Consistent ANOVA-type tests for various effect sizes

Analysis of variance (ANOVA) reveals some disadvantages, such as non-robustness against heteroscedastic or non-normal errors and using difference to overall mean as effect sizes only. As an alternative the multiple contrast test comparing to the overall mean is proposed for 7 effect sizes: ratio-to-OM, quantiles for both ratio or differences, odds ratios for continuous data, odds ratio for proportions, risk ratio/differences, relative effect size for continuous up to discrete data, and hazard ratio. Using CRAN packages the related analysis is simple.