Determination of the Sample Size on Different Independent K Group Comparisons by Power Analysis

Abstract

The purpose of this study was to determine the number of samples that should be used in independent treatment comparisons with different effect sizes (0.25-3.0), the number of treatments (2-5), and the power of the test (70% -95%) in single and multi-factor treatments. The material of the study was the random numbers drawn from the population that shows a normal distribution with N (0, 1) parameter. The power of the test was calculated by sampling with replacement from the population and after the differences between the treatments in terms of standard deviation were established, 10000 simulations were performed. This setup was carried out for experiments with one, two, and three factors. In the comparison of single factor independent treatment means, when the effect size was larger than Δ = 2 and the test power was between 70% and 95%, the sample sizes varied between 3 and 7. In the comparison of two-factor independent treatment means, when the effect size was larger than Δ = 2 and the test power was between 70% and 95%, the sample sizes varied between 2 and 3. In the comparison of three-factor independent treatment means, when the effect size was larger than Δ= 1.5 and the test power was between 70% and 95%, the sample size was 2. If all treatment comparisons were generalized; it was observed that when the effect size increased, and the power of the test decreased, the sample size decreased In the t-test and F tests used in independent treatment comparisons, a power analysis was performed under different situations, and the number of experimental units for each 5% power increment between 70% and 95% were presented in tables. These tables, may help researchers to determine the number of samples without power analysis in independent group comparisons.

Keywords

• independent treatment comparisons
• power analysis
• effect size
• sample size
• f-t test
• simulation