Evaluation of a decided sample size in machine learning applications

An appropriate sample size is essential for obtaining a precise and reliable outcome of a study. In machine learning (ML), studies with inadequate samples suffer from overfitting of data and have a lower probability of producing true effects, while the increment in sample size increases the accuracy of prediction but may not cause a significant change after a certain sample size. Existing statistical approaches using standardized mean difference, effect size, and statistical power for determining sample size are potentially biased due to miscalculations or lack of experimental details. This study aims to design criteria for evaluating sample size in ML studies. We examined the average and grand effect sizes and the performance of five ML methods using simulated datasets and three real datasets to derive the criteria for sample size. We systematically increase the sample size, starting from 16, by randomly sampling and examine the impact of sample size on classifiers' performance and both effect sizes. Tenfold cross-validation was used to quantify the accuracy.

The results demonstrate that the effect sizes and the classification accuracies increase while the variances in effect sizes shrink with the increment of samples when the datasets have a good discriminative power between two classes. By contrast, indeterminate datasets had poor effect sizes and classification accuracies, which did not improve by increasing sample size in both simulated and real datasets. A good dataset exhibited a significant difference in average and grand effect sizes. We derived two criteria based on the above findings to assess a decided sample size by combining the effect size and the ML accuracy. The sample size is considered suitable when it has appropriate effect sizes (≥ 0.5) and ML accuracy (≥ 80%). After an appropriate sample size, the increment in samples will not benefit as it will not significantly change the effect size and accuracy, thereby resulting in a good cost-benefit ratio.