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LINEAR MIXED MODEL (days x tDCS) -- scenario: lme_unmerged_full
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model: success ~ day * tDCS + (1|subject)   [tDCS: Electrode-Box-B2 = 1 vs Electrode-Box-A2 = 0]
N = 6 subjects, 71 sessions
day coverage: Box-B2 0..14, Box-A2 0..13
(day is raw and 0-indexed: our day 0 = the paper's "Day 1", so the tDCS
 main effect below is the group difference on Day 1 -- comparable to the paper.)

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FULL MODEL SUMMARY -- fitlme: success ~ day*tDCS + (1|subject)
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Linear mixed-effects model fit by ML

Model information:
    Number of observations              71
    Fixed effects coefficients           4
    Random effects coefficients          6
    Covariance parameters                2

Formula:
    success ~ 1 + day*tDCS + (1 | subject)

Model fit statistics:
    AIC       BIC      LogLikelihood    Deviance
    596.33    609.9    -292.16          584.33  

Fixed effects coefficients (95% CIs):
    Name                   Estimate    SE         tStat     DF    pValue    
    {'(Intercept)'}          21.53      5.5382    3.8874    67    0.00023506
    {'day'        }         6.6587     0.72367    9.2014    67    1.6706e-13
    {'tDCS'       }         8.0204      7.6977    1.0419    67        0.3012
    {'day:tDCS'   }        0.93747      0.9187    1.0204    67        0.3112


    Lower       Upper 
      10.475    32.584
      5.2143    8.1032
     -7.3444    23.385
    -0.89627    2.7712

Random effects covariance parameters (95% CIs):
Group: subject (6 Levels)
    Name1                  Name2                  Type           Estimate
    {'(Intercept)'}        {'(Intercept)'}        {'std'}        5.7931  


    Lower     Upper 
    2.4723    13.574

Group: Error
    Name               Estimate    Lower    Upper 
    {'Res Std'}        14.163      11.93    16.813


effect                      t (df)         F (df1)       p
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days x tDCS (interaction)   t(67)=  1.02  F(1)=   1.041  p=0.3112
days (learning)             t(67)=  9.20  F(1)=  84.665  p=1.671e-13
tDCS (main, at Day 1)       t(67)=  1.04  F(1)=   1.086  p=0.3012

INTERPRETATION
  - days x tDCS interaction: n.s. (p=0.3112, slope diff=0.94) -> slopes are parallel (no differential change over training).
  - days (learning): SIGNIFICANT (p=1.7e-13) -> performance improves with training.
  - tDCS main effect on Day 1 (our day 0): n.s. (p=0.3012) -> the groups are comparable (as in the paper) on Day 1.

Paper reference (N=24): interaction t(227)=2.68, F(1)=7.12, p=0.008;
  days t(227)=9.64, F(1)=267.64, p=1.2e-18; tDCS t(227)=0.23, F(1)=0.053, p=0.81.
  (Our N and exact statistics differ; this replicates the MODEL FORM on our data.)