Level: Intermediate
Traditional experimental design is an analytical method that is based on decomposing the sum of squares using sigma, known as analysis of variance, on the premise that factors are mutually orthogonal, not limited to orthogonal arrays. However, this method cannot be applied when missing values occur, so it is necessary to carry out analysis using "linear estimation theory," which has provided a theoretical framework for analysis of variance. However, it is difficult to find books that explain this.
JMP's "Model Fit" also supports the analysis of orthogonal arrays with missing values, but how can one obtain an "estimate of the 95% confidence interval for the difference between the current level and the optimal level," a standard in orthogonal array analysis? Are the "Taguchi formula" or "Ina formula" for estimating these error variances built into JMP? It takes courage to trust the results of JMP as is without a book that explains the analytical procedures used to calculate them.
Here, we will show an analysis method using Excel's matrix functions when there is one missing value in an L8 orthogonal array, and by comparing it with the analysis results using JMP, we will deepen understanding of the calculation principles of "model fitting" and show a basic calculation method that can be used for further applications.
