In this paper, we assume the error distribution of one-way ANOVA as alpha-skew normal distribution. Alpha-skew gives us exibility for modelling data which has heavy tailness, skewness, bimodality and also symmetricity. We obtain maximum likelihood estimator model parameters test statistics based on these estimators. Monte Carlo simulation study states that estimators interest are more efficient...

Download the file ANOVA1.sas from my SAS programs page and run it. The contrived data (I created them with SAS' normal random number generator) are within the program. We shall imagine that we are evaluating the effectiveness of a new drug (Athenopram HBr) for the treatment of persons with depressive and anxiety disorders. Our independent variable is the daily dose of the drug given to such per...

Analysis of variance (ANOVA) is one of the most frequently used statistical methods in medical research. The need for ANOVA arises from the error of alpha level inflation, which increases Type 1 error probability (false positive) and is caused by multiple comparisons. ANOVA uses the statistic F, which is the ratio of between and within group variances. The main interest of analysis is focused o...

Eta squared is a popular effect size, but contains positive bias. Bootstrapping can be used to remove the bias from eta squared. Compared epsilon and omega squared, bootstrap correction does not make distributional assumption, it easy implement. A real example computer simulations are included illustrate its application. The bias-corrected shows very...

We consider testing the main treatment effects and interaction effects in crossed two-way layout when one factor or both factors have large number of levels. Random errors are allowed to be nonnormal and heteroscedastic. In heteroscedastic case, we propose new test statistics. The asymptotic distributions of our test statistics are derived under both the null hypothesis and local alternatives. ...