Author: Clemens Draxler and Andreas Kurz

# Testing in Conditional Likelihood Context: The R Package tcl

#### Clemens Draxler and Andreas Kurz

Abstract

An implementation of hypothesis testing in an extended Rasch modelling framework, including sample size planning procedures and power computations. Provides 4 statistical tests, i.e., gradient test (GR), likelihood ratio test (LR), Rao score or Lagrange multiplier test (RS), and Wald test, for testing a number of hypotheses referring to the Rasch model (RM), linear logistic test model (LLTM), rating scale model (RSM), and partial credit model (PCM). Three types of functions for power and sample size computations are provided. Firstly, functions to compute the sample size given a user-specified (predetermined) deviation from the hypothesis to be tested, the level alpha, and the power of the test. Secondly, functions to evaluate the power of the tests given a user-specified (predetermined) deviation from the hypothesis to be tested, the level alpha of the test, and the sample size. Thirdly, functions to evaluate the so-called post hoc power of the tests. This is the power of the tests given the observed deviation of the data from the hypothesis to be tested and a user-specified level alpha of the test. Power and sample size computations are based on a Monte Carlo simulation approach. It is computationally very efficient. The variance of the random error in computing power and sample size arising from the simulation approach is analytically derived by using the delta method.