2.8 Data Analysis
Descriptive data including means and standard deviations are reported. To provide a better comparison between means with differing standard deviations, coefficients of variation (CV ), a measure of relative variability calculated as the ratio of the standard deviation to the mean, are reported.
The reliability of the STP approach was evaluated for each component by conducting both split-half and test-retest reliability tests on each participant’s trial-by-trial baseline-to-peak data using the Pearson’s Product Moment correlation procedures in MATLAB (R2020b). For split-half reliability, the mean baseline-to-peak amplitudes for each participant’s even trials were correlated to the mean baseline-to-peak amplitudes of their odd trials separately for Block One (trials 1 – 240) and for Block Two (trials 241-480). A similar process was utilized for the peak-to-peak and STW data. For test-retest reliability, the mean baseline-to-peak amplitudes of trials in Block One (trials 1 – 240) for each participant were correlated to their mean baseline-to-peak amplitudes of trials in Block Two (trials 241 – 480). The test-retest reliability for the peak-to-peak data of the STP and for STW data were conducted in a similar manner. When deriving the mean of the amplitudes for each component in all approaches, trials with scores of null and 0 values were eliminated, resulting in data loss of 0.2% to 1.6% of all trials (See Table 6).
Two statistical approaches were used to provide evidence of the validity of the STP approach. The first approach used the Standard Error of Measurement (SEM) to compare the variability of the trial-by-trail STP data to the variability of the trial-by-trail STW data. The SEM of each component was calculated across all trials for each participant (Luck et al., 2021). The SEM was calculated by dividing the standard deviation of the baseline-to-peak single trial ERP amplitudes by the square root of the number of trials. A Pearson’s correlation coefficient was calculated in SPSS 26 to compare the STP and STW approaches, where an rvalue can be interpreted as: < 0.5 poor, 0.5-0.75 moderate, .075 - 0.9 good, > 0.9 excellent (Koo & Li, 2016; Portney & Watkins, 2009). The STW approach does not yield latency information; therefore, SEMs for latency were only calculated for the STP approach.
To provide further evidence of the validity of the STP approach, separate linear regression analyses across all participants were completed for each of the components (P1, N1, P2, N2 and P3) to determine the extent to which measures derived from the STP approach accounted for the variance of the component’s amplitude measures derived from the averaged ERP. Analyses of each component began by determining for each participant their mean and the standard deviation of trial-by-trial baseline-to-peak amplitudes from the STP approach, their mean and standard deviation of the trial-by-trial peak latencies from the STP approach, and their mean of the trial-by-trial noise measures. Then the regression analysis was conducted using the general model of four input variables entered in three steps. In the first step the mean of the baseline-to-peak amplitudes was the sole predictor variable. The second step added the two standard deviations, one for the baseline-to-peak amplitudes and one for the latencies. The third step added the mean of the noise measure.
The possibility of systematic change across the single trial data was evaluated using an exploratory curve-fitting approach implemented via the Curve Fitting app in MATLAB (2020b). Curve fitting for each component within each trial began by computing the mean of the ST baseline-to-peak ERP amplitudes across all participants. Scatterplots of these mean amplitudes (y-axis) as a function of trial number (x-axis) were then created and then followed by curve fits performed using sum of sines models where the number of terms was varied from one to four until overfitting was observed (e.g., Figure 1). For purposes of comparison, this curve fitting approach was also applied to peak-to-peak ERP amplitudes and latencies from the STP approach, amplitudes from the STW approach, and response time data. The degree of fit for each curve is reported as R 2, the portion of variance of the amplitude measures accounted for by the curve plotted across trials.