FFT Data Analysis

Grand Average Data (n = 24 participants).

LINEAR MIXED EFFECT MODEL and ANOVA Analysis of Individual Mean Z-scores for all Duty Cycle conditions : independent variable Stimulus Zscore

Shapiro-Wilk Test for Normality by Duty Cycle
	DutyCycle	W	p_value
25.W	25	0.9504829	0.2775412
50.W	50	0.9124321	0.0398379
75.W	75	0.9684628	0.6291927
100.W	100	0.9511739	0.2872247

Levene’s Test for Homogeneity of Variance
Df	F.value	Pr..F.
3	0.6434267	0.5890433
92	NA	NA

Summary :

Normality: The meanZscore is normally distributed in the 25%, 75%, and 100% DutyCycle groups, but not in the 50% group.
Homogeneity of Variance: The assumption of homogeneity of variances is satisfied.

Linear mixed effect model with lmer and effect of stimulus z-score on tapping z-score

## Warning: 'r.squaredGLMM' now calculates a revised statistic. See the help page.

ANOVA Table with Marginal and Conditional R²
	F	Df	Df.res	Pr(>F)	Marginal R²	Conditional R²
stimcochZscore	4.464571	1	71	0.0381215	0.006744	0.8564975

Linear mixed effect model with duty cycle as categorical fixed effect

ANOVA Table with CATEGORICAL DUTY CYCLE and Marginal and Conditional R²
	F	Df	Df.res	Pr(>F)	Marginal R²	Conditional R²
DutyCycle	1.649764	3	69	0.185929	0.0076058	0.8540083

## Warning: Using `size` aesthetic for lines was deprecated in ggplot2 3.4.0.
## ℹ Please use `linewidth` instead.
## This warning is displayed once every 8 hours.
## Call `lifecycle::last_lifecycle_warnings()` to see where this warning was
## generated.

## Warning: Removed 672 rows containing missing values (`geom_flat_violin()`).

## Warning: Using the `size` aesthetic with geom_polygon was deprecated in ggplot2 3.4.0.
## ℹ Please use the `linewidth` aesthetic instead.
## This warning is displayed once every 8 hours.
## Call `lifecycle::last_lifecycle_warnings()` to see where this warning was
## generated.

## Warning: Removed 672 rows containing missing values (`geom_flat_violin()`).

Model 1: The effect of stimcochZscore (as a continuous variable) on the mean Z-score is statistically significant (p = 0.038). This suggests that there is a significant relationship between the continuous stimulus Z-score and the mean Z-score.

Model 2: The effect of DutyCycle (as a categorical variable) on the mean Z-score is not statistically significant (p = 0.186). This means that, according to this model, there is no strong evidence that the mean Z-score differs significantly across the different DutyCycle conditions.

Explained Variance (R² Values):

Marginal R²: Both models have very low Marginal R² values (0.0076 for Model 1 and 0.0067 for Model 2), indicating that the fixed effects (either DutyCycle or stimcochZscore) explain only a small portion of the variance in the mean Z-score. Conditional R²: The Conditional R² values are quite high for both models (0.8540 for Model 1 and 0.8565 for Model 2), suggesting that most of the variance in the mean Z-score is explained by the combination of the fixed effects and the random effects (mainly individual differences across subjects).

T-test against stim Zscore

T-test Results and Cohen’s d by Duty Cycle
	DutyCycle	t_statistic	p_value	mean_diff	cohen_d
t	25	7.338818	0.0000002	0.7080176	1.4980299
t1	50	4.599911	0.0001262	0.4885974	0.9389529
t2	75	5.227172	0.0000266	0.4567302	1.0669921
t3	100	3.875900	0.0007652	0.3769385	0.7911648

Summary :

t-tests against stimulus z-score : For all Duty Cycle conditions, the mean Z-scores are significantly different from the stimulus Z-scores, with large effect sizes for all conditions.

Linear mixed effect model to see if EEG z-scores predict tapping z-scores

ANOVA Table with fixed effect EEG-zscore and random effect Subject and Marginal and Conditional R²
	F	Df	Df.res	Pr(>F)	Marginal R²	Conditional R²
meanZscore_eeg	0.0970441	1	75.20113	0.756268	0.0002615	0.8462149

Stability Data Analysis.

Statistical Analysis

Friedman test

Shapiro-Wilk Test for Normality by Duty Cycle
	DutyCycle	W	p_value
25.W	25	0.8911232	0.0140223
50.W	50	0.8554714	0.0027667
75.W	75	0.8668455	0.0045657
100.W	100	0.8522073	0.0024030

Levene’s Test for Homogeneity of Variance
Df	F.value	Pr..F.
3	0.5530682	0.6473648
92	NA	NA

Friedman with Duty Cycle as independent variable

Friedman Test Results for Mean Z-scores by Duty Cycle
	Test	Chi_Squared	df	p_value	Kendall_W
df	Friedman	8.85	3	0.0313531	0.1229167

Conover Test Results with Bonferroni Correction for Rvalues by Duty Cycle
Comparison	DutyCycle	p_value
50	25	1.0000000
50	50	NA
50	75	NA
75	25	0.0540225
75	50	0.0540225
75	75	NA
100	25	1.0000000
100	50	1.0000000
100	75	0.6381821

Summary :

Normality: The R value does not follow a normal distribution in any of the duty cycle groups.
Homogeneity of Variance: The assumption of homogeneity of variances is satisfied
Friedman rank sum test: significant differences in the Rvalue distributions across the duty cycle groups, BUT small effect size !!.
Post-hoc analysis: Pairwise comparisons are not significant when pvalue is corrected for multiple comparisons.

Correlation between FFT and Stability Analysis of Tapping

Spearman Correlation between Stability and FFT Z-scores by Duty Cycle
DutyCycle	correlation	p_value
25	0.9034783	2.7e-06
50	0.8843478	2.7e-06
75	0.8782609	2.6e-06
100	0.9173913	2.5e-06

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

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

Correlation between EEG FFT and TAP FFT

Spearman Correlation between EEG and Tap Z-scores by Duty Cycle
DutyCycle	correlation	p_value
25	0.2982609	0.1566372
50	0.1895652	0.3732832
75	0.4443478	0.0307593
100	0.2626087	0.2142305

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

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

Correlation between EEG FFT and Stability

Spearman Correlation between EEG and Tap Z-scores by Duty Cycle
DutyCycle	correlation	p_value
25	0.1852174	0.3845155
50	0.2878261	0.1721935
75	0.3704348	0.0755451
100	0.2252174	0.2886250

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

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

ACF Data Analysis

Shapiro-Wilk Test for Normality by Duty Cycle
	DutyCycle	W	p_value
25.W	25	0.8911232	0.0140223
50.W	50	0.8554714	0.0027667
75.W	75	0.8668455	0.0045657
100.W	100	0.8522073	0.0024030

Levene’s Test for Homogeneity of Variance
Df	F.value	Pr..F.
3	0.5530682	0.6473648
92	NA	NA

LINEAR MIXED EFFECT MODEL WITH CATEGORICAL DATA

##  DutyCycle emmean    SE   df lower.CL upper.CL t.ratio p.value
##  25         0.787 0.152 26.9    0.475     1.10   5.181  <.0001
##  50         0.688 0.152 26.9    0.376     1.00   4.529  0.0001
##  75         0.696 0.152 26.9    0.384     1.01   4.581  0.0001
##  100        0.728 0.152 26.9    0.416     1.04   4.794  0.0001
## 
## Degrees-of-freedom method: kenward-roger 
## Confidence level used: 0.95

##  DutyCycle emmean    SE   df t.ratio p.value
##  25         0.787 0.152 26.9   5.181  <.0001
##  50         0.688 0.152 26.9   4.529  0.0001
##  75         0.696 0.152 26.9   4.581  0.0001
##  100        0.728 0.152 26.9   4.794  0.0001
## 
## Degrees-of-freedom method: kenward-roger

##  DutyCycle emmean    SE   df   null t.ratio p.value
##  25         0.787 0.152 26.9 -0.330   7.351  <.0001
##  50         0.688 0.152 26.9 -0.361   6.903  <.0001
##  75         0.696 0.152 26.9 -0.372   7.028  <.0001
##  100        0.728 0.152 26.9 -0.398   7.417  <.0001
## 
## Degrees-of-freedom method: kenward-roger

##  DutyCycle emmean    SE   df t.ratio p.value
##  25         0.787 0.152 26.9   5.181  <.0001
##  50         0.688 0.152 26.9   4.529  0.0001
##  75         0.696 0.152 26.9   4.581  0.0001
##  100        0.728 0.152 26.9   4.794  0.0001
## 
## Degrees-of-freedom method: kenward-roger

## 
##  Shapiro-Wilk normality test
## 
## data:  residuals(model_acf)
## W = 0.91287, p-value = 8.842e-06

## 
##  Anderson-Darling normality test
## 
## data:  residuals(model_acf)
## A = 2.5856, p-value = 1.427e-06

ANOVA Table with Marginal and Conditional R² and Post-hoc Comparisons
	F	Df	Df.res	Pr(>F)	Marginal R²	Conditional R²	Comparison
DutyCycle	0.8602011	3	69	0.4660186	0.006744	0.8564975	ANOVA Main Effect

Friedman test

Friedman Test Results for ACF Mean Z-scores by Duty Cycle
	Test	Chi_Squared	df	p_value	Kendall_W
df	Friedman	2.45	3	0.484395	0.0340278

Wilcoxon against zero

Wilcoxon Signed-Rank Test Against Zero for Mean Z-scores by Duty Cycle
	DutyCycle	W	p_value
25.V	25	273	0.0001496
50.V	50	255	0.0017796
75.V	75	268	0.0003223
100.V	100	261	0.0008463

All significantly different from zero

Wilcoxon against stimulus

Wilcoxon Signed-Rank Test Against Stim for Mean Z-scores by Duty Cycle
	DutyCycle	W	p_value
25.V	25	293	2.3e-06
50.V	50	294	1.7e-06
75.V	75	297	6.0e-07
100.V	100	298	4.0e-07

## Warning: Removed 354 rows containing missing values (`geom_flat_violin()`).

## Warning: Removed 354 rows containing missing values (`geom_flat_violin()`).

Summary :

Normality: The meter-related z-scores do not follow a normal distribution in any of the duty cycle groups.
Homogeneity of Variance: Variances are homogeneous across the groups.
Friedman rank sum test: NO significant differences in the meter-related z-scores distributions across the duty cycle groups, BUT small effect size !!.
The Wilcoxon Signed-Rank Test indicates significant differences between the mean Z-scores and the stimulus Z-score across all duty cycle conditions..

Tapping Results

Flora

2024-09-04

FFT Data Analysis

Grand Average Data (n = 24 participants).

LINEAR MIXED EFFECT MODEL and ANOVA Analysis of Individual Mean Z-scores for all Duty Cycle conditions : independent variable Stimulus Zscore

Summary :

Linear mixed effect model with lmer and effect of stimulus z-score on tapping z-score

Linear mixed effect model with duty cycle as categorical fixed effect

T-test against stim Zscore

Summary :

Linear mixed effect model to see if EEG z-scores predict tapping z-scores

Stability Data Analysis.

Statistical Analysis

Friedman test

Friedman with Duty Cycle as independent variable

Summary :

Correlation between FFT and Stability Analysis of Tapping

Correlation between EEG FFT and TAP FFT

Correlation between EEG FFT and Stability

ACF Data Analysis

LINEAR MIXED EFFECT MODEL WITH CATEGORICAL DATA

Friedman test

Wilcoxon against zero

All significantly different from zero

Wilcoxon against stimulus

Summary :