Determination of Minimum Sample Size Requirement for Multiple Linear Regression and Analysis of Covariance Based on Experimental and Non-experimental Studies

Background: MLR and ANCOVA are common statistical techniques and are used for both experimental and non-experimental studies. However, both types of study designs may require different basis of sample size requirement. Therefore, this study aims to proposed sample size guidelines for MLR and ANCOVA for both experimental and non-experimental studies. Methods: We estimated the minimum sample sizes required for MLR and ANCOVA by using Power and Sample Size software (PASS) based on the pre-specified values of alpha, power and effect size (R2). In addition, we also performed validation of the estimates using a real clinical data to evaluate how close the approximations of selected statistics which were derived from the samples were to the actual parameters in the targeted populations. All the coefficients, effect sizes and r-squared obtained from the sample were then compared with their respective parameters in the population. Results: Small minimum sample sizes required for performing both MLR and ANCOVA when r-squared is used as the effect size. However, the validation results based on an evaluation from a real-life dataset suggest that a minimum sample size of 300 or more is necessary to generate a close approximation of estimates with the parameters in the population. Conclusions: We proposed sample size calculation when r-squared is used as an effect size is more suitable for experimental studies. However, taking a larger sample size such as 300 or more is necessary for clinical survey that is conducted in a non-experimental manner.