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LINEAR MIXED MODEL (days x tDCS) -- scenario: lme_mergeA2_d0_13
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model: success ~ day * tDCS + (1|subject)   [tDCS: Electrode-Box-B2 = 1 vs Electrode-Box-A2 = 0]
N = 8 subjects, 98 sessions
day coverage: Box-B2 0..13, 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              98
    Fixed effects coefficients           4
    Random effects coefficients          8
    Covariance parameters                2

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

Model fit statistics:
    AIC       BIC       LogLikelihood    Deviance
    809.08    824.59    -398.54          797.08  

Fixed effects coefficients (95% CIs):
    Name                   Estimate    SE         tStat     DF    pValue    
    {'(Intercept)'}        19.458       3.7166    5.2352    94    1.0011e-06
    {'day'        }        7.1842      0.54693    13.135    94    5.4028e-23
    {'tDCS'       }         5.841       5.1946    1.1244    94       0.26369
    {'day:tDCS'   }        1.0024      0.73807    1.3581    94       0.17769


    Lower      Upper 
     12.078    26.837
     6.0982    8.2701
     -4.473    16.155
    -0.4631    2.4678

Random effects covariance parameters (95% CIs):
Group: subject (8 Levels)
    Name1                  Name2                  Type           Estimate
    {'(Intercept)'}        {'(Intercept)'}        {'std'}        0       


    Lower    Upper
    NaN      NaN  

Group: Error
    Name               Estimate    Lower     Upper 
    {'Res Std'}        14.123      12.278    16.245


effect                      t (df)         F (df1)       p
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days x tDCS (interaction)   t(94)=  1.36  F(1)=   1.844  p=0.1777
days (learning)             t(94)= 13.14  F(1)= 172.537  p=5.403e-23
tDCS (main, at Day 1)       t(94)=  1.12  F(1)=   1.264  p=0.2637

INTERPRETATION
  - days x tDCS interaction: n.s. (p=0.1777, slope diff=1.00) -> slopes are parallel (no differential change over training).
  - days (learning): SIGNIFICANT (p=5.4e-23) -> performance improves with training.
  - tDCS main effect on Day 1 (our day 0): n.s. (p=0.2637) -> 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.)