ANOVA is a test that provides a global assessment of a statistical difference in more than two independent means. In this example, we find that there is a statistically significant difference in mean weight loss among the four diets considered. In addition to reporting the results of the statistical test of hypothesis (., that there is a statistically significant difference in mean weight losses at α=), investigators should also report the observed sample means to facilitate interpretation of the results. In this example, participants in the low calorie diet lost an average of pounds over 8 weeks, as compared to and pounds in the low fat and low carbohydrate groups, respectively. Participants in the control group lost an average of pounds which could be called the placebo effect because these participants were not participating in an active arm of the trial specifically targeted for weight loss. Are the observed weight losses clinically meaningful?

Hello Charles,

Thank you very much for your reply!

1) For experiment 1, both data sets that failed the normality test (p= and p=) are not symmetric, according to the box plot. Therefore, a nonparametric test should be used for the analysis, right?

2) For experiment 2, there are two experimental groups. I only have three values for each group. The data for group A are: , , (normality test P<). The data for group B are: , , (normality test P=). The results from t-test (p=) and Mann-Whitney Rank sum test (p=) are very different.

Thank you!

Often, the reason you use a nested anova is because the higher level groups are expensive and lower levels are cheaper. Raising a rat is expensive, but looking at a tissue sample with a microscope is relatively cheap, so you want to reach an optimal balance of expensive rats and cheap observations. If the higher level groups are very inexpensive relative to the lower levels, you don't need a nested design; the most powerful design will be to take just one observation per higher level group. For example, let's say you're studying protein uptake in fruit flies ( Drosophila melanogaster ). You could take multiple tissue samples per fly and make multiple observations per tissue sample, but because raising 100 flies doesn't cost any more than raising 10 flies, it will be better to take one tissue sample per fly and one observation per tissue sample, and use as many flies as you can afford; you'll then be able to analyze the data with one-way anova. The variation among flies in this design will include the variation among tissue samples and among observations, so this will be the most statistically powerful design. The only reason for doing a nested anova in this case would be to see whether you're getting a lot of variation among tissue samples or among observations within tissue samples, which could tell you that you need to make your laboratory technique more consistent.

Mauchly's test is a commonly used test to determine whether the Sphericity assumption can be held. In the Mauchly's Test of Sphericity table of Origin result sheet, if the value of Prob>ChiSq is greater than or equal to , Sphericity can be assumed. In contrast, when the value Prob>ChiSq is less than , sphericity can not be assumed, and this leads to an increase in the Type I error. Therefore, modifications need to be made to the degrees of freedom so as to obtain a valid F-ratio. Luckily, the statistic epsilon of three correlations in the tests of within-subjects effects table can be used to evaluated that to which degree Sphericity has been violated and also make modifications to the degrees of freedom. In Origin, epsilons are generated using three methods: Greenhouse-Geisser , Huynh-Feldt , and Lower-bound . When epsilon is equal to 1, Sphericity is perfectly met. And the smaller the value of epsilon , the more serious the violation of Sphericity.

Mauchly's test is a commonly used test to determine whether the Sphericity assumption can be held. In the Mauchly's Test of Sphericity table of Origin result sheet, if the value of Prob>ChiSq is greater than or equal to , Sphericity can be assumed. In contrast, when the value Prob>ChiSq is less than , sphericity can not be assumed, and this leads to an increase in the Type I error. Therefore, modifications need to be made to the degrees of freedom so as to obtain a valid F-ratio. Luckily, the statistic epsilon of three correlations in the tests of within-subjects effects table can be used to evaluated that to which degree Sphericity has been violated and also make modifications to the degrees of freedom. In Origin, epsilons are generated using three methods: Greenhouse-Geisser , Huynh-Feldt , and Lower-bound . When epsilon is equal to 1, Sphericity is perfectly met. And the smaller the value of epsilon , the more serious the violation of Sphericity.