Efficient determination of the size of experiments by using graphs in balanced design of experiments

Purpose: The algorithm described in Lim(1998) is available to determine the sample size directly given specified significance level, power and signal-to-noise ratio. We research on the efficient determination of the sample size by visual methods. Methods: We propose three graphs for investigating the mutual relationship between the sample size r, power $1-{\beta}$ and the detectable signal-to-noise ratio ${\Delta}$. First graph shows the relationship between ${\Delta}$ and $1-{\beta}$ for the given r and it can be checked whether the power is sufficient enough. Second graph shows the relationship between r and ${\Delta}$ for the given power $1-{\beta}$. Third graph shows the relationship between r and $1-{\beta}$ for the given ${\Delta}$. It can be checked that which effects are sensitive to the efficient sample size by investigating those graphs. Results: In factorial design, randomized block design and the split plot design how to determine the sample size directly given specified significance level, power and signal-to-noise ratio is programmed by using R. A experiment to study the split plot design in Hicks(1982) is used as an example. We compare the sample sizes calculated by randomized block design with those by split plot design. By using graphs, we can check the possibility of reducing the sample size efficiently. Conclusion: The proposed visual methods can help an engineer to make a proper plan to reduce the sample size.

균형된 실험계획법에서 그래프를 활용한 실험의 크기의 효율적인 결정