Results

Main Effects Only Bayesian Repeated Measures ANOVA

Model Comparison
Models P(M) P(M|data) BFM BF10 error %
BeerType + CorrectIdentify 0.250 0.542 3.545 1.000  
BeerType 0.250 0.458 2.539 0.846 3.874
Null model (incl. subject and random slopes) 0.250 4.875×10-6 1.462×10-5 9.000×10-6 1.459
CorrectIdentify 0.250 4.580×10-6 1.374×10-5 8.456×10-6 1.865
Note.  All models include subject, and random slopes for all repeated measures factors.
Analysis of Effects
Effects P(incl) P(excl) P(incl|data) P(excl|data) BFincl
BeerType 0.500 0.500 1.000 9.455×10-6 105766.059
CorrectIdentify 0.500 0.500 0.542 0.458 1.182
Model Averaged Posterior Summary
95% Credible Interval
Variable Level Mean SD Lower Upper
Intercept 47.521 2.590 42.391 52.653
BeerType Alcoholic 9.681 1.807 6.015 13.184
NonAlcoholic -9.681 1.807 -13.400 -6.187
CorrectIdentify 0 4.111 2.433 -0.732 9.050
1 -4.111 2.433 -9.138 0.505

Single Model Inference

Single Model Posterior Summary
95% Credible Interval
Variable Level Mean SD Lower Upper
Intercept 48.314 2.482 43.483 53.102
BeerType Alcoholic 9.649 1.769 6.090 13.132
NonAlcoholic -9.649 1.769 -13.132 -6.090
CorrectIdentify 0 4.081 2.488 -0.658 9.144
1 -4.081 2.488 -9.144 0.658

Based on these posterior estimates, what would we estimate for certain participants in certain situations?

For instance, if we had to give our best guess of a person tasting a non-alcoholic beer, who correctly identified it? Using the main effects model (two main effects and no interaction):

48.340 + (-9.637) + (-4.151) = 34.552

If they would have guess incorrectly:

48.340 + (-9.637) + (4.151) = 42.854


Single Model Posterior Distributions

BeerType
CorrectIdentify
Single Model R²
95% Credible Interval
  Mean Lower Upper
R² 0.356 0.220 0.482

Descriptives

Descriptives
95% Credible Interval
BeerType CorrectIdentify N Mean SD SE Coefficient of variation Lower Upper
Alcoholic 0 15 49.467 20.406 5.269 0.413 38.166 60.767
  1 42 59.155 19.821 3.058 0.335 52.978 65.331
NonAlcoholic 0 15 57.667 20.166 5.207 0.350 46.499 68.834
  1 42 28.714 17.425 2.689 0.607 23.284 34.144

Descriptives plots

Bayesian Repeated Measures ANOVA: Interaction

Model Comparison
Models P(M) P(M|data) BFM BF10 error %
BeerType + CorrectIdentify + BeerType ✻  CorrectIdentify 0.200 1.000 205687.037 1.000  
BeerType + CorrectIdentify 0.200 1.054×10-5 4.218×10-5 1.055×10-5 3.565
BeerType 0.200 8.902×10-6 3.561×10-5 8.902×10-6 4.479
Null model (incl. subject and random slopes) 0.200 9.190×10-11 3.676×10-10 9.190×10-11 1.603
CorrectIdentify 0.200 8.590×10-11 3.436×10-10 8.590×10-11 1.897
Note.  All models include subject, and random slopes for all repeated measures factors.
Analysis of Effects
Effects P(incl) P(excl) P(incl|data) P(excl|data) BFincl
BeerType 0.400 0.400 1.945×10-5 1.778×10-10 109370.612
CorrectIdentify 0.400 0.400 1.055×10-5 8.902×10-6 1.185
BeerType ✻  CorrectIdentify 0.200 0.200 1.000 1.054×10-5 94830.521
Note.  Compares models that contain the effect to equivalent models stripped of the effect. Higher-order interactions are excluded. Analysis suggested by Sebastiaan Mathôt.

Single Model Inference

Single Model Posterior Summary
95% Credible Interval
Variable Level Mean SD Lower Upper
Intercept 48.564 2.287 44.107 52.984
BeerType Alcoholic 5.398 1.718 2.165 8.773
NonAlcoholic -5.398 1.718 -8.773 -2.165
CorrectIdentify 0 4.124 2.317 -0.672 8.555
1 -4.124 2.317 -8.555 0.672
BeerType ✻  CorrectIdentify Alcoholic & 0 -9.346 1.796 -12.785 -5.817
Alcoholic & 1 9.346 1.796 5.817 12.785
NonAlcoholic & 0 9.346 1.796 5.817 12.785
NonAlcoholic & 1 -9.346 1.796 -12.785 -5.817

Based on these posterior estimates, what would we estimate for certain participants in certain situations?

For instance, if we had to give our best guess of a person tasting a non-alcholic beer, who correctly identified it? Using the full model (two main effects and interaction):

48.340 + (-5.278) + (-0.4039) + (-9.403) = 33.255

If they would have guess incorrectly:

48.340 + (-5.278) + (0.4039) + (9.403) = 52.869


Single Model Posterior Distributions

BeerType
CorrectIdentify
BeerType ✻ CorrectIdentify

Descriptives

Descriptives
95% Credible Interval
BeerType CorrectIdentify N Mean SD SE Coefficient of variation Lower Upper
Alcoholic 0 15 49.467 20.406 5.269 0.413 38.166 60.767
  1 42 59.155 19.821 3.058 0.335 52.978 65.331
NonAlcoholic 0 15 57.667 20.166 5.207 0.350 46.499 68.834
  1 42 28.714 17.425 2.689 0.607 23.284 34.144

Descriptives plots