Event-related potentials (ERPs) are estimated by averaging time-locked single trial electroencephalography (EEG) signals in response to specific events or stimuli. Classifying ERPs accurately is a challenge because (a) single trials have poor signal-to-noise-ratios (SNRs) and (b) it is difficult to collect large single trial ensembles to generate high SNR ERPs for classifier training and testing. The m-subsample averaging (m-SA) strategy which generates small-sample ERPs by repeated averaging of a small number of single trials drawn without replacement, has been proposed as a solution to the two problems. An ERP formed by averaging m single trials is referred to as an m-ERP where m is referred to as the averaging parameter. In this study, we conduct thorough analyses of m-SA and focus on issues not addressed in previous studies to better understand the beneficial properties of m-SA and to further support its application for ERP classification. Specifically, we (a) analyze the improvement in SNR as a function of m using the mean-root-mean-square SNR and visual analyses of m-ERP plots with confidence intervals, (b) analyze the improvement in interclass separation as a function of m, (c) determine how the SNR and interclass separation analyses can help to select the averaging parameter m, (d) determine the number of distinct m-ERPs that can be drawn from a single-trial ensemble, and (e) determine several probabilities related to the generation of distinct m-ERPs. Furthermore, an extensive set of experiments are designed to analyze the performance of support vector machine and convolution neural network classifiers employing m-SA with various combinations of the averaging parameters used for generating the training and test sets. The results confirm that ERPs can be classified accurately using small subsample averaging. Most importantly, it is concluded that m-SA can be deployed in practice to accurately classify ERPs in brain activity research and in clinical applications without having to collect a prohibitively large number of single trials.

Abstract Background: Cluster randomized controlled trials are increasingly becoming popular in public health research interventions and health services research in primary health care design and use in low and middle-income countries. However, the majority of researchers in these trials did not account correctly for the effect of confounders and clustering in the design and analysis stages. Objectives: This article aimed to review the main implications of implementing a cluster randomized controlled trials design in public health research and emphasize the practical application of proper analytical methods and the performance of different statistical models. Methods: The practical application of various analytical methods is validated via the utilization of experimental data from a public health research case study. This article also demonstrated the performance of hierarchical models and made comparisons in terms of empirically precise effect size estimates. Results: Three hierarchical statistical models were provided with highly varied effect sizes during the analysis of the intervention effect on outcome, such as model 1 (AOR: 14.32; 95% CI: 3.75–54.68), model 2 (ARR: 3.52; 95% CI: 2.16–5.77), and model 3 (ARR: 4.79; 95% CI: 2.69–5.52).Conclusion: Inaccurate results and potentially misleading conclusions can arise from improper cluster randomized controlled trial designs and analyses. This article has shown that real-world data can be adjusted for the effects of confounders and clustering, and we advocate for the routine use of suitable design and analytical methods. This article concludes that researchers should be careful when selecting hierarchical models to analyze cluster randomized controlled trials.