The design of experiment (DOE) functions and plots can be used for constructing experimental design matrices, for analyzing and screening factors, for developing statistical models, and for performing Monte Carlo simulations.

You can create design matrices using built-in functions. With the DOE utility functions, you can analyze the properties of fractional factorial design matrices or you can modify design matrices. For example, use the doelabel function to convert the coded values of a design matrix into real values. You can also use vector and matrix functions to further modify design matrices. For example, use stack to add center points to a full or fractional factorial design, or use augment to add an outer array accounting for the noise factors in Taguchi designs.

To screen factors, you can calculate the effects or the level effects of factors, interactions, or of the design blocking. The quickscreen function is ideal for screening 2–level coded designs. The effects function is a more general function that calculates level effects for any design matrices.

You can display the experiment results in a box plot, an effects plot, or a Pareto plot to decide whether factors are significant. You can also perform an analysis of variance (ANOVA) with the anova function to test if factors are significant.

You can use the polyfit function to quickly map a multivariate polynomial regression surface. If you want to work with regression coefficients instead, use the polyfitc function. This function also returns additional information about each regression coefficient. For a more complete set of diagnostics, use polyfitstat. This function returns model parameters, the output of polyfitc, an ANOVA for regression, and a detailed analysis for each run or data point used to create the multivariate polynomial regression surface. To enhance numerical accuracy, the data is scaled internally by the standard deviation in all the polynomial regression functions if a full-order model is specified. If a partial or incomplete polynomial is specified, no scaling is performed.

For other types of fitting functions, use the multidfit function to calculate their fitting parameters.

All of the above functions accept design matrices.

Monte Carlo methods build up, over many iterations, the statistical behavior of a complex system made of components with unique variances. Instead of finding algorithmic, closed-form solutions, these methods iteratively apply random values to each component value to model the statistical behavior of the complex system.

You can generate random numbers for Monte Carlo simulations using one of the following functions: LogNormal, Normal, Uniform, Weibull. You can also use the montecarlo function to create a Monte Carlo sample for a given function. This is useful, for example, to predict the behavior of future experiments using regression models created from previous experiments.