Analysis of Variance (ANOVA) is a well-known method to test the equality of mean for two or more
groups. ANOVA is a robust test under the normality assumption. Arithmetic mean is used in the
computation of the ANOVA test. Mean is known to be sensitive towards outlier and this problem will
affect the robustness and power of ANOVA. In this study, modification of ANOVA was created using
one type of mean to replace arithmetic mean namely trimmed mean. New approaches were be obtained
for the computation of ANOVA. This study was conducted based on a simulation study and application
on real data. The performance of the modified ANOVA is then compared with the classical ANOVA
test in terms of Type I error rate. This innovation enhances the ability of modified ANOVA to provide
good control of Type I error rates. The findings were in favor of the modified ANOVA or better known
as ANOVATM.
This article investigates the performance of two-sample pseudo-median based procedure in testing differences between groups. The procedure is a modification of the one-sample Wilcoxon procedure using the pseudo-median of differences between group values as the central measure of location. The test was conducted on two groups with moderate sample
sizes of symmetric and asymmetric distributions. The performance of the procedure was measured in terms of Type I error and power rates computed via Monte Carlo methods. The performance of the procedure was compared against the t-test and Mann-Whitney-Wilcoxon test. The findings from this study revealed that the pseudo-median procedure performed very
well in controlling Type I error rates close to the nominal value. The pseudo-median procedure outperformed the MannWhitney-Wilcoxon test and is comparable to the t-test in controlling Type I error and maintaining adequate power.
The classical procedures of comparing two groups, such as t-test are, usually restricted with the assumptions of normality and equal variances. When these assumptions are violated, the rates of the Type I errors of the independent samples t-test are affected, particularly when the sample sizes are small. In this situation, the bootstrap procedure has an advantage over the parametric t-test. In this study, the performances of the bootstrap procedure and the independent sample t-test were investigated. The investigation focused on the power of both the test procedures to compare the two groups under different design specifications for normal and chi-square distributions. The results showed that the bootstrap procedure has a slight edge over the conventional t-test in term of the rate of achieving the benchmark level for both the distributions. In fact, the bootstrap procedure consistently outperformed the conventional t-test across all the combinations of the test conditions.
In many statistical analyses, data need to be approximately normal or normally distributed. The Kolmogorov-Smirnov test, Anderson-Darling test, Cramer-von Mises test, and Shapiro-Wilk test are four statistical tests that are widely used for checking normality. One of the factors that influence these tests is the sample size. Given any test of normality mentioned, this study determined the sample sizes at which the tests would indicate that the data is not normal. The performance of the tests was evaluated under various spectrums of non-normal distributions and different sample sizes. The results showed that the Shapiro-Wilk test is the best normality test because this test rejects the null hypothesis of normality test at the smallest sample size compared to the other tests, for all levels of skewness and kurtosis of these distributions.