First of all I wanted to thank you for this really helpful website and resource pack!
As a practice example I used Ex#2 of Basic concepts for ANOVA to perform, Shapiro-Wilk-Test, Levene-Test, and ANOVA. When I do the Shapiro-Wilk-Test on each of the groups I find that groups/methods 2-4 follow a normal distribution but group/method 1 does not. I thought in the case of a non-normal distribution I wasn’t allowed to perform ANOVA. I’m not very advanced in statistics, so I would really appreciate your help.
Also, look at the very general and elegant power/sample-size calculator by Russel Lenth (U of Iowa). It handles tests of means (one or two samples), tests of proportions (one or two samples), linear regression, generic chi-square and Poisson tests, and an amazing variety of ANOVAs -- 1-, 2-, and 3-way; randomized complete-block; Latin and Greco-Latin squares; 1-stage, 2-stage, and factorial nested designs; crossover; split-plot; strip-plot; and more! This calculator is implemented in Java, and can be run as a web page, or can be downloaded to your computer to run offline as a stand-alone application.