An accurate and efficient numerical approximation of the multivariate normal (MVN) distribution function is necessary for obtaining maximum likeli- hood estimates for models involving the MVN distribution. Numerical integration through simulation (Monte Carlo) or number-theoretic (quasi-Monte...

The development and use of synthetic regression models has proven to assist statisticians in better understanding bias in data, as well as how to best interpret various statistics associated with a modeling situation. In this article, I present code that can be easily amended for the creation of...

This article concerns the nonparametric Fisher-Pitman tests for paired replicates and independent samples. After outlining the theory of exact tests, I derive Monte Carlo simulations for both of them. Simulations can be useful if one deals with many observations because of the complexity of the...

I introduce the new mgof command to compute distributional tests for discrete (categorical, multinomial) variables. The command supports large-sample tests for complex survey designs and exact tests for small samples as well as classic large-sample Chi^2-approximation tests based on Pearson’s...

We outline a novel approach to calculate exact p-levels for two-sample randomization tests. The approach closely resembles permute in its applications, with the main difference being that the results are approximated only if the execution time needed to calculate exact p-levels would exceed a...

I present applications of Stata to conduct power analysis for multiple regression. Simple power analyses are provided through the Stata command power and the user-written command powerreg. However, tools for power analysis for multiple regression coefficients are limited. I present strategies...