Abstract :
The nonparametric Mann-Whitney U test is an alternative to parametric Student’s t-test, when the assumptions of t-test cannot be respected. However as one understood, it is more reliable to use the t-test if its assumptions can be met. The purpose of this study is to analyze the performances of the Mann- Whitney U test and Student’s t test in cases of normal populations and various sample sizes. A Monte Carlo simulation study is cariried out via data which were produced from standard normal distribution. Dual combinations of populations were used, with a difference between the means of δ=0, δ=0.5σ, δ=1σ and, variance ratios of 1:1, 1:4, 1:9. To compute Type I error rate and test power, 20000 trial were made for each condition. For each combination, two samples with various sample sizes were randomly selected; both tests were applied, and the number of rejected null hypotheses was recorded. The MWU test gave fewer errors in small samples (n≤30). MWU and t tests gave the same result at 98% rate in rejecting or accepting the H0 hypothesis. In case of unequal variance, as sample size increased, the type I error ratio increased, particularly for the U test; both tests gave the same result in approximately 97% of simulations.
NaturalLanguageKeyword :
Type I error , Test power , Mann , Whitney U test , Students’ t test , Monte Carlo Simulation
