Population 2 = 

95% credible interval: (0.981, 1.02)

Probability that the odds ratio is in the ROPE, defined to be (0.952,1.05) = 1


----------

Prior shape parameters were not supplied.
Jeffrey's prior will be used.

----------

2-way table test for independence using Bayesian techniques

----------

Prior used: Dirichlet with shape parameters = 
      column_1 column_2 column_3
row_1 0.5      0.5      0.5     
row_2 0.5      0.5      0.5     
row_3 0.5      0.5      0.5     
row_4 0.5      0.5      0.5     
row_5 0.5      0.5      0.5     


Posterior mean:
      column_1 column_2 column_3
row_1 0.08340  0.04610  0.01860 
row_2 0.05400  0.00294  0.07360 
row_3 0.09130  0.04020  0.01280 
row_4 0.12300  0.01470  0.12500 
row_5 0.06970  0.10900  0.13600 


95% (marginal) credible intervals: 
      column_1         column_2            column_3         
row_1 (0.061, 0.109)   (0.0297, 0.0659)    (0.00879, 0.0321)
row_2 (0.0361, 0.0752) (0.000212, 0.00915) (0.0526, 0.0978) 
row_3 (0.0678, 0.118)  (0.025, 0.0589)     (0.00494, 0.0242)
row_4 (0.0957, 0.152)  (0.00618, 0.0268)   (0.0974, 0.155)  
row_5 (0.0492, 0.0933) (0.0834, 0.137)     (0.108, 0.167)   


Probability that p_ij < p_(i.) x p_(.j):
      column_1 column_2 column_3
row_1 0.002650 0.018300 1.000000
row_2 0.553000 1.000000 0.000241
row_3 0.000000 0.072400 1.000000
row_4 0.096700 1.000000 0.001450
row_5 1.000000 0.000000 0.016200


Probability of direction:
      column_1 column_2 column_3
row_1 0.997    0.982    1.000   
row_2 0.553    1.000    1.000   
row_3 1.000    0.928    1.000   
row_4 0.903    1.000    0.999   
row_5 1.000    1.000    0.984   


Probability that all odds ratios (unrestricted vs. independence) are in the ROPE, defined to be (0.889,1.12) = 0

The marginal probabilities that each odds ratio is in the ROPE:
      column_1 column_2 column_3
row_1 0.03420  0.06150  0.00000 
row_2 0.58100  0.00000  0.00362 
row_3 0.00145  0.17000  0.00000 
row_4 0.47500  0.00000  0.03160 
row_5 0.00000  0.00000  0.18200 


Bayes factor in favor of dependence: 478000000000000000000;
      =>Level of evidence: Decisive


----------

Prior shape parameters were not supplied.
Jeffrey's prior will be used.

----------

2-way table test for independence using Bayesian techniques

----------

Prior used: Dirichlet with shape parameters = 
      column_1 column_2 column_3
row_1 0.5      0.5      0.5     
row_2 0.5      0.5      0.5     
row_3 0.5      0.5      0.5     
row_4 0.5      0.5      0.5     
row_5 0.5      0.5      0.5     


Posterior mean:
      column_1 column_2 column_3
row_1 0.0621   0.0305   0.0542  
row_2 0.0562   0.0286   0.0483  
row_3 0.0601   0.0305   0.0522  
row_4 0.1110   0.0562   0.0956  
row_5 0.1330   0.0660   0.1150  


95% (marginal) credible intervals: 
      column_1         column_2         column_3        
row_1 (0.0428, 0.0846) (0.0174, 0.0472) (0.0362, 0.0755)
row_2 (0.0379, 0.0778) (0.0159, 0.0447) (0.0314, 0.0685)
row_3 (0.0411, 0.0823) (0.0174, 0.0472) (0.0346, 0.0732)
row_4 (0.0855, 0.14)   (0.0379, 0.0778) (0.0716, 0.123) 
row_5 (0.105, 0.164)   (0.0461, 0.0892) (0.089, 0.144)  


Probability that p_ij < p_(i.) x p_(.j):
      column_1 column_2 column_3
row_1 0.509    0.546    0.473   
row_2 0.502    0.502    0.524   
row_3 0.522    0.490    0.508   
row_4 0.490    0.487    0.531   
row_5 0.497    0.529    0.487   


Probability of direction:
      column_1 column_2 column_3
row_1 0.509    0.546    0.527   
row_2 0.502    0.502    0.524   
row_3 0.522    0.510    0.508   
row_4 0.510    0.513    0.531   
row_5 0.503    0.529    0.513   


Probability that all odds ratios (unrestricted vs. independence) are in the ROPE, defined to be (0.889,1.12) = 0.00509

The marginal probabilities that each odds ratio is in the ROPE:
      column_1 column_2 column_3
row_1 0.625    0.417    0.575   
row_2 0.599    0.400    0.547   
row_3 0.619    0.411    0.565   
row_4 0.774    0.560    0.722   
row_5 0.819    0.604    0.772   


Bayes factor in favor of dependence: 0.000000000251;
      =>Level of evidence: Decisive


----------

Prior shape parameters were not supplied.
A uniform prior will be used.

----------

2-way table test for independence using Bayesian techniques

----------

Prior used: Dirichlet with shape parameters = 
      column_1 column_2 column_3
row_1 1        1        1       
row_2 1        1        1       
row_3 1        1        1       
row_4 1        1        1       
row_5 1        1        1       


Posterior mean:
      column_1 column_2 column_3
row_1 0.08320  0.04640  0.01930 
row_2 0.05420  0.00387  0.07350 
row_3 0.09090  0.04060  0.01350 
row_4 0.12200  0.01550  0.12400 
row_5 0.06960  0.10800  0.13500 


95% (marginal) credible intervals: 
      column_1         column_2          column_3         
row_1 (0.061, 0.108)   (0.03, 0.0661)    (0.00933, 0.0329)
row_2 (0.0364, 0.0752) (0.00047, 0.0108) (0.0526, 0.0975) 
row_3 (0.0677, 0.117)  (0.0254, 0.0592)  (0.00547, 0.0251)
row_4 (0.0951, 0.151)  (0.00672, 0.0278) (0.0968, 0.153)  
row_5 (0.0493, 0.0931) (0.083, 0.136)    (0.107, 0.166)   


Probability that p_ij < p_(i.) x p_(.j):
      column_1 column_2 column_3
row_1 0.004140 0.016800 1.000000
row_2 0.556000 1.000000 0.000244
row_3 0.000000 0.075300 1.000000
row_4 0.099900 1.000000 0.001220
row_5 1.000000 0.000000 0.017300


Probability of direction:
      column_1 column_2 column_3
row_1 0.996    0.983    1.000   
row_2 0.556    1.000    1.000   
row_3 1.000    0.925    1.000   
row_4 0.900    1.000    0.999   
row_5 1.000    1.000    0.983   


Probability that all odds ratios (unrestricted vs. independence) are in the ROPE, defined to be (0.889,1.12) = 0

The marginal probabilities that each odds ratio is in the ROPE:
      column_1 column_2 column_3
row_1 0.04000  0.05680  0.00000 
row_2 0.58400  0.00000  0.00487 
row_3 0.00122  0.17800  0.00000 
row_4 0.49500  0.00000  0.02950 
row_5 0.00000  0.00000  0.19700 


Bayes factor in favor of dependence: 2330000000000000063086660;
      =>Level of evidence: Decisive


----------


----------

2-way table test for independence using Bayesian techniques

----------

Prior used: Dirichlet with shape parameters = 
      column_1 column_2 column_3
row_1 2        2        2       
row_2 2        2        2       
row_3 2        2        2       
row_4 2        2        2       
row_5 2        2        2       


Posterior mean:
      column_1 column_2 column_3
row_1 0.08270  0.04700  0.02070 
row_2 0.05450  0.00564  0.07330 
row_3 0.09020  0.04140  0.01500 
row_4 0.12000  0.01690  0.12200 
row_5 0.06950  0.10700  0.13300 


95% (marginal) credible intervals: 
      column_1         column_2          column_3        
row_1 (0.0609, 0.108)  (0.0307, 0.0665)  (0.0104, 0.0344)
row_2 (0.0369, 0.0753) (0.00117, 0.0135) (0.0527, 0.0969)
row_3 (0.0674, 0.116)  (0.0261, 0.0598)  (0.00653, 0.027)
row_4 (0.0941, 0.149)  (0.00778, 0.0295) (0.0958, 0.151) 
row_5 (0.0495, 0.0926) (0.0823, 0.135)   (0.106, 0.164)  


Probability that p_ij < p_(i.) x p_(.j):
      column_1 column_2 column_3
row_1 0.003670 0.020300 1.000000
row_2 0.569000 1.000000 0.000431
row_3 0.000000 0.079200 1.000000
row_4 0.101000 1.000000 0.001290
row_5 1.000000 0.000000 0.016400


Probability of direction:
      column_1 column_2 column_3
row_1 0.996    0.980    1.000   
row_2 0.569    1.000    1.000   
row_3 1.000    0.921    1.000   
row_4 0.899    1.000    0.999   
row_5 1.000    1.000    0.984   


Probability that all odds ratios (unrestricted vs. independence) are in the ROPE, defined to be (0.889,1.12) = 0

The marginal probabilities that each odds ratio is in the ROPE:
      column_1 column_2 column_3
row_1 0.044400 0.068600 0.000000
row_2 0.594000 0.000000 0.004100
row_3 0.001510 0.190000 0.000000
row_4 0.496000 0.000000 0.032800
row_5 0.000000 0.000431 0.208000


Bayes factor in favor of dependence: 91399999999999997904808;
      =>Level of evidence: Decisive


----------


----------

2-way table test for independence using Bayesian techniques

----------

Prior used: Dirichlet with shape parameters = 
      column_1 column_2 column_3
row_1  1        6       11      
row_2  2        7       12      
row_3  3        8       13      
row_4  4        9       14      
row_5  5       10       15      


Posterior mean:
      column_1 column_2 column_3
row_1 0.0691   0.0466   0.0322  
row_2 0.0466   0.0129   0.0788  
row_3 0.0788   0.0450   0.0305  
row_4 0.1060   0.0257   0.1240  
row_5 0.0643   0.1050   0.1350  


95% (marginal) credible intervals: 
      column_1         column_2          column_3        
row_1 (0.0506, 0.0903) (0.0315, 0.0645)  (0.0198, 0.0474)
row_2 (0.0315, 0.0645) (0.00558, 0.0231) (0.0589, 0.101) 
row_3 (0.0589, 0.101)  (0.0302, 0.0626)  (0.0185, 0.0454)
row_4 (0.0832, 0.131)  (0.0148, 0.0395)  (0.0991, 0.151) 
row_5 (0.0464, 0.0849) (0.0817, 0.13)    (0.109, 0.163)  


Probability that p_ij < p_(i.) x p_(.j):
      column_1 column_2 column_3
row_1 0.013400 0.028600 1.000000
row_2 0.728000 1.000000 0.000692
row_3 0.000755 0.082900 1.000000
row_4 0.063500 1.000000 0.006600
row_5 1.000000 0.000000 0.068400


Probability of direction:
      column_1 column_2 column_3
row_1 0.987    0.971    1.000   
row_2 0.728    1.000    0.999   
row_3 0.999    0.917    1.000   
row_4 0.936    1.000    0.993   
row_5 1.000    1.000    0.932   


Probability that all odds ratios (unrestricted vs. independence) are in the ROPE, defined to be (0.889,1.12) = 0

The marginal probabilities that each odds ratio is in the ROPE:
      column_1  column_2  column_3 
row_1 0.1030000 0.1080000 0.0006920
row_2 0.5190000 0.0005660 0.0064200
row_3 0.0141000 0.2280000 0.0000629
row_4 0.3870000 0.0000000 0.1230000
row_5 0.0000629 0.0010100 0.4850000


Bayes factor in favor of dependence: 98400000000000000;
      =>Level of evidence: Decisive


----------


----------

2-way table test for independence using Bayesian techniques

----------

Prior used: Dirichlet with shape parameters = 
      column_1 column_2 column_3
row_1 2        2        2       
row_2 2        2        2       
row_3 2        2        2       
row_4 2        2        2       
row_5 2        2        2       


Posterior mean:
      column_1 column_2 column_3
row_1 0.08270  0.04700  0.02070 
row_2 0.05450  0.00564  0.07330 
row_3 0.09020  0.04140  0.01500 
row_4 0.12000  0.01690  0.12200 
row_5 0.06950  0.10700  0.13300 


95% (marginal) credible intervals: 
      column_1         column_2          column_3        
row_1 (0.0609, 0.108)  (0.0307, 0.0665)  (0.0104, 0.0344)
row_2 (0.0369, 0.0753) (0.00117, 0.0135) (0.0527, 0.0969)
row_3 (0.0674, 0.116)  (0.0261, 0.0598)  (0.00653, 0.027)
row_4 (0.0941, 0.149)  (0.00778, 0.0295) (0.0958, 0.151) 
row_5 (0.0495, 0.0926) (0.0823, 0.135)   (0.106, 0.164)  


Probability that p_ij < p_(i.) x p_(.j):
      column_1 column_2 column_3
row_1 0.003670 0.020300 1.000000
row_2 0.569000 1.000000 0.000431
row_3 0.000000 0.079200 1.000000
row_4 0.101000 1.000000 0.001290
row_5 1.000000 0.000000 0.016400


Probability of direction:
      column_1 column_2 column_3
row_1 0.996    0.980    1.000   
row_2 0.569    1.000    1.000   
row_3 1.000    0.921    1.000   
row_4 0.899    1.000    0.999   
row_5 1.000    1.000    0.984   


Probability that all odds ratios (unrestricted vs. independence) are in the ROPE, defined to be (0.889,1.12) = 0

The marginal probabilities that each odds ratio is in the ROPE:
      column_1 column_2 column_3
row_1 0.044400 0.068600 0.000000
row_2 0.594000 0.000000 0.004100
row_3 0.001510 0.190000 0.000000
row_4 0.496000 0.000000 0.032800
row_5 0.000000 0.000431 0.208000


Bayes factor in favor of dependence: 91399999999999997904808;
      =>Level of evidence: Decisive


----------

Prior shape parameters were not supplied.
Jeffrey's prior will be used.

----------

2-way table test for independence using Bayesian techniques

----------

Prior used: Dirichlet with shape parameters = 
      column_1 column_2 column_3
row_1 0.5      0.5      0.5     
row_2 0.5      0.5      0.5     
row_3 0.5      0.5      0.5     
row_4 0.5      0.5      0.5     
row_5 0.5      0.5      0.5     


Posterior mean:
      column_1 column_2 column_3
row_1 0.5630   0.3110   0.1260  
row_2 0.4140   0.0226   0.5640  
row_3 0.6330   0.2790   0.0884  
row_4 0.4680   0.0562   0.4760  
row_5 0.2210   0.3460   0.4330  


95% (marginal) credible intervals: 
      column_1       column_2          column_3       
row_1 (0.451, 0.672) (0.213, 0.419)    (0.0615, 0.209)
row_2 (0.299, 0.533) (0.00165, 0.0691) (0.444, 0.68)  
row_3 (0.52, 0.738)  (0.183, 0.386)    (0.0353, 0.163)
row_4 (0.384, 0.553) (0.0239, 0.101)   (0.392, 0.56)  
row_5 (0.161, 0.288) (0.274, 0.421)    (0.357, 0.51)  


Probability that p_ij < p_(i.) x p_(.j):
      column_1 column_2 column_3
row_1 0.002980 0.013500 1.000000
row_2 0.554000 1.000000 0.000106
row_3 0.000000 0.069300 1.000000
row_4 0.097400 1.000000 0.000532
row_5 1.000000 0.000000 0.016600


Probability of direction:
      column_1 column_2 column_3
row_1 0.997    0.986    1.000   
row_2 0.554    1.000    1.000   
row_3 1.000    0.931    1.000   
row_4 0.903    1.000    0.999   
row_5 1.000    1.000    0.983   


Probability that all odds ratios (unrestricted vs. independence) are in the ROPE, defined to be (0.889,1.12) = 0

The marginal probabilities that each odds ratio is in the ROPE:
      column_1 column_2 column_3
row_1 0.012600 0.042800 0.000000
row_2 0.392000 0.000000 0.000638
row_3 0.000319 0.139000 0.000000
row_4 0.282000 0.000000 0.009680
row_5 0.000000 0.000000 0.105000


Bayes factor in favor of dependence: 4720000000000000000000;
      =>Level of evidence: Decisive


----------

Prior shape parameters were not supplied.
Jeffrey's prior will be used.

----------

2-way table test for independence using Bayesian techniques

----------

Prior used: Dirichlet with shape parameters = 
      column_1 column_2 column_3
row_1 0.5      0.5      0.5     
row_2 0.5      0.5      0.5     
row_3 0.5      0.5      0.5     
row_4 0.5      0.5      0.5     
row_5 0.5      0.5      0.5     


Posterior mean:
      column_1 column_2 column_3
row_1 0.423    0.208    0.369   
row_2 0.422    0.215    0.363   
row_3 0.421    0.214    0.366   
row_4 0.423    0.213    0.363   
row_5 0.423    0.210    0.367   


95% (marginal) credible intervals: 
      column_1       column_2       column_3      
row_1 (0.314, 0.536) (0.124, 0.307) (0.264, 0.481)
row_2 (0.308, 0.541) (0.126, 0.32)  (0.253, 0.48) 
row_3 (0.31, 0.535)  (0.128, 0.314) (0.259, 0.479)
row_4 (0.341, 0.508) (0.148, 0.287) (0.284, 0.446)
row_5 (0.348, 0.5)   (0.151, 0.276) (0.294, 0.443)


Probability that p_ij < p_(i.) x p_(.j):
      column_1 column_2 column_3
row_1 0.502    0.556    0.474   
row_2 0.509    0.491    0.531   
row_3 0.517    0.513    0.501   
row_4 0.490    0.478    0.534   
row_5 0.493    0.526    0.497   


Probability of direction:
      column_1 column_2 column_3
row_1 0.502    0.556    0.526   
row_2 0.509    0.509    0.531   
row_3 0.517    0.513    0.501   
row_4 0.510    0.522    0.534   
row_5 0.507    0.526    0.503   


Probability that all odds ratios (unrestricted vs. independence) are in the ROPE, defined to be (0.889,1.12) = 0.000253

The marginal probabilities that each odds ratio is in the ROPE:
      column_1 column_2 column_3
row_1 0.427    0.346    0.398   
row_2 0.382    0.328    0.375   
row_3 0.406    0.336    0.393   
row_4 0.560    0.503    0.542   
row_5 0.625    0.537    0.625   


Bayes factor in favor of dependence: 0.00000000247;
      =>Level of evidence: Decisive


----------

Prior shape parameters were not supplied.
A uniform prior will be used.

----------

2-way table test for independence using Bayesian techniques

----------

Prior used: Dirichlet with shape parameters = 
      column_1 column_2 column_3
row_1 1        1        1       
row_2 1        1        1       
row_3 1        1        1       
row_4 1        1        1       
row_5 1        1        1       


Posterior mean:
      column_1 column_2 column_3
row_1 0.5580   0.3120   0.1300  
row_2 0.4120   0.0294   0.5590  
row_3 0.6270   0.2800   0.0933  
row_4 0.4670   0.0593   0.4740  
row_5 0.2220   0.3460   0.4320  


95% (marginal) credible intervals: 
      column_1       column_2          column_3       
row_1 (0.447, 0.667) (0.214, 0.419)    (0.0649, 0.213)
row_2 (0.298, 0.53)  (0.00364, 0.0804) (0.44, 0.674)  
row_3 (0.515, 0.732) (0.185, 0.386)    (0.0389, 0.168)
row_4 (0.383, 0.551) (0.0261, 0.105)   (0.391, 0.558) 
row_5 (0.162, 0.289) (0.275, 0.42)     (0.357, 0.509) 


Probability that p_ij < p_(i.) x p_(.j):
      column_1 column_2 column_3
row_1 0.00383  0.01600  1.00000 
row_2 0.55400  1.00000  0.00000 
row_3 0.00000  0.07340  1.00000 
row_4 0.09920  1.00000  0.00138 
row_5 1.00000  0.00000  0.01780 


Probability of direction:
      column_1 column_2 column_3
row_1 0.996    0.984    1.000   
row_2 0.554    1.000    1.000   
row_3 1.000    0.927    1.000   
row_4 0.901    1.000    0.999   
row_5 1.000    1.000    0.982   


Probability that all odds ratios (unrestricted vs. independence) are in the ROPE, defined to be (0.889,1.12) = 0

The marginal probabilities that each odds ratio is in the ROPE:
      column_1 column_2 column_3
row_1 0.016700 0.042500 0.000000
row_2 0.387000 0.000000 0.002230
row_3 0.000319 0.142000 0.000000
row_4 0.279000 0.000000 0.013100
row_5 0.000000 0.000000 0.106000


Bayes factor in favor of dependence: 402000000000000012506222;
      =>Level of evidence: Decisive


----------


----------

2-way table test for independence using Bayesian techniques

----------

Prior used: Dirichlet with shape parameters = 
      column_1 column_2 column_3
row_1 2        2        2       
row_2 2        2        2       
row_3 2        2        2       
row_4 2        2        2       
row_5 2        2        2       


Posterior mean:
      column_1 column_2 column_3
row_1 0.5500   0.3120   0.1380  
row_2 0.4080   0.0423   0.5490  
row_3 0.6150   0.2820   0.1030  
row_4 0.4640   0.0652   0.4710  
row_5 0.2240   0.3450   0.4300  


95% (marginal) credible intervals: 
      column_1       column_2          column_3       
row_1 (0.441, 0.657) (0.216, 0.418)    (0.0716, 0.22) 
row_2 (0.298, 0.524) (0.00893, 0.0994) (0.433, 0.663) 
row_3 (0.506, 0.72)  (0.188, 0.386)    (0.0459, 0.178)
row_4 (0.381, 0.547) (0.0305, 0.112)   (0.389, 0.554) 
row_5 (0.164, 0.291) (0.275, 0.419)    (0.356, 0.506) 


Probability that p_ij < p_(i.) x p_(.j):
      column_1 column_2 column_3
row_1 0.004670 0.014900 1.000000
row_2 0.550000 1.000000 0.000539
row_3 0.000000 0.074200 1.000000
row_4 0.089300 1.000000 0.001440
row_5 1.000000 0.000000 0.017900


Probability of direction:
      column_1 column_2 column_3
row_1 0.995    0.985    1.000   
row_2 0.550    1.000    0.999   
row_3 1.000    0.926    1.000   
row_4 0.911    1.000    0.999   
row_5 1.000    1.000    0.982   


Probability that all odds ratios (unrestricted vs. independence) are in the ROPE, defined to be (0.889,1.12) = 0

The marginal probabilities that each odds ratio is in the ROPE:
      column_1 column_2 column_3
row_1 0.018600 0.047800 0.000000
row_2 0.394000 0.000000 0.002610
row_3 0.000449 0.145000 0.000000
row_4 0.281000 0.000000 0.013500
row_5 0.000000 0.000000 0.114000


Bayes factor in favor of dependence: 75899999999999992666228;
      =>Level of evidence: Decisive


----------


----------

2-way table test for independence using Bayesian techniques

----------

Prior used: Dirichlet with shape parameters = 
      column_1 column_2 column_3
row_1  1        6       11      
row_2  2        7       12      
row_3  3        8       13      
row_4  4        9       14      
row_5  5       10       15      


Posterior mean:
      column_1 column_2 column_3
row_1 0.467    0.315    0.217   
row_2 0.337    0.093    0.570   
row_3 0.510    0.292    0.198   
row_4 0.415    0.101    0.484   
row_5 0.212    0.344    0.444   


95% (marginal) credible intervals: 
      column_1       column_2        column_3      
row_1 (0.367, 0.569) (0.225, 0.413)  (0.14, 0.307) 
row_2 (0.242, 0.44)  (0.0415, 0.162) (0.464, 0.672)
row_3 (0.411, 0.609) (0.206, 0.386)  (0.125, 0.283)
row_4 (0.34, 0.492)  (0.059, 0.152)  (0.407, 0.562)
row_5 (0.157, 0.272) (0.278, 0.413)  (0.374, 0.516)


Probability that p_ij < p_(i.) x p_(.j):
      column_1 column_2 column_3
row_1 0.010700 0.028100 1.000000
row_2 0.704000 1.000000 0.000862
row_3 0.000503 0.094400 1.000000
row_4 0.051300 1.000000 0.006400
row_5 1.000000 0.000000 0.072100


Probability of direction:
      column_1 column_2 column_3
row_1 0.989    0.972    1.000   
row_2 0.704    1.000    0.999   
row_3 0.999    0.906    1.000   
row_4 0.949    1.000    0.994   
row_5 1.000    1.000    0.928   


Probability that all odds ratios (unrestricted vs. independence) are in the ROPE, defined to be (0.889,1.12) = 0

The marginal probabilities that each odds ratio is in the ROPE:
      column_1 column_2 column_3
row_1 0.047200 0.083400 0.000216
row_2 0.371000 0.000647 0.002660
row_3 0.004170 0.192000 0.000000
row_4 0.218000 0.000000 0.056100
row_5 0.000000 0.000575 0.312000


Bayes factor in favor of dependence: 123000000000000000;
      =>Level of evidence: Decisive


----------


----------

2-way table test for independence using Bayesian techniques

----------

Prior used: Dirichlet with shape parameters = 
      column_1 column_2 column_3
row_1 2        2        2       
row_2 2        2        2       
row_3 2        2        2       
row_4 2        2        2       
row_5 2        2        2       


Posterior mean:
      column_1 column_2 column_3
row_1 0.5500   0.3120   0.1380  
row_2 0.4080   0.0423   0.5490  
row_3 0.6150   0.2820   0.1030  
row_4 0.4640   0.0652   0.4710  
row_5 0.2240   0.3450   0.4300  


95% (marginal) credible intervals: 
      column_1       column_2          column_3       
row_1 (0.441, 0.657) (0.216, 0.418)    (0.0716, 0.22) 
row_2 (0.298, 0.524) (0.00893, 0.0994) (0.433, 0.663) 
row_3 (0.506, 0.72)  (0.188, 0.386)    (0.0459, 0.178)
row_4 (0.381, 0.547) (0.0305, 0.112)   (0.389, 0.554) 
row_5 (0.164, 0.291) (0.275, 0.419)    (0.356, 0.506) 


Probability that p_ij < p_(i.) x p_(.j):
      column_1 column_2 column_3
row_1 0.004670 0.014900 1.000000
row_2 0.550000 1.000000 0.000539
row_3 0.000000 0.074200 1.000000
row_4 0.089300 1.000000 0.001440
row_5 1.000000 0.000000 0.017900


Probability of direction:
      column_1 column_2 column_3
row_1 0.995    0.985    1.000   
row_2 0.550    1.000    0.999   
row_3 1.000    0.926    1.000   
row_4 0.911    1.000    0.999   
row_5 1.000    1.000    0.982   


Probability that all odds ratios (unrestricted vs. independence) are in the ROPE, defined to be (0.889,1.12) = 0

The marginal probabilities that each odds ratio is in the ROPE:
      column_1 column_2 column_3
row_1 0.018600 0.047800 0.000000
row_2 0.394000 0.000000 0.002610
row_3 0.000449 0.145000 0.000000
row_4 0.281000 0.000000 0.013500
row_5 0.000000 0.000000 0.114000


Bayes factor in favor of dependence: 75899999999999992666228;
      =>Level of evidence: Decisive


----------

Prior shape parameters were not supplied.
Jeffrey's prior will be used.

----------

2-way table test for independence using Bayesian techniques

----------

Prior used: Dirichlet with shape parameters = 
      column_1 column_2 column_3
row_1 0.5      0.5      0.5     
row_2 0.5      0.5      0.5     
row_3 0.5      0.5      0.5     
row_4 0.5      0.5      0.5     
row_5 0.5      0.5      0.5     


Posterior mean:
      column_1 column_2 column_3
row_1 0.1980   0.2170   0.0509  
row_2 0.1280   0.0138   0.2010  
row_3 0.2170   0.1890   0.0349  
row_4 0.2910   0.0691   0.3400  
row_5 0.1660   0.5120   0.3730  


95% (marginal) credible intervals: 
      column_1       column_2          column_3        
row_1 (0.148, 0.254) (0.145, 0.298)    (0.0243, 0.0867)
row_2 (0.087, 0.176) (0.00101, 0.0426) (0.147, 0.261)  
row_3 (0.164, 0.274) (0.121, 0.267)    (0.0136, 0.0654)
row_4 (0.233, 0.354) (0.0296, 0.124)   (0.274, 0.41)   
row_5 (0.119, 0.218) (0.418, 0.605)    (0.305, 0.443)  


Probability that p_ij < p_(i.) x p_(.j):
      column_1  column_2  column_3 
row_1 0.0029900 0.0142000 1.0000000
row_2 0.5680000 1.0000000 0.0003660
row_3 0.0000609 0.0781000 1.0000000
row_4 0.1010000 1.0000000 0.0012200
row_5 1.0000000 0.0000000 0.0140000


Probability of direction:
      column_1 column_2 column_3
row_1 0.997    0.986    1.000   
row_2 0.568    1.000    1.000   
row_3 1.000    0.922    1.000   
row_4 0.899    1.000    0.999   
row_5 1.000    1.000    0.986   


Probability that all odds ratios (unrestricted vs. independence) are in the ROPE, defined to be (0.889,1.12) = 0

The marginal probabilities that each odds ratio is in the ROPE:
      column_1  column_2  column_3 
row_1 0.0296000 0.0443000 0.0000000
row_2 0.5530000 0.0000000 0.0023200
row_3 0.0004880 0.1500000 0.0000000
row_4 0.3940000 0.0000000 0.0171000
row_5 0.0000000 0.0000609 0.1130000


Bayes factor in favor of dependence: 2450000000000000000000;
      =>Level of evidence: Decisive


----------

Prior shape parameters were not supplied.
Jeffrey's prior will be used.

----------

2-way table test for independence using Bayesian techniques

----------

Prior used: Dirichlet with shape parameters = 
      column_1 column_2 column_3
row_1 0.5      0.5      0.5     
row_2 0.5      0.5      0.5     
row_3 0.5      0.5      0.5     
row_4 0.5      0.5      0.5     
row_5 0.5      0.5      0.5     


Posterior mean:
      column_1 column_2 column_3
row_1 0.147    0.144    0.148   
row_2 0.133    0.135    0.132   
row_3 0.142    0.144    0.143   
row_4 0.263    0.265    0.261   
row_5 0.315    0.312    0.315   


95% (marginal) credible intervals: 
      column_1        column_2        column_3       
row_1 (0.103, 0.197)  (0.0847, 0.216) (0.101, 0.203) 
row_2 (0.0909, 0.181) (0.0774, 0.205) (0.0874, 0.184)
row_3 (0.0988, 0.192) (0.0847, 0.216) (0.0964, 0.197)
row_4 (0.207, 0.324)  (0.186, 0.352)  (0.201, 0.327) 
row_5 (0.254, 0.378)  (0.228, 0.402)  (0.251, 0.384) 


Probability that p_ij < p_(i.) x p_(.j):
      column_1 column_2 column_3
row_1 0.509    0.555    0.472   
row_2 0.504    0.486    0.537   
row_3 0.509    0.492    0.511   
row_4 0.496    0.493    0.534   
row_5 0.496    0.542    0.474   


Probability of direction:
      column_1 column_2 column_3
row_1 0.509    0.555    0.528   
row_2 0.504    0.514    0.537   
row_3 0.509    0.508    0.511   
row_4 0.504    0.507    0.534   
row_5 0.504    0.542    0.526   


Probability that all odds ratios (unrestricted vs. independence) are in the ROPE, defined to be (0.889,1.12) = 0.00056

The marginal probabilities that each odds ratio is in the ROPE:
      column_1 column_2 column_3
row_1 0.556    0.352    0.497   
row_2 0.561    0.349    0.507   
row_3 0.576    0.362    0.522   
row_4 0.675    0.448    0.621   
row_5 0.717    0.486    0.657   


Bayes factor in favor of dependence: 0.0000000013;
      =>Level of evidence: Decisive


----------

Prior shape parameters were not supplied.
A uniform prior will be used.

----------

2-way table test for independence using Bayesian techniques

----------

Prior used: Dirichlet with shape parameters = 
      column_1 column_2 column_3
row_1 1        1        1       
row_2 1        1        1       
row_3 1        1        1       
row_4 1        1        1       
row_5 1        1        1       


Posterior mean:
      column_1 column_2 column_3
row_1 0.1980   0.2160   0.0529  
row_2 0.1290   0.0180   0.2010  
row_3 0.2170   0.1890   0.0370  
row_4 0.2900   0.0721   0.3390  
row_5 0.1660   0.5050   0.3700  


95% (marginal) credible intervals: 
      column_1        column_2          column_3        
row_1 (0.148, 0.254)  (0.145, 0.297)    (0.0258, 0.0889)
row_2 (0.0879, 0.177) (0.00221, 0.0496) (0.147, 0.261)  
row_3 (0.164, 0.274)  (0.122, 0.267)    (0.0151, 0.0682)
row_4 (0.232, 0.352)  (0.0319, 0.127)   (0.273, 0.407)  
row_5 (0.12, 0.218)   (0.412, 0.597)    (0.303, 0.44)   


Probability that p_ij < p_(i.) x p_(.j):
      column_1 column_2 column_3
row_1 0.00323  0.01390  1.00000 
row_2 0.57100  1.00000  0.00000 
row_3 0.00000  0.07760  1.00000 
row_4 0.11100  1.00000  0.00231 
row_5 1.00000  0.00000  0.01390 


Probability of direction:
      column_1 column_2 column_3
row_1 0.997    0.986    1.000   
row_2 0.571    1.000    1.000   
row_3 1.000    0.922    1.000   
row_4 0.889    1.000    0.998   
row_5 1.000    1.000    0.986   


Probability that all odds ratios (unrestricted vs. independence) are in the ROPE, defined to be (0.889,1.12) = 0

The marginal probabilities that each odds ratio is in the ROPE:
      column_1 column_2 column_3
row_1 0.031400 0.046000 0.000000
row_2 0.554000 0.000000 0.003470
row_3 0.000924 0.152000 0.000000
row_4 0.411000 0.000000 0.015000
row_5 0.000000 0.000000 0.109000


Bayes factor in favor of dependence: 652000000000000008404808;
      =>Level of evidence: Decisive


----------


----------

2-way table test for independence using Bayesian techniques

----------

Prior used: Dirichlet with shape parameters = 
      column_1 column_2 column_3
row_1 2        2        2       
row_2 2        2        2       
row_3 2        2        2       
row_4 2        2        2       
row_5 2        2        2       


Posterior mean:
      column_1 column_2 column_3
row_1 0.1980   0.2160   0.0567  
row_2 0.1310   0.0259   0.2010  
row_3 0.2160   0.1900   0.0412  
row_4 0.2880   0.0776   0.3350  
row_5 0.1670   0.4910   0.3660  


95% (marginal) credible intervals: 
      column_1        column_2          column_3        
row_1 (0.149, 0.253)  (0.146, 0.294)    (0.0288, 0.0932)
row_2 (0.0897, 0.178) (0.00541, 0.0614) (0.148, 0.26)   
row_3 (0.165, 0.273)  (0.124, 0.265)    (0.0181, 0.0733)
row_4 (0.231, 0.349)  (0.0364, 0.132)   (0.271, 0.403)  
row_5 (0.121, 0.218)  (0.401, 0.582)    (0.3, 0.435)    


Probability that p_ij < p_(i.) x p_(.j):
      column_1 column_2 column_3
row_1 0.003880 0.016400 1.000000
row_2 0.593000 1.000000 0.000863
row_3 0.000000 0.087600 1.000000
row_4 0.112000 1.000000 0.001290
row_5 1.000000 0.000000 0.012900


Probability of direction:
      column_1 column_2 column_3
row_1 0.996    0.984    1.000   
row_2 0.593    1.000    0.999   
row_3 1.000    0.912    1.000   
row_4 0.888    1.000    0.999   
row_5 1.000    1.000    0.987   


Probability that all odds ratios (unrestricted vs. independence) are in the ROPE, defined to be (0.889,1.12) = 0

The marginal probabilities that each odds ratio is in the ROPE:
      column_1 column_2 column_3
row_1 0.035600 0.053500 0.000000
row_2 0.562000 0.000000 0.005390
row_3 0.000647 0.156000 0.000000
row_4 0.422000 0.000000 0.019400
row_5 0.000000 0.000000 0.109000


Bayes factor in favor of dependence: 86999999999999993712824;
      =>Level of evidence: Decisive


----------


----------

2-way table test for independence using Bayesian techniques

----------

Prior used: Dirichlet with shape parameters = 
      column_1 column_2 column_3
row_1  1        6       11      
row_2  2        7       12      
row_3  3        8       13      
row_4  4        9       14      
row_5  5       10       15      


Posterior mean:
      column_1 column_2 column_3
row_1 0.1890   0.1990   0.0803  
row_2 0.1280   0.0548   0.1970  
row_3 0.2160   0.1920   0.0763  
row_4 0.2910   0.1100   0.3090  
row_5 0.1760   0.4450   0.3370  


95% (marginal) credible intervals: 
      column_1        column_2         column_3       
row_1 (0.141, 0.243)  (0.138, 0.267)   (0.05, 0.117)  
row_2 (0.0876, 0.174) (0.0241, 0.0969) (0.15, 0.248)  
row_3 (0.165, 0.272)  (0.132, 0.259)   (0.0468, 0.112)
row_4 (0.234, 0.351)  (0.0644, 0.165)  (0.253, 0.368) 
row_5 (0.13, 0.228)   (0.366, 0.526)   (0.28, 0.397)  


Probability that p_ij < p_(i.) x p_(.j):
      column_1 column_2 column_3
row_1 0.012600 0.047200 1.000000
row_2 0.739000 1.000000 0.000770
row_3 0.000257 0.127000 1.000000
row_4 0.064100 1.000000 0.014400
row_5 1.000000 0.000000 0.021400


Probability of direction:
      column_1 column_2 column_3
row_1 0.987    0.953    1.000   
row_2 0.739    1.000    0.999   
row_3 1.000    0.873    1.000   
row_4 0.936    1.000    0.986   
row_5 1.000    1.000    0.979   


Probability that all odds ratios (unrestricted vs. independence) are in the ROPE, defined to be (0.889,1.12) = 0

The marginal probabilities that each odds ratio is in the ROPE:
      column_1 column_2 column_3
row_1 0.094000 0.128000 0.000514
row_2 0.505000 0.002310 0.008350
row_3 0.011400 0.256000 0.000000
row_4 0.342000 0.000000 0.125000
row_5 0.000000 0.000128 0.185000


Bayes factor in favor of dependence: 11600000000000000;
      =>Level of evidence: Decisive


----------


----------

2-way table test for independence using Bayesian techniques

----------

Prior used: Dirichlet with shape parameters = 
      column_1 column_2 column_3
row_1 2        2        2       
row_2 2        2        2       
row_3 2        2        2       
row_4 2        2        2       
row_5 2        2        2       


Posterior mean:
      column_1 column_2 column_3
row_1 0.1980   0.2160   0.0567  
row_2 0.1310   0.0259   0.2010  
row_3 0.2160   0.1900   0.0412  
row_4 0.2880   0.0776   0.3350  
row_5 0.1670   0.4910   0.3660  


95% (marginal) credible intervals: 
      column_1        column_2          column_3        
row_1 (0.149, 0.253)  (0.146, 0.294)    (0.0288, 0.0932)
row_2 (0.0897, 0.178) (0.00541, 0.0614) (0.148, 0.26)   
row_3 (0.165, 0.273)  (0.124, 0.265)    (0.0181, 0.0733)
row_4 (0.231, 0.349)  (0.0364, 0.132)   (0.271, 0.403)  
row_5 (0.121, 0.218)  (0.401, 0.582)    (0.3, 0.435)    


Probability that p_ij < p_(i.) x p_(.j):
      column_1 column_2 column_3
row_1 0.003880 0.016400 1.000000
row_2 0.593000 1.000000 0.000863
row_3 0.000000 0.087600 1.000000
row_4 0.112000 1.000000 0.001290
row_5 1.000000 0.000000 0.012900


Probability of direction:
      column_1 column_2 column_3
row_1 0.996    0.984    1.000   
row_2 0.593    1.000    0.999   
row_3 1.000    0.912    1.000   
row_4 0.888    1.000    0.999   
row_5 1.000    1.000    0.987   


Probability that all odds ratios (unrestricted vs. independence) are in the ROPE, defined to be (0.889,1.12) = 0

The marginal probabilities that each odds ratio is in the ROPE:
      column_1 column_2 column_3
row_1 0.035600 0.053500 0.000000
row_2 0.562000 0.000000 0.005390
row_3 0.000647 0.156000 0.000000
row_4 0.422000 0.000000 0.019400
row_5 0.000000 0.000000 0.109000


Bayes factor in favor of dependence: 86999999999999993712824;
      =>Level of evidence: Decisive


----------

Prior shape parameters were not supplied.
Jeffrey's prior will be used.

----------

2-way table test for independence using Bayesian techniques

----------

Prior used: Dirichlet with shape parameters = 
      column_1 column_2 column_3
row_1 0.5      0.5      0.5     
row_2 0.5      0.5      0.5     
row_3 0.5      0.5      0.5     
row_4 0.5      0.5      0.5     
row_5 0.5      0.5      0.5     


Posterior mean:
      column_1 column_2 column_3
row_1 0.5630   0.3110   0.1260  
row_2 0.4140   0.0226   0.5640  
row_3 0.6330   0.2790   0.0884  
row_4 0.4680   0.0562   0.4760  
row_5 0.2210   0.3460   0.4330  


95% (marginal) credible intervals: 
      column_1       column_2          column_3       
row_1 (0.451, 0.672) (0.213, 0.419)    (0.0615, 0.209)
row_2 (0.299, 0.533) (0.00165, 0.0691) (0.444, 0.68)  
row_3 (0.52, 0.738)  (0.183, 0.386)    (0.0353, 0.163)
row_4 (0.384, 0.553) (0.0239, 0.101)   (0.392, 0.56)  
row_5 (0.161, 0.288) (0.274, 0.421)    (0.357, 0.51)  


Probability that p_ij < p_(i.) x p_(.j):
      column_1 column_2 column_3
row_1 0.002980 0.013500 1.000000
row_2 0.554000 1.000000 0.000106
row_3 0.000000 0.069300 1.000000
row_4 0.097400 1.000000 0.000532
row_5 1.000000 0.000000 0.016600


Probability of direction:
      column_1 column_2 column_3
row_1 0.997    0.986    1.000   
row_2 0.554    1.000    1.000   
row_3 1.000    0.931    1.000   
row_4 0.903    1.000    0.999   
row_5 1.000    1.000    0.983   


Probability that all odds ratios (unrestricted vs. independence) are in the ROPE, defined to be (0.889,1.12) = 0

The marginal probabilities that each odds ratio is in the ROPE:
      column_1 column_2 column_3
row_1 0.012600 0.042800 0.000000
row_2 0.392000 0.000000 0.000638
row_3 0.000319 0.139000 0.000000
row_4 0.282000 0.000000 0.009680
row_5 0.000000 0.000000 0.105000


Bayes factor in favor of dependence: 4720000000000000000000;
      =>Level of evidence: Decisive


----------

Prior shape parameters were not supplied.
Jeffrey's prior will be used.

----------

2-way table test for independence using Bayesian techniques

----------

Prior used: Dirichlet with shape parameters = 
      column_1 column_2 column_3 column_4 column_5
row_1 0.5      0.5      0.5      0.5      0.5     
row_2 0.5      0.5      0.5      0.5      0.5     
row_3 0.5      0.5      0.5      0.5      0.5     


Posterior mean:
      column_1 column_2 column_3 column_4 column_5
row_1 0.5630   0.4140   0.6330   0.4680   0.2210  
row_2 0.3110   0.0226   0.2790   0.0562   0.3460  
row_3 0.1260   0.5640   0.0884   0.4760   0.4330  


95% (marginal) credible intervals: 
      column_1        column_2          column_3        column_4       
row_1 (0.451, 0.672)  (0.299, 0.533)    (0.52, 0.738)   (0.384, 0.553) 
row_2 (0.213, 0.419)  (0.00165, 0.0691) (0.183, 0.386)  (0.0239, 0.101)
row_3 (0.0615, 0.209) (0.444, 0.68)     (0.0353, 0.163) (0.392, 0.56)  
      column_5      
row_1 (0.161, 0.288)
row_2 (0.274, 0.421)
row_3 (0.357, 0.51) 


Probability that p_ij < p_(i.) x p_(.j):
      column_1 column_2 column_3 column_4 column_5
row_1 0.002980 0.554000 0.000000 0.097400 1.000000
row_2 0.013500 1.000000 0.069300 1.000000 0.000000
row_3 1.000000 0.000106 1.000000 0.000532 0.016600


Probability of direction:
      column_1 column_2 column_3 column_4 column_5
row_1 0.997    0.554    1.000    0.903    1.000   
row_2 0.986    1.000    0.931    1.000    1.000   
row_3 1.000    1.000    1.000    0.999    0.983   


Probability that all odds ratios (unrestricted vs. independence) are in the ROPE, defined to be (0.889,1.12) = 0

The marginal probabilities that each odds ratio is in the ROPE:
      column_1 column_2 column_3 column_4 column_5
row_1 0.012600 0.392000 0.000319 0.282000 0.000000
row_2 0.042800 0.000000 0.139000 0.000000 0.000000
row_3 0.000000 0.000638 0.000000 0.009680 0.105000


Bayes factor in favor of dependence: 4720000000000000000000;
      =>Level of evidence: Decisive


----------

Prior shape parameters were not supplied.
Beta(2,2) prior will be used.

----------

Analysis of Kendall's tau using Bayesian techniques

----------

Prior used (phi): Beta(2,2)

Posterior mean (tau): 0.0887

95% credible interval (tau): (0.0329, 0.144)

Probability that tau < 0 = 0.000928

Probability that tau is in the ROPE, defined to be (-0.05,0.05) = 0.0868


----------

Prior shape parameters were not supplied.
Beta(2,2) prior will be used.

----------

Analysis of Kendall's tau using Bayesian techniques

----------

Prior used (phi): Beta(2,2)

Posterior mean (tau): 0.0887

95% credible interval (tau): (0.0329, 0.144)

Probability that tau < 0 = 0.000928

Probability that tau is in the ROPE, defined to be (-0.05,0.05) = 0.0868


----------

Prior shape parameters were not supplied.
Beta(2,2) prior will be used.

----------

Analysis of Kendall's tau using Bayesian techniques

----------

Prior used (phi): Beta(2,2)

Posterior mean (tau): 0.0887

95% credible interval (tau): (0.0329, 0.144)

Probability that tau < 0.04 = 0.0435

Probability that tau is in the ROPE, defined to be (-0.01,0.09) = 0.517


----------

Prior shape parameters were not supplied.
Beta(2,2) prior will be used.

----------

Analysis of Kendall's tau using Bayesian techniques

----------

Prior used (phi): Beta(2,2)

Posterior mean (tau): 0.0887

95% credible interval (tau): (0.0329, 0.144)

Probability that tau < 0.1 = 0.654

Probability that tau is in the ROPE, defined to be (0.05,0.15) = 0.898


----------

Prior shape parameters were not supplied.
Beta(2,2) prior will be used.

----------

Analysis of Kendall's tau using Bayesian techniques

----------

Prior used (phi): Beta(2,2)

Posterior mean (tau): 0.0887

95% credible interval (tau): (0.0329, 0.144)

Probability that tau < 0 = 0.000928

Probability that tau is in the ROPE, defined to be (-0.1,0.1) = 0.654


----------

Prior shape parameters were not supplied.
Beta(2,2) prior will be used.

----------

Analysis of Kendall's tau using Bayesian techniques

----------

Prior used (phi): Beta(2,2)

Posterior mean (tau): 0.0887

95% credible interval (tau): (0.0329, 0.144)

Probability that tau < 0 = 0.000928

Probability that tau is in the ROPE, defined to be (-0.2,0.2) = 1


----------

Prior shape parameters were not supplied.
A uniform prior will be used.

----------

Analysis of Kendall's tau using Bayesian techniques

----------

Prior used (phi): Beta(1,1)

Posterior mean (tau): 0.0888

95% credible interval (tau): (0.033, 0.144)

Probability that tau < 0 = 0.00092

Probability that tau is in the ROPE, defined to be (-0.05,0.05) = 0.0862


----------

Prior shape parameters were not supplied.
Beta(2,3.9) prior will be used.

----------

Analysis of Kendall's tau using Bayesian techniques

----------

Prior used (phi): Beta(2,3.9)

Posterior mean (tau): 0.087

95% credible interval (tau): (0.0313, 0.142)

Probability that tau < 0 = 0.00112

Probability that tau is in the ROPE, defined to be (-0.05,0.05) = 0.0964


----------

Prior shape parameters were not supplied.
Beta(3.9,2) prior will be used.

----------

Analysis of Kendall's tau using Bayesian techniques

----------

Prior used (phi): Beta(3.9,2)

Posterior mean (tau): 0.0901

95% credible interval (tau): (0.0344, 0.146)

Probability that tau < 0 = 0.000778

Probability that tau is in the ROPE, defined to be (-0.05,0.05) = 0.0791


----------


----------

Analysis of Kendall's tau using Bayesian techniques

----------

Prior used (phi): Beta(10,10)

Posterior mean (tau): 0.0876

95% credible interval (tau): (0.0321, 0.143)

Probability that tau < 0 = 0.000993

Probability that tau is in the ROPE, defined to be (-0.05,0.05) = 0.0919


----------


The mu hyperparameter in the normal prior is not specified.  It will be set automatically to 0.


The hyperparameters for the residual variance were not provided. Instead, the prior will put 50% prior probability that R^2 is between 0.1^2 and 0.9^2.


The V hyperparameter in the normal prior is not specified.  It will be set automatically to 4/25Diag(s^2_{X_j})

The g hyperparameter in Zellner's g prior is not specified.  It will be set automatically to n.

Assuming all observations correspond to Bernoulli, i.e., Binomial with one trial.

----------

Values given in terms of odds ratios

----------

Assuming all observations correspond to Bernoulli, i.e., Binomial with one trial.
Assuming all observations correspond to Bernoulli, i.e., Binomial with one trial.
Assuming all observations correspond to Bernoulli, i.e., Binomial with one trial.
Assuming all observations correspond to Bernoulli, i.e., Binomial with one trial.
Assuming all observations correspond to Bernoulli, i.e., Binomial with one trial.
Assuming all observations correspond to Bernoulli, i.e., Binomial with one trial.

The mu hyperparameter in the normal prior is not specified.  It will be set automatically to 0.


The V hyperparameter in the normal prior is not specified.  It will be set automatically to 4/25Diag(s^2_{X_j})
Assuming all observations correspond to Bernoulli, i.e., Binomial with one trial.

The mu hyperparameter in the normal prior is not specified.  It will be set automatically to 0.


The V hyperparameter in the normal prior is not specified.  It will be set automatically to 4/25Diag(s^2_{X_j})
Assuming all observations correspond to Bernoulli, i.e., Binomial with one trial.

The mu hyperparameter in the normal prior is not specified.  It will be set automatically to 0.


The V hyperparameter in the normal prior is not specified.  It will be set automatically to 4/25Diag(s^2_{X_j})
Assuming all observations correspond to Bernoulli, i.e., Binomial with one trial.

The mu hyperparameter in the normal prior is not specified.  It will be set automatically to 0.


The V hyperparameter in the normal prior is not specified.  It will be set automatically to 4/25Diag(s^2_{X_j})
Assuming all observations correspond to Bernoulli, i.e., Binomial with one trial.

The mu hyperparameter in the normal prior is not specified.  It will be set automatically to 0.


The V hyperparameter in the normal prior is not specified.  It will be set automatically to 4/25Diag(s^2_{X_j})
Assuming all observations correspond to Bernoulli, i.e., Binomial with one trial.
Assuming all observations correspond to Bernoulli, i.e., Binomial with one trial.
Bayesian p-values measure GOF via 
Pr(T(y_obs) - T(y_pred) > 0 | y_obs).
Thus values close to 0.5 are ideal.  Be concerned if values are near 0 or 1.
This Bayesian p-value corresponds to the deviance.
Missing other covariate values in 'exemplar_covariates.'  Using medoid observation instead.
Missing other covariate values in 'exemplar_covariates.'  Using medoid observation instead.
Missing other covariate values in 'exemplar_covariates.'  Using medoid observation instead.
Bayesian p-values measure GOF via 
Pr(T(y_obs) - T(y_pred) > 0 | y_obs).
Thus values close to 0.5 are ideal.  Be concerned if values are near 0 or 1.
This Bayesian p-value corresponds to the deviance.
Missing other covariate values in 'exemplar_covariates.'  Using medoid observation instead.

The g hyperparameter in Zellner's g prior is not specified.  It will be set automatically to n.

Assuming all observations correspond to Bernoulli, i.e., Binomial with one trial.

----------

Values given in terms of odds ratios

----------

Assuming all observations correspond to Bernoulli, i.e., Binomial with one trial.
Assuming all observations correspond to Bernoulli, i.e., Binomial with one trial.
Assuming all observations correspond to Bernoulli, i.e., Binomial with one trial.
Assuming all observations correspond to Bernoulli, i.e., Binomial with one trial.
Assuming all observations correspond to Bernoulli, i.e., Binomial with one trial.
Assuming all observations correspond to Bernoulli, i.e., Binomial with one trial.

The mu hyperparameter in the normal prior is not specified.  It will be set automatically to 0.


The V hyperparameter in the normal prior is not specified.  It will be set automatically to 4/25Diag(s^2_{X_j})
Assuming all observations correspond to Bernoulli, i.e., Binomial with one trial.

The mu hyperparameter in the normal prior is not specified.  It will be set automatically to 0.


The V hyperparameter in the normal prior is not specified.  It will be set automatically to 4/25Diag(s^2_{X_j})
Assuming all observations correspond to Bernoulli, i.e., Binomial with one trial.

The mu hyperparameter in the normal prior is not specified.  It will be set automatically to 0.


The V hyperparameter in the normal prior is not specified.  It will be set automatically to 4/25Diag(s^2_{X_j})
Assuming all observations correspond to Bernoulli, i.e., Binomial with one trial.

The mu hyperparameter in the normal prior is not specified.  It will be set automatically to 0.


The V hyperparameter in the normal prior is not specified.  It will be set automatically to 4/25Diag(s^2_{X_j})
Assuming all observations correspond to Bernoulli, i.e., Binomial with one trial.

The mu hyperparameter in the normal prior is not specified.  It will be set automatically to 0.


The V hyperparameter in the normal prior is not specified.  It will be set automatically to 4/25Diag(s^2_{X_j})
Assuming all observations correspond to Bernoulli, i.e., Binomial with one trial.
Assuming all observations correspond to Bernoulli, i.e., Binomial with one trial.

The g hyperparameter in Zellner's g prior is not specified.  It will be set automatically to n.

Assuming all observations correspond to Bernoulli, i.e., Binomial with one trial.

The g hyperparameter in Zellner's g prior is not specified.  It will be set automatically to n.

Assuming all observations correspond to Bernoulli, i.e., Binomial with one trial.
Bayesian p-values measure GOF via 
Pr(T(y_obs) - T(y_pred) > 0 | y_obs).
Thus values close to 0.5 are ideal.  Be concerned if values are near 0 or 1.
This Bayesian p-value corresponds to the deviance.
Missing other covariate values in 'exemplar_covariates.'  Using medoid observation instead.
Missing other covariate values in 'exemplar_covariates.'  Using medoid observation instead.
Missing other covariate values in 'exemplar_covariates.'  Using medoid observation instead.
Bayesian p-values measure GOF via 
Pr(T(y_obs) - T(y_pred) > 0 | y_obs).
Thus values close to 0.5 are ideal.  Be concerned if values are near 0 or 1.
This Bayesian p-value corresponds to the deviance.
Missing other covariate values in 'exemplar_covariates.'  Using medoid observation instead.

The g hyperparameter in Zellner's g prior is not specified.  It will be set automatically to n.

Assuming all observations correspond to Bernoulli, i.e., Binomial with one trial.

----------

Values given in terms of odds ratios

----------

Assuming all observations correspond to Bernoulli, i.e., Binomial with one trial.
Assuming all observations correspond to Bernoulli, i.e., Binomial with one trial.
Assuming all observations correspond to Bernoulli, i.e., Binomial with one trial.
Assuming all observations correspond to Bernoulli, i.e., Binomial with one trial.
Assuming all observations correspond to Bernoulli, i.e., Binomial with one trial.
Assuming all observations correspond to Bernoulli, i.e., Binomial with one trial.

The mu hyperparameter in the normal prior is not specified.  It will be set automatically to 0.


The V hyperparameter in the normal prior is not specified.  It will be set automatically to 4/25Diag(s^2_{X_j})
Assuming all observations correspond to Bernoulli, i.e., Binomial with one trial.

The mu hyperparameter in the normal prior is not specified.  It will be set automatically to 0.


The V hyperparameter in the normal prior is not specified.  It will be set automatically to 4/25Diag(s^2_{X_j})
Assuming all observations correspond to Bernoulli, i.e., Binomial with one trial.

The mu hyperparameter in the normal prior is not specified.  It will be set automatically to 0.


The V hyperparameter in the normal prior is not specified.  It will be set automatically to 4/25Diag(s^2_{X_j})
Assuming all observations correspond to Bernoulli, i.e., Binomial with one trial.

The mu hyperparameter in the normal prior is not specified.  It will be set automatically to 0.


The V hyperparameter in the normal prior is not specified.  It will be set automatically to 4/25Diag(s^2_{X_j})
Assuming all observations correspond to Bernoulli, i.e., Binomial with one trial.

The mu hyperparameter in the normal prior is not specified.  It will be set automatically to 0.


The V hyperparameter in the normal prior is not specified.  It will be set automatically to 4/25Diag(s^2_{X_j})
Assuming all observations correspond to Bernoulli, i.e., Binomial with one trial.
Assuming all observations correspond to Bernoulli, i.e., Binomial with one trial.
Bayesian p-values measure GOF via 
Pr(T(y_obs) - T(y_pred) > 0 | y_obs).
Thus values close to 0.5 are ideal.  Be concerned if values are near 0 or 1.
This Bayesian p-value corresponds to the deviance.
Missing other covariate values in 'exemplar_covariates.'  Using medoid observation instead.
Missing other covariate values in 'exemplar_covariates.'  Using medoid observation instead.
Missing other covariate values in 'exemplar_covariates.'  Using medoid observation instead.
Bayesian p-values measure GOF via 
Pr(T(y_obs) - T(y_pred) > 0 | y_obs).
Thus values close to 0.5 are ideal.  Be concerned if values are near 0 or 1.
This Bayesian p-value corresponds to the deviance.
Missing other covariate values in 'exemplar_covariates.'  Using medoid observation instead.

The g hyperparameter in Zellner's g prior is not specified.  It will be set automatically to n.


The g hyperparameter in Zellner's g prior is not specified.  It will be set automatically to n.


The g hyperparameter in Zellner's g prior is not specified.  It will be set automatically to n.


The g hyperparameter in Zellner's g prior is not specified.  It will be set automatically to n.


The g hyperparameter in Zellner's g prior is not specified.  It will be set automatically to n.


The g hyperparameter in Zellner's g prior is not specified.  It will be set automatically to n.


The g hyperparameter in Zellner's g prior is not specified.  It will be set automatically to n.


----------

Values given in terms of rate ratios

----------


The mu hyperparameter in the normal prior is not specified.  It will be set automatically to 0.


The V hyperparameter in the normal prior is not specified.  It will be set automatically to 4/25Diag(s^2_{X_j})

The mu hyperparameter in the normal prior is not specified.  It will be set automatically to 0.


The V hyperparameter in the normal prior is not specified.  It will be set automatically to 4/25Diag(s^2_{X_j})

The mu hyperparameter in the normal prior is not specified.  It will be set automatically to 0.


The V hyperparameter in the normal prior is not specified.  It will be set automatically to 4/25Diag(s^2_{X_j})

The mu hyperparameter in the normal prior is not specified.  It will be set automatically to 0.


The V hyperparameter in the normal prior is not specified.  It will be set automatically to 4/25Diag(s^2_{X_j})

The mu hyperparameter in the normal prior is not specified.  It will be set automatically to 0.


The V hyperparameter in the normal prior is not specified.  It will be set automatically to 4/25Diag(s^2_{X_j})
Bayesian p-values measure GOF via 
Pr(T(y_obs) - T(y_pred) > 0 | y_obs).
Thus values close to 0.5 are ideal.  Be concerned if values are near 0 or 1.
This Bayesian p-value corresponds to the deviance.
Missing other covariate values in 'exemplar_covariates.'  Using medoid observation instead.
Missing other covariate values in 'exemplar_covariates.'  Using medoid observation instead.
Missing other covariate values in 'exemplar_covariates.'  Using medoid observation instead.
Missing other covariate values in 'exemplar_covariates.'  Using medoid observation instead.
Missing other covariate values in 'exemplar_covariates.'  Using medoid observation instead.
Bayesian p-values measure GOF via 
Pr(T(y_obs) - T(y_pred) > 0 | y_obs).
Thus values close to 0.5 are ideal.  Be concerned if values are near 0 or 1.
This Bayesian p-value corresponds to the deviance.
Missing other covariate values in 'exemplar_covariates.'  Using medoid observation instead.

The g hyperparameter in Zellner's g prior is not specified.  It will be set automatically to n.


----------

Values given in terms of rate ratios

----------


The mu hyperparameter in the normal prior is not specified.  It will be set automatically to 0.


The V hyperparameter in the normal prior is not specified.  It will be set automatically to 4/25Diag(s^2_{X_j})

The mu hyperparameter in the normal prior is not specified.  It will be set automatically to 0.


The V hyperparameter in the normal prior is not specified.  It will be set automatically to 4/25Diag(s^2_{X_j})

The mu hyperparameter in the normal prior is not specified.  It will be set automatically to 0.


The V hyperparameter in the normal prior is not specified.  It will be set automatically to 4/25Diag(s^2_{X_j})

The mu hyperparameter in the normal prior is not specified.  It will be set automatically to 0.


The V hyperparameter in the normal prior is not specified.  It will be set automatically to 4/25Diag(s^2_{X_j})

The mu hyperparameter in the normal prior is not specified.  It will be set automatically to 0.


The V hyperparameter in the normal prior is not specified.  It will be set automatically to 4/25Diag(s^2_{X_j})
Bayesian p-values measure GOF via 
Pr(T(y_obs) - T(y_pred) > 0 | y_obs).
Thus values close to 0.5 are ideal.  Be concerned if values are near 0 or 1.
This Bayesian p-value corresponds to the deviance.
Missing other covariate values in 'exemplar_covariates.'  Using medoid observation instead.
Missing other covariate values in 'exemplar_covariates.'  Using medoid observation instead.
Missing other covariate values in 'exemplar_covariates.'  Using medoid observation instead.
Missing other covariate values in 'exemplar_covariates.'  Using medoid observation instead.
Missing other covariate values in 'exemplar_covariates.'  Using medoid observation instead.
Bayesian p-values measure GOF via 
Pr(T(y_obs) - T(y_pred) > 0 | y_obs).
Thus values close to 0.5 are ideal.  Be concerned if values are near 0 or 1.
This Bayesian p-value corresponds to the deviance.
Missing other covariate values in 'exemplar_covariates.'  Using medoid observation instead.

The g hyperparameter in Zellner's g prior is not specified.  It will be set automatically to n.


----------

Values given in terms of rate ratios

----------


The mu hyperparameter in the normal prior is not specified.  It will be set automatically to 0.


The V hyperparameter in the normal prior is not specified.  It will be set automatically to 4/25Diag(s^2_{X_j})

The mu hyperparameter in the normal prior is not specified.  It will be set automatically to 0.


The V hyperparameter in the normal prior is not specified.  It will be set automatically to 4/25Diag(s^2_{X_j})

The mu hyperparameter in the normal prior is not specified.  It will be set automatically to 0.


The V hyperparameter in the normal prior is not specified.  It will be set automatically to 4/25Diag(s^2_{X_j})

The mu hyperparameter in the normal prior is not specified.  It will be set automatically to 0.


The V hyperparameter in the normal prior is not specified.  It will be set automatically to 4/25Diag(s^2_{X_j})

The mu hyperparameter in the normal prior is not specified.  It will be set automatically to 0.


The V hyperparameter in the normal prior is not specified.  It will be set automatically to 4/25Diag(s^2_{X_j})
Bayesian p-values measure GOF via 
Pr(T(y_obs) - T(y_pred) > 0 | y_obs).
Thus values close to 0.5 are ideal.  Be concerned if values are near 0 or 1.
This Bayesian p-value corresponds to the deviance.
Missing other covariate values in 'exemplar_covariates.'  Using medoid observation instead.
Missing other covariate values in 'exemplar_covariates.'  Using medoid observation instead.
Missing other covariate values in 'exemplar_covariates.'  Using medoid observation instead.
Missing other covariate values in 'exemplar_covariates.'  Using medoid observation instead.
Missing other covariate values in 'exemplar_covariates.'  Using medoid observation instead.
Bayesian p-values measure GOF via 
Pr(T(y_obs) - T(y_pred) > 0 | y_obs).
Thus values close to 0.5 are ideal.  Be concerned if values are near 0 or 1.
This Bayesian p-value corresponds to the deviance.
Missing other covariate values in 'exemplar_covariates.'  Using medoid observation instead.

The g hyperparameter in Zellner's g prior is not specified.  It will be set automatically to n.


----------

Values given in terms of rate ratios

----------


The mu hyperparameter in the normal prior is not specified.  It will be set automatically to 0.


The V hyperparameter in the normal prior is not specified.  It will be set automatically to 4/25Diag(s^2_{X_j})

The mu hyperparameter in the normal prior is not specified.  It will be set automatically to 0.


The V hyperparameter in the normal prior is not specified.  It will be set automatically to 4/25Diag(s^2_{X_j})

The mu hyperparameter in the normal prior is not specified.  It will be set automatically to 0.


The V hyperparameter in the normal prior is not specified.  It will be set automatically to 4/25Diag(s^2_{X_j})

The mu hyperparameter in the normal prior is not specified.  It will be set automatically to 0.


The V hyperparameter in the normal prior is not specified.  It will be set automatically to 4/25Diag(s^2_{X_j})

The mu hyperparameter in the normal prior is not specified.  It will be set automatically to 0.


The V hyperparameter in the normal prior is not specified.  It will be set automatically to 4/25Diag(s^2_{X_j})
Bayesian p-values measure GOF via 
Pr(T(y_obs) - T(y_pred) > 0 | y_obs).
Thus values close to 0.5 are ideal.  Be concerned if values are near 0 or 1.
This Bayesian p-value corresponds to the deviance.
Missing other covariate values in 'exemplar_covariates.'  Using medoid observation instead.
Missing other covariate values in 'exemplar_covariates.'  Using medoid observation instead.
Missing other covariate values in 'exemplar_covariates.'  Using medoid observation instead.
Missing other covariate values in 'exemplar_covariates.'  Using medoid observation instead.
Missing other covariate values in 'exemplar_covariates.'  Using medoid observation instead.
Bayesian p-values measure GOF via 
Pr(T(y_obs) - T(y_pred) > 0 | y_obs).
Thus values close to 0.5 are ideal.  Be concerned if values are near 0 or 1.
This Bayesian p-value corresponds to the deviance.
Missing other covariate values in 'exemplar_covariates.'  Using medoid observation instead.

The g hyperparameter in Zellner's g prior is not specified.  It will be set automatically to n.


----------

Values given in terms of rate ratios

----------


The mu hyperparameter in the normal prior is not specified.  It will be set automatically to 0.


The V hyperparameter in the normal prior is not specified.  It will be set automatically to 4/25Diag(s^2_{X_j})

The mu hyperparameter in the normal prior is not specified.  It will be set automatically to 0.


The V hyperparameter in the normal prior is not specified.  It will be set automatically to 4/25Diag(s^2_{X_j})

The mu hyperparameter in the normal prior is not specified.  It will be set automatically to 0.


The V hyperparameter in the normal prior is not specified.  It will be set automatically to 4/25Diag(s^2_{X_j})

The mu hyperparameter in the normal prior is not specified.  It will be set automatically to 0.


The V hyperparameter in the normal prior is not specified.  It will be set automatically to 4/25Diag(s^2_{X_j})

The mu hyperparameter in the normal prior is not specified.  It will be set automatically to 0.


The V hyperparameter in the normal prior is not specified.  It will be set automatically to 4/25Diag(s^2_{X_j})
Bayesian p-values measure GOF via 
Pr(T(y_obs) - T(y_pred) > 0 | y_obs).
Thus values close to 0.5 are ideal.  Be concerned if values are near 0 or 1.
This Bayesian p-value corresponds to the deviance.
Missing other covariate values in 'exemplar_covariates.'  Using medoid observation instead.
Missing other covariate values in 'exemplar_covariates.'  Using medoid observation instead.
Missing other covariate values in 'exemplar_covariates.'  Using medoid observation instead.
Missing other covariate values in 'exemplar_covariates.'  Using medoid observation instead.
Missing other covariate values in 'exemplar_covariates.'  Using medoid observation instead.
Bayesian p-values measure GOF via 
Pr(T(y_obs) - T(y_pred) > 0 | y_obs).
Thus values close to 0.5 are ideal.  Be concerned if values are near 0 or 1.
This Bayesian p-value corresponds to the deviance.
Missing other covariate values in 'exemplar_covariates.'  Using medoid observation instead.

The g hyperparameter in Zellner's g prior is not specified.  It will be set automatically to n.


----------

Values given in terms of rate ratios

----------


The mu hyperparameter in the normal prior is not specified.  It will be set automatically to 0.


The V hyperparameter in the normal prior is not specified.  It will be set automatically to 4/25Diag(s^2_{X_j})

The mu hyperparameter in the normal prior is not specified.  It will be set automatically to 0.


The V hyperparameter in the normal prior is not specified.  It will be set automatically to 4/25Diag(s^2_{X_j})

The mu hyperparameter in the normal prior is not specified.  It will be set automatically to 0.


The V hyperparameter in the normal prior is not specified.  It will be set automatically to 4/25Diag(s^2_{X_j})

The mu hyperparameter in the normal prior is not specified.  It will be set automatically to 0.


The V hyperparameter in the normal prior is not specified.  It will be set automatically to 4/25Diag(s^2_{X_j})

The mu hyperparameter in the normal prior is not specified.  It will be set automatically to 0.


The V hyperparameter in the normal prior is not specified.  It will be set automatically to 4/25Diag(s^2_{X_j})
Bayesian p-values measure GOF via 
Pr(T(y_obs) - T(y_pred) > 0 | y_obs).
Thus values close to 0.5 are ideal.  Be concerned if values are near 0 or 1.
This Bayesian p-value corresponds to the deviance.
Missing other covariate values in 'exemplar_covariates.'  Using medoid observation instead.
Missing other covariate values in 'exemplar_covariates.'  Using medoid observation instead.
Missing other covariate values in 'exemplar_covariates.'  Using medoid observation instead.
Missing other covariate values in 'exemplar_covariates.'  Using medoid observation instead.
Missing other covariate values in 'exemplar_covariates.'  Using medoid observation instead.
Bayesian p-values measure GOF via 
Pr(T(y_obs) - T(y_pred) > 0 | y_obs).
Thus values close to 0.5 are ideal.  Be concerned if values are near 0 or 1.
This Bayesian p-value corresponds to the deviance.
Missing other covariate values in 'exemplar_covariates.'  Using medoid observation instead.

The mu hyperparameter in the normal prior is not specified.  It will be set automatically to 0.


The hyperparameters for the residual variance were not provided. Instead, the prior will put 50% prior probability that R^2 is between 0.1^2 and 0.9^2.


The V hyperparameter in the normal prior is not specified.  It will be set automatically to 4/25Diag(s^2_{X_j})

The mu hyperparameter in the normal prior is not specified.  It will be set automatically to 0.


The hyperparameters for the residual variance were not provided. Instead, the prior will put 50% prior probability that R^2 is between 0.1^2 and 0.9^2.


The V hyperparameter in the normal prior is not specified.  It will be set automatically to 4/25Diag(s^2_{X_j})

The g hyperparameter in Zellner's g prior is not specified.  It will be set automatically to n.


The hyperparameters for the residual variance were not provided. Instead, the prior will put 50% prior probability that R^2 is between 0.1^2 and 0.9^2.


The g hyperparameter in Zellner's g prior is not specified.  It will be set automatically to n.


The hyperparameters for the residual variance were not provided. Instead, the prior will put 50% prior probability that R^2 is between 0.1^2 and 0.9^2.


----------

Test for heteroscedasticity in 1-way ANOVA models.


Bayes factor in favor of homoscedasticity = 592366584.582148
Level of evidence: Decisive in favor of homoscedasticity

----------


----------

Test for heteroscedasticity in 1-way ANOVA models.


Bayes factor in favor of homoscedasticity = 0.028467538606378
Level of evidence: Strong in favor of heteroscedasticity

----------


The mu hyperparameter in the normal prior is not specified.  It will be set automatically to 0.


The hyperparameters for the residual variance were not provided. Instead, the prior will put 50% prior probability that R^2 is between 0.1^2 and 0.9^2.


The V hyperparameter in the normal prior is not specified.  It will be set automatically to 4/25Diag(s^2_{X_j})

The mu hyperparameter in the normal prior is not specified.  It will be set automatically to 0.


The hyperparameters for the residual variance were not provided. Instead, the prior will put 50% prior probability that R^2 is between 0.1^2 and 0.9^2.


The V hyperparameter in the normal prior is not specified.  It will be set automatically to 4/25Diag(s^2_{X_j})

The mu hyperparameter in the normal prior is not specified.  It will be set automatically to 0.


The hyperparameters for the residual variance were not provided. Instead, the prior will put 50% prior probability that R^2 is between 0.1^2 and 0.9^2.


The V hyperparameter in the normal prior is not specified.  It will be set automatically to 4/25Diag(s^2_{X_j})

The mu hyperparameter in the normal prior is not specified.  It will be set automatically to 0.


The hyperparameters for the residual variance were not provided. Instead, the prior will put 50% prior probability that R^2 is between 0.1^2 and 0.9^2.


The V hyperparameter in the normal prior is not specified.  It will be set automatically to 4/25Diag(s^2_{X_j})

The mu hyperparameter in the normal prior is not specified.  It will be set automatically to 0.


The hyperparameters for the residual variance were not provided. Instead, the prior will put 50% prior probability that R^2 is between 0.1^2 and 0.9^2.


The V hyperparameter in the normal prior is not specified.  It will be set automatically to 4/25Diag(s^2_{X_j})

The mu hyperparameter in the normal prior is not specified.  It will be set automatically to 0.


The hyperparameters for the residual variance were not provided. Instead, the prior will put 50% prior probability that R^2 is between 0.1^2 and 0.9^2.


The V hyperparameter in the normal prior is not specified.  It will be set automatically to 4/25Diag(s^2_{X_j})
Missing other covariate values in 'exemplar_covariates.'  Using medoid observation instead.
Missing other covariate values in 'exemplar_covariates.'  Using medoid observation instead.
Missing other covariate values in 'exemplar_covariates.'  Using medoid observation instead.
Missing other covariate values in 'exemplar_covariates.'  Using medoid observation instead.
Missing other covariate values in 'exemplar_covariates.'  Using medoid observation instead.
Missing other covariate values in 'exemplar_covariates.'  Using medoid observation instead.

The mu hyperparameter in the normal prior is not specified.  It will be set automatically to 0.


The hyperparameters for the residual variance were not provided. Instead, the prior will put 50% prior probability that R^2 is between 0.1^2 and 0.9^2.


The V hyperparameter in the normal prior is not specified.  It will be set automatically to 4/25Diag(s^2_{X_j})
Missing other covariate values in 'exemplar_covariates.'  Using medoid observation instead.

The g hyperparameter in Zellner's g prior is not specified.  It will be set automatically to n.


The hyperparameters for the residual variance were not provided. Instead, the prior will put 50% prior probability that R^2 is between 0.1^2 and 0.9^2.


The g hyperparameter in Zellner's g prior is not specified.  It will be set automatically to n.


The hyperparameters for the residual variance were not provided. Instead, the prior will put 50% prior probability that R^2 is between 0.1^2 and 0.9^2.


The g hyperparameter in Zellner's g prior is not specified.  It will be set automatically to n.


The hyperparameters for the residual variance were not provided. Instead, the prior will put 50% prior probability that R^2 is between 0.1^2 and 0.9^2.


The g hyperparameter in Zellner's g prior is not specified.  It will be set automatically to n.


The hyperparameters for the residual variance were not provided. Instead, the prior will put 50% prior probability that R^2 is between 0.1^2 and 0.9^2.


The g hyperparameter in Zellner's g prior is not specified.  It will be set automatically to n.


The hyperparameters for the residual variance were not provided. Instead, the prior will put 50% prior probability that R^2 is between 0.1^2 and 0.9^2.


The g hyperparameter in Zellner's g prior is not specified.  It will be set automatically to n.


The hyperparameters for the residual variance were not provided. Instead, the prior will put 50% prior probability that R^2 is between 0.1^2 and 0.9^2.


The g hyperparameter in Zellner's g prior is not specified.  It will be set automatically to n.


The hyperparameters for the residual variance were not provided. Instead, the prior will put 50% prior probability that R^2 is between 0.1^2 and 0.9^2.


The hyperparameters for the residual variance were not provided. Instead, the prior will put 50% prior probability that R^2 is between 0.1^2 and 0.9^2.

Missing other covariate values in 'exemplar_covariates.'  Using medoid observation instead.
Missing other covariate values in 'exemplar_covariates.'  Using medoid observation instead.
Missing other covariate values in 'exemplar_covariates.'  Using medoid observation instead.
Missing other covariate values in 'exemplar_covariates.'  Using medoid observation instead.
Missing other covariate values in 'exemplar_covariates.'  Using medoid observation instead.
Missing other covariate values in 'exemplar_covariates.'  Using medoid observation instead.
Missing other covariate values in 'exemplar_covariates.'  Using medoid observation instead.
Missing other covariate values in 'exemplar_covariates.'  Using medoid observation instead.
Missing other covariate values in 'exemplar_covariates.'  Using medoid observation instead.
Missing other covariate values in 'exemplar_covariates.'  Using medoid observation instead.
Missing other covariate values in 'exemplar_covariates.'  Using medoid observation instead.
Missing other covariate values in 'exemplar_covariates.'  Using medoid observation instead.

The mu hyperparameter in the normal prior is not specified.  It will be set automatically to 0.


The hyperparameters for the residual variance were not provided. Instead, the prior will put 50% prior probability that R^2 is between 0.1^2 and 0.9^2.


The V hyperparameter in the normal prior is not specified.  It will be set automatically to 4/25Diag(s^2_{X_j})

The mu hyperparameter in the normal prior is not specified.  It will be set automatically to 0.


The hyperparameters for the residual variance were not provided. Instead, the prior will put 50% prior probability that R^2 is between 0.1^2 and 0.9^2.


The V hyperparameter in the normal prior is not specified.  It will be set automatically to 4/25Diag(s^2_{X_j})

The mu hyperparameter in the normal prior is not specified.  It will be set automatically to 0.


The hyperparameters for the residual variance were not provided. Instead, the prior will put 50% prior probability that R^2 is between 0.1^2 and 0.9^2.


The V hyperparameter in the normal prior is not specified.  It will be set automatically to 4/25Diag(s^2_{X_j})

The g hyperparameter in Zellner's g prior is not specified.  It will be set automatically to n.


The hyperparameters for the residual variance were not provided. Instead, the prior will put 50% prior probability that R^2 is between 0.1^2 and 0.9^2.


The g hyperparameter in Zellner's g prior is not specified.  It will be set automatically to n.


The hyperparameters for the residual variance were not provided. Instead, the prior will put 50% prior probability that R^2 is between 0.1^2 and 0.9^2.


The g hyperparameter in Zellner's g prior is not specified.  It will be set automatically to n.


The hyperparameters for the residual variance were not provided. Instead, the prior will put 50% prior probability that R^2 is between 0.1^2 and 0.9^2.


The mu hyperparameter in the normal prior is not specified.  It will be set automatically to 0.


The hyperparameters for the residual variance were not provided. Instead, the prior will put 50% prior probability that R^2 is between 0.1^2 and 0.9^2.


The V hyperparameter in the normal prior is not specified.  It will be set automatically to 4/25Diag(s^2_{X_j})
Missing other covariate values in 'exemplar_covariates.'  Using medoid observation instead.

The mu hyperparameter in the normal prior is not specified.  It will be set automatically to 0.


The hyperparameters for the residual variance were not provided. Instead, the prior will put 50% prior probability that R^2 is between 0.1^2 and 0.9^2.


The V hyperparameter in the normal prior is not specified.  It will be set automatically to 4/25Diag(s^2_{X_j})
Missing other covariate values in 'exemplar_covariates.'  Using medoid observation instead.

The mu hyperparameter in the normal prior is not specified.  It will be set automatically to 0.


The hyperparameters for the residual variance were not provided. Instead, the prior will put 50% prior probability that R^2 is between 0.1^2 and 0.9^2.


The V hyperparameter in the normal prior is not specified.  It will be set automatically to 4/25Diag(s^2_{X_j})

The mu hyperparameter in the normal prior is not specified.  It will be set automatically to 0.


The hyperparameters for the residual variance were not provided. Instead, the prior will put 50% prior probability that R^2 is between 0.1^2 and 0.9^2.


The V hyperparameter in the normal prior is not specified.  It will be set automatically to 4/25Diag(s^2_{X_j})
Missing other covariate values in 'exemplar_covariates.'  Using medoid observation instead.

The mu hyperparameter in the normal prior is not specified.  It will be set automatically to 0.


The hyperparameters for the residual variance were not provided. Instead, the prior will put 50% prior probability that R^2 is between 0.1^2 and 0.9^2.


The V hyperparameter in the normal prior is not specified.  It will be set automatically to 4/25Diag(s^2_{X_j})
Missing other covariate values in 'exemplar_covariates.'  Using medoid observation instead.

The g hyperparameter in Zellner's g prior is not specified.  It will be set automatically to n.


The hyperparameters for the residual variance were not provided. Instead, the prior will put 50% prior probability that R^2 is between 0.1^2 and 0.9^2.


The g hyperparameter in Zellner's g prior is not specified.  It will be set automatically to n.


Finished with 500 preliminary posterior draws.
Bayesian p-values measure GOF via 
Pr(T(y_obs) - T(y_pred) > 0 | y_obs).
Thus values close to 0.5 are ideal.  Be concerned if values are near 0 or 1.
This Bayesian p-value corresponds to the deviance.
Bayesian p-values measure GOF via 
Pr(T(y_obs) - T(y_pred) > 0 | y_obs).
Thus values close to 0.5 are ideal.  Be concerned if values are near 0 or 1.
This Bayesian p-value corresponds to the deviance.

The g hyperparameter in Zellner's g prior is not specified.  It will be set automatically to n.


The hyperparameters for the residual variance were not provided. Instead, the prior will put 50% prior probability that R^2 is between 0.1^2 and 0.9^2.


The g hyperparameter in Zellner's g prior is not specified.  It will be set automatically to n.


Finished with 500 preliminary posterior draws.
control_value missing; set to be the 1st quintile of tr
treat_value missing; set to be the 4th quintile of tr

Finished with 500 preliminary posterior draws.

Finished with 500 preliminary posterior draws.
Bayesian p-values measure GOF via 
Pr(T(y_obs) - T(y_pred) > 0 | y_obs).
Thus values close to 0.5 are ideal.  Be concerned if values are near 0 or 1.
This Bayesian p-value corresponds to the deviance.
Bayesian p-values measure GOF via 
Pr(T(y_obs) - T(y_pred) > 0 | y_obs).
Thus values close to 0.5 are ideal.  Be concerned if values are near 0 or 1.
This Bayesian p-value corresponds to the deviance.

The g hyperparameter in Zellner's g prior is not specified.  It will be set automatically to n.


The hyperparameters for the residual variance were not provided. Instead, the prior will put 50% prior probability that R^2 is between 0.1^2 and 0.9^2.


The g hyperparameter in Zellner's g prior is not specified.  It will be set automatically to n.


The hyperparameters for the residual variance were not provided. Instead, the prior will put 50% prior probability that R^2 is between 0.1^2 and 0.9^2.

Assuming all observations correspond to Bernoulli, i.e., Binomial with one trial.

----------

Values given in terms of odds ratios

----------

Assuming all observations correspond to Bernoulli, i.e., Binomial with one trial.
Assuming all observations correspond to Bernoulli, i.e., Binomial with one trial.
Assuming all observations correspond to Bernoulli, i.e., Binomial with one trial.
Assuming all observations correspond to Bernoulli, i.e., Binomial with one trial.
Assuming all observations correspond to Bernoulli, i.e., Binomial with one trial.
Assuming all observations correspond to Bernoulli, i.e., Binomial with one trial.
Assuming all observations correspond to Bernoulli, i.e., Binomial with one trial.
Assuming all observations correspond to Bernoulli, i.e., Binomial with one trial.
Missing other covariate values in 'exemplar_covariates.'  Using medoid observation instead.
Missing other covariate values in 'exemplar_covariates.'  Using medoid observation instead.
Missing other covariate values in 'exemplar_covariates.'  Using medoid observation instead.

----------

Values given in terms of rate ratios

----------

Missing other covariate values in 'exemplar_covariates.'  Using medoid observation instead.
Missing other covariate values in 'exemplar_covariates.'  Using medoid observation instead.
Missing other covariate values in 'exemplar_covariates.'  Using medoid observation instead.

----------

Values given in terms of rate ratios

----------

Missing other covariate values in 'exemplar_covariates.'  Using medoid observation instead.
Missing other covariate values in 'exemplar_covariates.'  Using medoid observation instead.
Missing other covariate values in 'exemplar_covariates.'  Using medoid observation instead.
Missing other covariate values in 'exemplar_covariates.'  Using medoid observation instead.
Missing other covariate values in 'exemplar_covariates.'  Using medoid observation instead.
Missing other covariate values in 'exemplar_covariates.'  Using medoid observation instead.
Prior shape parameters were not supplied.
Jeffrey's prior will be used.

----------

Analysis of a single population rate using Bayesian techniques

----------

Number of events: 12

Time/area base for event counts: 1

Prior used: Gamma(0.5,0)

Posterior mean of the rate: 12.5

95% credible interval: (6.56, 20.3)


----------

Prior shape parameters were not supplied.
Jeffrey's prior will be used.

----------

Analysis of a single population rate using Bayesian techniques

----------

Number of events: 12

Time/area base for event counts: 2

Prior used: Gamma(0.5,0)

Posterior mean of the rate: 6.25

95% credible interval: (3.28, 10.2)


----------

Prior shape parameters were not supplied.
Jeffrey's prior will be used.

----------

Analysis of a single population rate using Bayesian techniques

----------

Number of events: 12

Time/area base for event counts: 2

Prior used: Gamma(0.5,0)

Posterior mean of the rate: 6.25

95% credible interval: (3.28, 10.2)

Probability that rate < 10: 0.971


----------

Prior shape parameters were not supplied.
A flat Gamma(0.001,0.001) prior will be used.

----------

Analysis of a single population rate using Bayesian techniques

----------

Number of events: 12

Time/area base for event counts: 2

Prior used: Gamma(0.001,0.001)

Posterior mean of the rate: 6

95% credible interval: (3.1, 9.84)

Probability that rate < 11: 0.992


----------


----------

Analysis of a single population rate using Bayesian techniques

----------

Number of events: 12

Time/area base for event counts: 2

Prior used: Gamma(1,1)

Posterior mean of the rate: 4.33

95% credible interval: (2.31, 6.99)

Probability that rate < 11: 1


----------

Prior shape parameters were not supplied.
Jeffrey's prior will be used.

----------

Analysis of two population rates using Bayesian techniques

----------

Number of events: Population 1 = 12; Population 2 = 20

Time/area base for event counts: Population 1 = 1; Population 2 = 1

Prior used: Gamma(0.5,0)

Posterior mean: Population 1 = 12.5; Population 2 = 20.5

95% credible interval: Population 1 = (6.56, 20.3); Population 2 = (12.6, 30.3)

95% credible interval: (Population 1) / (Population 2) = (0.288, 1.21)

Probability that the rate ratio (pop 1 vs. pop 2) is in the ROPE, defined to be (0.889,1.12) = 0.098


----------

Prior shape parameters were not supplied.
Jeffrey's prior will be used.

----------

Analysis of two population rates using Bayesian techniques

----------

Number of events: Population 1 = 12; Population 2 = 20

Time/area base for event counts: Population 1 = 10; Population 2 = 9

Prior used: Gamma(0.5,0)

Posterior mean: Population 1 = 1.25; Population 2 = 2.28

95% credible interval: Population 1 = (0.656, 2.03); Population 2 = (1.4, 3.36)

95% credible interval: (Population 1) / (Population 2) = (0.26, 1.09)

Probability that the rate ratio (pop 1 vs. pop 2) is in the ROPE, defined to be (0.889,1.12) = 0.0638


----------

Prior shape parameters were not supplied.
Jeffrey's prior will be used.

----------

Analysis of two population rates using Bayesian techniques

----------

Number of events: Population 1 = 12; Population 2 = 20

Time/area base for event counts: Population 1 = 10; Population 2 = 9

Prior used: Gamma(0.5,0)

Posterior mean: Population 1 = 1.25; Population 2 = 2.28

95% credible interval: Population 1 = (0.656, 2.03); Population 2 = (1.4, 3.36)

95% credible interval: (Population 1) / (Population 2) = (0.26, 1.09)

Probability that the rate ratio (pop 1 vs. pop 2) is in the ROPE, defined to be (0.889,1.12) = 0.0638


----------

Prior shape parameters were not supplied.
A flat Gamma(0.001,0.001) prior will be used.

----------

Analysis of two population rates using Bayesian techniques

----------

Number of events: Population 1 = 12; Population 2 = 20

Time/area base for event counts: Population 1 = 10; Population 2 = 9

Prior used: Gamma(0.001,0.001)

Posterior mean: Population 1 = 1.2; Population 2 = 2.22

95% credible interval: Population 1 = (0.62, 1.97); Population 2 = (1.36, 3.3)

95% credible interval: (Population 1) / (Population 2) = (0.252, 1.08)

Probability that the rate ratio (pop 1 vs. pop 2) is in the ROPE, defined to be (0.889,1.12) = 0.0595


----------


----------

Analysis of two population rates using Bayesian techniques

----------

Number of events: Population 1 = 12; Population 2 = 20

Time/area base for event counts: Population 1 = 10; Population 2 = 9

Prior used: Gamma(1,1)

Posterior mean: Population 1 = 1.18; Population 2 = 2.1

95% credible interval: Population 1 = (0.629, 1.91); Population 2 = (1.3, 3.09)

95% credible interval: (Population 1) / (Population 2) = (0.27, 1.1)

Probability that the rate ratio (pop 1 vs. pop 2) is in the ROPE, defined to be (0.889,1.12) = 0.0692


----------

Prior shape parameters were not supplied.
Jeffrey's prior will be used.

----------

Analysis of a single population proportion using Bayesian techniques

----------

Number of successes: 14

Number of failures: 19

Prior used: Beta(0.5,0.5)

Posterior mean: 0.426

95% credible interval: (0.268, 0.593)

95% prediction interval for another 33 trials: (7, 24)


----------

Prior shape parameters were not supplied.
Jeffrey's prior will be used.

----------

Analysis of a single population proportion using Bayesian techniques

----------

Number of successes: 14

Number of failures: 19

Prior used: Beta(0.5,0.5)

Posterior mean: 0.426

95% credible interval: (0.268, 0.593)

95% prediction interval for another 33 trials: (7, 24)


----------

Prior shape parameters were not supplied.
Jeffrey's prior will be used.

----------

Analysis of a single population proportion using Bayesian techniques

----------

Number of successes: 14

Number of failures: 19

Prior used: Beta(0.5,0.5)

Posterior mean: 0.426

95% credible interval: (0.268, 0.593)

Probability that p < 0.45: 0.615

95% prediction interval for another 33 trials: (7, 24)


----------

Prior shape parameters were not supplied.
Jeffrey's prior will be used.

----------

Analysis of two population proportions using Bayesian techniques

----------

Number of successes: Population 1 = 14; Population 2 = 22

Number of failures: Population 1 = 19; Population 2 = 45

Prior used: Beta(0.5,0.5)

Posterior mean: Population 1 = 0.426; Population 2 = 0.331

95% credible interval: Population 1 = (0.268, 0.593); Population 2 = (0.225, 0.446)

95% credible interval: (Population 1) - (Population 2) = (-0.1, 0.295)

Probability that the odds ratio (pop 1 vs. pop 2) is in the ROPE, defined to be (0.889,1.12) = 0.138

95% prediction interval for another 33 trials for population 1: (7, 24)

95% prediction interval for another 67 trials for population 2: (12, 35)


----------

Prior shape parameters were not supplied.
Jeffrey's prior will be used.

----------

Analysis of two population proportions using Bayesian techniques

----------

Number of successes: Population 1 = 14; Population 2 = 22

Number of failures: Population 1 = 19; Population 2 = 45

Prior used: Beta(0.5,0.5)

Posterior mean: Population 1 = 0.426; Population 2 = 0.331

95% credible interval: Population 1 = (0.268, 0.593); Population 2 = (0.225, 0.446)

95% credible interval: (Population 1) - (Population 2) = (-0.1, 0.295)

Probability that the odds ratio (pop 1 vs. pop 2) is in the ROPE, defined to be (0.889,1.12) = 0.138

95% prediction interval for another 33 trials for population 1: (7, 24)

95% prediction interval for another 67 trials for population 2: (12, 35)


----------

Prior shape parameters were not supplied.
Jeffrey's prior will be used.

----------

Analysis of two population proportions using Bayesian techniques

----------

Number of successes: Population 1 = 14; Population 2 = 22

Number of failures: Population 1 = 19; Population 2 = 45

Prior used: Beta(0.5,0.5)

Posterior mean: Population 1 = 0.426; Population 2 = 0.331

95% credible interval: Population 1 = (0.268, 0.593); Population 2 = (0.225, 0.446)

95% credible interval: (Population 1) - (Population 2) = (-0.1, 0.295)

Probability that the odds ratio (pop 1 vs. pop 2) is in the ROPE, defined to be (0.889,1.12) = 0.138

95% prediction interval for another 33 trials for population 1: (7, 24)

95% prediction interval for another 67 trials for population 2: (12, 35)


----------

Prior shape parameters were not supplied.
Jeffrey's prior will be used.

----------

 Non-parametric sign test using Bayesian techniques

----------

Prior used: Beta(0.5,0.5)

Posterior mean: 0.52

95% credible interval: (0.384, 0.654)

Probability that p < 0.5: 0.389

Probability that 0.45 < p < 0.55: 0.506


----------

Prior shape parameters were not supplied.
Jeffrey's prior will be used.

----------

 Non-parametric sign test using Bayesian techniques

----------

Prior used: Beta(0.5,0.5)

Posterior mean: 0.696

95% credible interval: (0.564, 0.813)

Probability that p < 0.5: 0.0021

Probability that 0.45 < p < 0.55: 0.0151


----------

Prior shape parameters were not supplied.
A uniform prior will be used.

----------

 Non-parametric sign test using Bayesian techniques

----------

Prior used: Beta(1,1)

Posterior mean: 0.308

95% credible interval: (0.191, 0.438)

Probability that p < 0.5: 0.998

Probability that 0.45 < p < 0.55: 0.0165


----------


----------

 Non-parametric sign test using Bayesian techniques

----------

Prior used: Beta(1,1)

Posterior mean: 0.308

95% credible interval: (0.191, 0.438)

Probability that p < 0.5: 0.998

Probability that 0.45 < p < 0.55: 0.0165


----------


----------

 Non-parametric sign test using Bayesian techniques

----------

Prior used: Beta(2,2)

Posterior mean: 0.315

95% credible interval: (0.199, 0.443)

Probability that p < 0.5: 0.997

Probability that 0.45 < p < 0.55: 0.0197


----------

Prior shape parameters were not supplied.
Jeffrey's prior will be used.

----------

 Non-parametric sign test using Bayesian techniques

----------

Prior used: Beta(0.5,0.5)

Posterior mean: 0.304

95% credible interval: (0.187, 0.436)

Probability that p < 0.5: 0.998

Probability that 0.4 < p < 0.6: 0.0725


----------

Prior shape parameters were not supplied.
Jeffrey's prior will be used.

----------

 Non-parametric sign test using Bayesian techniques

----------

Prior used: Beta(0.5,0.5)

Posterior mean: 0.304

95% credible interval: (0.187, 0.436)

Probability that p < 0.5: 0.998

Probability that 0.35 < p < 0.65: 0.232


----------

Prior shape parameters were not supplied.
Jeffrey's prior will be used.

----------

 Non-parametric sign test using Bayesian techniques

----------

Prior used: Beta(0.5,0.5)

Posterior mean: 0.304

95% credible interval: (0.187, 0.436)

Probability that p < 0.5: 0.998

Probability that 0.4 < p < 0.6: 0.0725


----------

Prior shape parameters were not supplied.
Jeffrey's prior will be used.

----------

 Non-parametric sign test using Bayesian techniques

----------

Prior used: Beta(0.5,0.5)

Posterior mean: 0.304

95% credible interval: (0.187, 0.436)

Probability that p < 0.7: 1

Probability that 0.65 < p < 0.75: 0.000000235


----------


---
Bayes factor in favor of the full vs. null model: 1.02e-04;
      =>Level of evidence: Decisive



--- Summary of factor level means ---
# A tibble: 4 x 5
  Variable         `Post Mean`   Lower Upper `Prob Dir`
  <chr>                  <dbl>   <dbl> <dbl>      <dbl>
1 Mean : group : x       0.183 -0.0943 0.461      0.905
2 Mean : group : y       0.890  0.390  1.39       0.999
3 Var : group : x        0.994  0.668  1.47      NA    
4 Var : group : y        0.954  0.451  1.98      NA    




--- Summary of pairwise differences ---
# A tibble: 1 x 9
  Comparison `Post Mean` Lower  Upper `Prob Dir` `ROPE (0.1)`   EPR `EPR Lower`
  <chr>            <dbl> <dbl>  <dbl>      <dbl>        <dbl> <dbl>       <dbl>
1 x-y             -0.707 -1.28 -0.138      0.992       0.0149 0.307       0.177
# i 1 more variable: `EPR Upper` <dbl>


   *Note: EPR (Exceedence in Pairs Rate) for a Comparison of g-h = Pr(Y_(gi) > Y_(hi)|parameters) 
---
Bayes factor in favor of the full vs. null model: 3.85e-04;
      =>Level of evidence: Decisive



--- Summary of factor level means ---
# A tibble: 4 x 5
  Variable        `Post Mean`  Lower Upper `Prob Dir`
  <chr>                 <dbl>  <dbl> <dbl>      <dbl>
1 Mean : asdf : a     -0.0239 -0.302 0.254      0.568
2 Mean : asdf : b      0.833   0.152 1.51       0.990
3 Var : asdf : a       0.995   0.669 1.48      NA    
4 Var : asdf : b       1.76    0.834 3.66      NA    




--- Summary of pairwise differences ---
# A tibble: 1 x 9
  Comparison `Post Mean` Lower  Upper `Prob Dir` `ROPE (0.1)`   EPR `EPR Lower`
  <chr>            <dbl> <dbl>  <dbl>      <dbl>        <dbl> <dbl>       <dbl>
1 a-b             -0.856 -1.59 -0.119      0.988       0.0175 0.303       0.165
# i 1 more variable: `EPR Upper` <dbl>


   *Note: EPR (Exceedence in Pairs Rate) for a Comparison of g-h = Pr(Y_(gi) > Y_(hi)|parameters) Prior shape parameters were not supplied.
Beta(2,2) prior will be used.

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`geom_smooth()` using formula = 'y ~ x'

----------

Wilcoxon signed-rank analysis using Bayesian techniques

----------

Prior used: Beta(2,2)

Posterior mean: 0.105

95% credible interval: (0.0136, 0.271)

Probability that Pr(x > y) > 0.5 = 0.0000764

Probability that Pr(x > y) is in the ROPE, defined to be (0.45,0.55) = 0.000318

Bayes factor in favor of phi>0.5 vs. phi<=0.5: 0.0000764;
      =>Level of evidence: Decisive


----------

Prior shape parameters were not supplied.
Beta(2,2) prior will be used.

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`geom_smooth()` using formula = 'y ~ x'

----------

Wilcoxon signed-rank analysis using Bayesian techniques

----------

Prior used: Beta(2,2)

Posterior mean: 0.105

95% credible interval: (0.0135, 0.273)

Probability that Pr(x > y) > 0.5 = 0.000114

Probability that Pr(x > y) is in the ROPE, defined to be (0.45,0.55) = 0.000305

Bayes factor in favor of phi>0.5 vs. phi<=0.5: 0.000114;
      =>Level of evidence: Decisive


----------

Prior shape parameters were not supplied.
A uniform prior will be used.

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`geom_smooth()` using formula = 'y ~ x'

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Wilcoxon signed-rank analysis using Bayesian techniques

----------

Prior used: Beta(1,1)

Posterior mean: 0.0588

95% credible interval: (0.00162, 0.206)

Probability that Pr(x > y) > 0.5 = 0.000016

Probability that Pr(x > y) is in the ROPE, defined to be (0.45,0.55) = 0.0000721

Bayes factor in favor of phi>0.5 vs. phi<=0.5: 0.000016;
      =>Level of evidence: Decisive


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`geom_smooth()` using formula = 'y ~ x'

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Wilcoxon signed-rank analysis using Bayesian techniques

----------

Prior used: Beta(5,5)

Posterior mean: 0.2

95% credible interval: (0.0712, 0.377)

Probability that Pr(x > y) > 0.5 = 0.00106

Probability that Pr(x > y) is in the ROPE, defined to be (0.45,0.55) = 0.00406

Bayes factor in favor of phi>0.5 vs. phi<=0.5: 0.00106;
      =>Level of evidence: Decisive


----------

Prior shape parameters were not supplied.
Beta(2,2) prior will be used.

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`geom_smooth()` using formula = 'y ~ x'

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Wilcoxon signed-rank analysis using Bayesian techniques

----------

Prior used: Beta(2,2)

Posterior mean: 0.105

95% credible interval: (0.0136, 0.271)

Probability that Pr(x > y) > 0.5 = 0.0000762

Probability that Pr(x > y) is in the ROPE, defined to be (0.4,0.6) = 0.00121

Bayes factor in favor of phi>0.5 vs. phi<=0.5: 0.0000762;
      =>Level of evidence: Decisive


----------

Prior shape parameters were not supplied.
Beta(2,2) prior will be used.

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`geom_smooth()` using formula = 'y ~ x'

----------

Wilcoxon signed-rank analysis using Bayesian techniques

----------

Prior used: Beta(2,2)

Posterior mean: 0.105

95% credible interval: (0.0135, 0.273)

Probability that Pr(x > y) > 0.5 = 0.0000891

Probability that Pr(x > y) is in the ROPE, defined to be (0.4,0.65) = 0.00115

Bayes factor in favor of phi>0.5 vs. phi<=0.5: 0.0000892;
      =>Level of evidence: Decisive


----------

Prior shape parameters were not supplied.
Beta(2,2) prior will be used.

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Wilcoxon signed-rank analysis using Bayesian techniques

----------

Prior used: Beta(2,2)

Posterior mean: 0.0662

95% credible interval: (0.0287, 0.118)

Probability that Pr(x > y) > 0.5 = 0

Probability that Pr(x > y) is in the ROPE, defined to be (0.45,0.55) = 0

Bayes factor in favor of phi>0.5 vs. phi<=0.5: 0;
      =>Level of evidence: Decisive


----------

Prior shape parameters were not supplied.
Beta(2,2) prior will be used.

----------

Wilcoxon signed-rank analysis using Bayesian techniques

----------

Prior used: Beta(2,2)

Posterior mean: 0.0662

95% credible interval: (0.0287, 0.118)

Probability that Pr(x > y) > 0.5 = 0

Probability that Pr(x > y) is in the ROPE, defined to be (0.45,0.55) = 0

Bayes factor in favor of phi>0.5 vs. phi<=0.5: 0;
      =>Level of evidence: Decisive


----------

Prior shape parameters were not supplied.
A uniform prior will be used.

----------

Wilcoxon signed-rank analysis using Bayesian techniques

----------

Prior used: Beta(1,1)

Posterior mean: 0.0586

95% credible interval: (0.0235, 0.108)

Probability that Pr(x > y) > 0.5 = 0

Probability that Pr(x > y) is in the ROPE, defined to be (0.45,0.55) = 0

Bayes factor in favor of phi>0.5 vs. phi<=0.5: 0;
      =>Level of evidence: Decisive


----------


----------

Wilcoxon signed-rank analysis using Bayesian techniques

----------

Prior used: Beta(5,5)

Posterior mean: 0.0875

95% credible interval: (0.0444, 0.143)

Probability that Pr(x > y) > 0.5 = 0

Probability that Pr(x > y) is in the ROPE, defined to be (0.45,0.55) = 0

Bayes factor in favor of phi>0.5 vs. phi<=0.5: 0;
      =>Level of evidence: Decisive


----------

Prior shape parameters were not supplied.
Beta(2,2) prior will be used.

----------

Wilcoxon signed-rank analysis using Bayesian techniques

----------

Prior used: Beta(2,2)

Posterior mean: 0.0662

95% credible interval: (0.0287, 0.118)

Probability that Pr(x > y) > 0.5 = 0

Probability that Pr(x > y) is in the ROPE, defined to be (0.4,0.6) = 0

Bayes factor in favor of phi>0.5 vs. phi<=0.5: 0;
      =>Level of evidence: Decisive


----------

Prior shape parameters were not supplied.
Beta(2,2) prior will be used.

----------

Wilcoxon signed-rank analysis using Bayesian techniques

----------

Prior used: Beta(2,2)

Posterior mean: 0.0662

95% credible interval: (0.0287, 0.118)

Probability that Pr(x > y) > 0.5 = 0

Probability that Pr(x > y) is in the ROPE, defined to be (0.4,0.65) = 0

Bayes factor in favor of phi>0.5 vs. phi<=0.5: 0;
      =>Level of evidence: Decisive


----------

Prior shape parameters were not supplied.
Beta(2,2) prior will be used.

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`geom_smooth()` using formula = 'y ~ x'

----------

Wilcoxon rank sum analysis using Bayesian techniques

----------

NOTE: Estimand is Omega_x := Proportion of (non-tied) pairs where x is bigger than y

----------

Prior used: Beta(2,2)

Posterior mean: 0.277

95% credible interval: (0.132, 0.455)

Probability that Omega_x > 0.5 = 0.00923

Probability that Omega_x is in the ROPE, defined to be (0.45,0.55) = 0.0259

Bayes factor in favor of phi>0.5 vs. phi<=0.5: 0.00932;
      =>Level of evidence: Decisive


----------

Prior shape parameters were not supplied.
A uniform prior will be used.

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`geom_smooth()` using formula = 'y ~ x'

----------

Wilcoxon rank sum analysis using Bayesian techniques

----------

NOTE: Estimand is Omega_x := Proportion of (non-tied) pairs where x is bigger than y

----------

Prior used: Beta(1,1)

Posterior mean: 0.261

95% credible interval: (0.115, 0.446)

Probability that Omega_x > 0.5 = 0.00637

Probability that Omega_x is in the ROPE, defined to be (0.45,0.55) = 0.0218

Bayes factor in favor of phi>0.5 vs. phi<=0.5: 0.00641;
      =>Level of evidence: Decisive


----------


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`geom_smooth()` using formula = 'y ~ x'

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Wilcoxon rank sum analysis using Bayesian techniques

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NOTE: Estimand is Omega_x := Proportion of (non-tied) pairs where x is bigger than y

----------

Prior used: Beta(5,5)

Posterior mean: 0.319

95% credible interval: (0.175, 0.485)

Probability that Omega_x > 0.5 = 0.0166

Probability that Omega_x is in the ROPE, defined to be (0.45,0.55) = 0.0562

Bayes factor in favor of phi>0.5 vs. phi<=0.5: 0.0169;
      =>Level of evidence: Strong


----------

Prior shape parameters were not supplied.
Beta(2,2) prior will be used.

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`geom_smooth()` using formula = 'y ~ x'

----------

Wilcoxon rank sum analysis using Bayesian techniques

----------

NOTE: Estimand is Omega_x := Proportion of (non-tied) pairs where x is bigger than y

----------

Prior used: Beta(2,2)

Posterior mean: 0.278

95% credible interval: (0.131, 0.459)

Probability that Omega_x > 0.5 = 0.00894

Probability that Omega_x is in the ROPE, defined to be (0.4,0.6) = 0.0836

Bayes factor in favor of phi>0.5 vs. phi<=0.5: 0.00902;
      =>Level of evidence: Decisive


----------

Prior shape parameters were not supplied.
Beta(2,2) prior will be used.

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`geom_smooth()` using formula = 'y ~ x'

----------

Wilcoxon rank sum analysis using Bayesian techniques

----------

NOTE: Estimand is Omega_x := Proportion of (non-tied) pairs where x is bigger than y

----------

Prior used: Beta(2,2)

Posterior mean: 0.278

95% credible interval: (0.133, 0.456)

Probability that Omega_x > 0.5 = 0.0088

Probability that Omega_x is in the ROPE, defined to be (0.1,0.8) = 0.995

Bayes factor in favor of phi>0.5 vs. phi<=0.5: 0.00888;
      =>Level of evidence: Decisive


----------

Prior shape parameters were not supplied.
Beta(2,2) prior will be used.

----------

Wilcoxon rank sum analysis using Bayesian techniques

----------

NOTE: Estimand is Omega_x := Proportion of (non-tied) pairs where x is bigger than y

----------

Prior used: Beta(2,2)

Posterior mean: 0.135

95% credible interval: (0.0957, 0.179)

Probability that Omega_x > 0.5 = 0

Probability that Omega_x is in the ROPE, defined to be (0.45,0.55) = 0

Bayes factor in favor of phi>0.5 vs. phi<=0.5: 0;
      =>Level of evidence: Decisive


----------

Prior shape parameters were not supplied.
A uniform prior will be used.

----------

Wilcoxon rank sum analysis using Bayesian techniques

----------

NOTE: Estimand is Omega_x := Proportion of (non-tied) pairs where x is bigger than y

----------

Prior used: Beta(1,1)

Posterior mean: 0.132

95% credible interval: (0.0931, 0.176)

Probability that Omega_x > 0.5 = 0

Probability that Omega_x is in the ROPE, defined to be (0.45,0.55) = 0

Bayes factor in favor of phi>0.5 vs. phi<=0.5: 0;
      =>Level of evidence: Decisive


----------


----------

Wilcoxon rank sum analysis using Bayesian techniques

----------

NOTE: Estimand is Omega_x := Proportion of (non-tied) pairs where x is bigger than y

----------

Prior used: Beta(5,5)

Posterior mean: 0.143

95% credible interval: (0.103, 0.188)

Probability that Omega_x > 0.5 = 0

Probability that Omega_x is in the ROPE, defined to be (0.45,0.55) = 0

Bayes factor in favor of phi>0.5 vs. phi<=0.5: 0;
      =>Level of evidence: Decisive


----------

Prior shape parameters were not supplied.
Beta(2,2) prior will be used.

----------

Wilcoxon rank sum analysis using Bayesian techniques

----------

NOTE: Estimand is Omega_x := Proportion of (non-tied) pairs where x is bigger than y

----------

Prior used: Beta(2,2)

Posterior mean: 0.135

95% credible interval: (0.0957, 0.179)

Probability that Omega_x > 0.5 = 0

Probability that Omega_x is in the ROPE, defined to be (0.4,0.6) = 0

Bayes factor in favor of phi>0.5 vs. phi<=0.5: 0;
      =>Level of evidence: Decisive


----------

Prior shape parameters were not supplied.
Beta(2,2) prior will be used.

----------

Wilcoxon rank sum analysis using Bayesian techniques

----------

NOTE: Estimand is Omega_x := Proportion of (non-tied) pairs where x is bigger than y

----------

Prior used: Beta(2,2)

Posterior mean: 0.135

95% credible interval: (0.0957, 0.179)

Probability that Omega_x > 0.5 = 0

Probability that Omega_x is in the ROPE, defined to be (0.1,0.8) = 0.957

Bayes factor in favor of phi>0.5 vs. phi<=0.5: 0;
      =>Level of evidence: Decisive


----------

[ FAIL 0 | WARN 0 | SKIP 0 | PASS 1475 ]
> 
> proc.time()
   user  system elapsed 
2087.21  115.53 2266.14