JASP

First round of data collection results

Results for the first round of data collenction (i.e. participant #1 to participant #24):

Repeated Measures ANOVA

Frequentist RM ANOVA 2 X 2 X 3 with group (placebo, control), time (pretest, posttest), and eccentricity (10º, 20º, 30º) as factors.  

Within Subjects Effects
  Sphericity Correction Sum of Squares df Mean Square F p η²
Eccentricities Greenhouse-Geisser 0.200 1.718 0.117 14.288 < .001 0.390
Eccentricities ✻ Group Greenhouse-Geisser 0.004 1.718 0.003 0.320 0.695 0.009
Residual Greenhouse-Geisser 0.309 37.800 0.008    
Time Greenhouse-Geisser 0.135 1.000 0.135 28.128 < .001 0.509
Time ✻ Group Greenhouse-Geisser 0.025 1.000 0.025 5.147 0.033 0.093
Residual Greenhouse-Geisser 0.106 22.000 0.005    
Eccentricities ✻ Time Greenhouse-Geisser 0.035 ᵃ 1.584 ᵃ 0.022 ᵃ 9.381 ᵃ 0.001 ᵃ 0.299
Eccentricities ✻ Time ✻ Group Greenhouse-Geisser 1.063e -4 ᵃ 1.584 ᵃ 6.713e -5 ᵃ 0.028 ᵃ 0.948 ᵃ 0.001
Residual Greenhouse-Geisser 0.083 34.848 0.002    
Note.  Type III Sum of Squares
ᵃ Mauchly's test of sphericity indicates that the assumption of sphericity is violated (p < .05).

Here the results reveal a significant interaction between Time and Group factors. Therefore presenting evidence that groups' performance changed differently over time.

Between Subjects Effects
  Sum of Squares df Mean Square F p η²
Group 1.834e -4 1 1.834e -4 0.002 0.969 0.000
Residual 2.680 22 0.122    
Note.  Type III Sum of Squares

Descriptives

Descriptives Plots

Mean accuracy of stimulus detection as a function of eccentricities (10º, 20º, and 30º) for the placebo (leftmost) and the control group (rightmost). Error bars denote 95% confidence interval.

Group: Placebo
Group: Control

The interaction of time * group is significative.

Bayesian Repeated Measures ANOVA

Here we run a Bayesian mixed ANOVA using “default” priors (i.e., r = 0.5 for the fixed effects) with group (placebo, control), time (pretest, posttest), and eccentricity (10º, 20º, 30º) as factors. 

Model Comparison
Models P(M) P(M|data) BF M BF 10 error %
Null model (incl. subject) 0.053 1.020e  -10 1.836e -9 1.000
Time 0.053 1.502e  -7 2.703e -6 1472.303 0.843
Eccentricities 0.053 4.192e  -6 7.546e -5 41102.132 1.036
Time + Eccentricities 0.053 0.093 1.847 9.122e +8 1.313
Time + Eccentricities + Time  ✻  Eccentricities 0.053 0.198 4.445 1.942e +9 1.837
Group 0.053 5.202e -11 9.363e -10 0.510 1.984
Time + Group 0.053 8.122e  -8 1.462e -6 796.381 2.298
Eccentricities + Group 0.053 2.379e  -6 4.282e -5 23323.103 2.558
Time + Eccentricities + Group 0.053 0.055 1.041 5.362e +8 2.959
Time + Eccentricities + Time  ✻  Eccentricities + Group 0.053 0.117 2.376 1.143e +9 3.741
Time + Group + Time  ✻  Group 0.053 1.020e  -7 1.836e -6 999.993 2.669
Time + Eccentricities + Group + Time  ✻  Group 0.053 0.119 2.433 1.167e +9 3.459
Time + Eccentricities + Time  ✻  Eccentricities + Group + Time  ✻  Group 0.053 0.306 7.930 2.999e +9 4.224
Eccentricities + Group + Eccentricities  ✻  Group 0.053 3.549e  -7 6.389e -6 3480.221 3.698
Time + Eccentricities + Group + Eccentricities  ✻  Group 0.053 0.009 0.168 9.082e +7 4.412
Time + Eccentricities + Time  ✻  Eccentricities + Group + Eccentricities  ✻  Group 0.053 0.020 0.375 2.000e +8 5.442
Time + Eccentricities + Group + Time  ✻  Group + Eccentricities  ✻  Group 0.053 0.020 0.373 1.989e +8 5.063
Time + Eccentricities + Time  ✻  Eccentricities + Group + Time  ✻  Group + Eccentricities  ✻  Group 0.053 0.054 1.026 5.286e +8 5.968
Time + Eccentricities + Time  ✻  Eccentricities + Group + Time  ✻  Group + Eccentricities  ✻  Group + Time  ✻  Eccentricities  ✻  Group 0.053 0.009 0.161 8.717e +7 7.687
Note.  All models include subject.
Analysis of Effects
Effects P(incl) P(incl|data) BF Inclusion
Time 0.737 1.000 51566.701
Eccentricities 0.737 1.000 1.071e +6
Group 0.737 0.709 0.870
Time  ✻  Eccentricities 0.316 0.704 5.145
Time  ✻  Group 0.316 0.508 2.237
Eccentricities  ✻  Group 0.316 0.113 0.275
Time  ✻  Eccentricities  ✻  Group 0.053 0.009 0.161

The Model Comparison and the Analysis of Effects show evidences that there is an effect of the interaction of Time and group. Therefore presenting evidence that groups' performance changed differently over time.

Descriptives

Descriptive Statistics
Acuraccy 10._Pre Accuracy 20._Pre Accuracy 30._Pre Acuraccy 10._Post Acuraccy 20._Post Acuraccy 30._Post
  Placebo Control Placebo Control Placebo Control Placebo Control Placebo Control Placebo Control
Valid 12 12 12 12 12 12 12 12 12 12 12 12
Missing 0 0 0 0 0 0 0 0 0 0 0 0
Mean 0.8219 0.8281 0.7656 0.7948 0.6792 0.7156 0.8760 0.8344 0.8417 0.8177 0.8115 0.7917
Median 0.8062 0.8500 0.8187 0.8250 0.6937 0.7312 0.9000 0.8625 0.8438 0.8812 0.8375 0.8000
Std. Deviation 0.1286 0.1689 0.1513 0.1618 0.1483 0.1515 0.1198 0.1781 0.1080 0.1786 0.1406 0.2009