Determination of sample size for 80% power in different correlation structures in multiple linear regression analysis

Nowadays, statistical inference methods are used in almost all science branches. As for linear regression analysis, it is one of the oldest and the most commonly used of these inference methods. If findings obtained from statistical methods, parameters estimated and inferences are to be sound and reliable, assumptions related to these methods must be ensured. In order to avoid these errors checklists concerning to the qualifications which a study should have are utilized. In today's studies giving only the p values is not regarded as acceptable, instead the information like standart error, confidence interval, effect size and statistical power is asked to be presented in the report of the study. In this context, it is very important for the sample size to be determined correctly so that a planned linear regression analysis can have enough statistical power. In linear regression analyses, sample size is determined with simple and practical approaches called Rules of Thumb. However, sample sizes determined with rules of thumb do not convey any information about the power of the study. Therefore, for a planned linear regression analysis sample size should be calculated with effect size and power calculation methods. In this study, sample size will be determined for 80% power in different correlation structures in multiple linear regression analysis, using simulation method. For the desired statistical power sample sizes obtained with both rules of thumb approach and simulation study will be compared and discussed. Key Words: Multiple Linear Regression Analysis, Effect Size, Statistical Power, Sample Size, Simulation Study