Sensitivity and robustness of randomization test and F‐test in some experimental designs

Abstract

AbstractThis work examined the sensitivity of randomization test and F‐test in completely randomized design, randomized complete block design and Latin square design in order to ascertain which is more robust in terms of power (sensitivity) of the test and type I error rate in cases with normal error, skewed error (Chi‐square and Exponential distributions), by varying the sample sizes. Using Monte Carlo simulation, response observations were generated for normal error, skewed error at various sample sizes for each of the experimental designs. The results showed that for the normal error, the power and type I error rate of the F‐test were slightly smaller and greater respectively in each of the designs than that of the randomization test. Furthermore, for the skewed error, the randomization test was more sensitive than the F‐test, and also, the type I error was smaller in each of the designs.