You can try factorial arrangement anovs. Regards

Hello Abdul,

Two basic approaches are popular with such data sets:

1. Use anova (or the corresponding regression model) to evaluate a one-between subjects (group membership: 3 levels ), one within-subjects (occasion: before, after) design. In such a design, the most interesting effect is often the group by occasion interaction (as that would show evidence for a differential change from pre- to post- due to group/treatment).

2. Use the pre- scores as a covariate, and run a one-way ancova (the lone factor being group membership), using post- scores as the DV. These results may be easier to explain, especially if groups are not equivalent on the measure at the outset of the study. As is the case for #1, there is an analogous regression model that would allow for the same tests.

Both approaches require assumptions about model residuals ("errors"); the ancova also requires an assumption of homogeneity of regression slopes across groups.

Good luck with your work.

Choosing an appropriate statistical procedure to examine differences between data sets from three unmatched groups depends on the measurement level of your outcome variable and whether your data meet the normality assumption. For instance, if you have interval or ratio data that is normally distributed, you could go for one-way ANOVA. In case of having ordinal or non-normal data, you would better opt for the Kruskal-Wallis test. On the other hand, the chi-square test of independence can be the most appropriate procedure if your data is nominal. Here is a helpful read.

Beath, A., & Jones, M. P. (2018). Guided by the research design: Choosing the right statistical test. Med J Aust, 208(4), 163-165. https://doi.org/10.5694/mja17.00422

Good luck,

Thank you very much David Morse for your replying. I would like to know

1. which type of anova can i used in this case.

2. You mentioned that one-way ancova can be used in this data set and I wonder, can i use one-way ancova if I want to measure the differences of mean at PRE and POST treatment within/between three groups of treatments.

Thanks again

Hello again Abdul,

Via ancova, you can answer your question, about differences among groups across occasion. The distinction is, your estimated/predicted group scores on the DV, after adjustment on for differences on the covariate, can be compared to the grand mean of all groups on the covariate. This gives an "equal" start point for each group.

A number of studies about the measurement of change have indicated that either ancova or using estimated true scores for pre- and post- results is superior to using (fallible) pre- and post-treatment results as an indicator of score change.

However, if this is the statistic that is of utmost importance to you, then carry on with the one-between, one-within anova.

Good luck with your work.

Thank a lot David Morse for explanation.

You talk about Anova and Ancova, but at no time there was given even a faint information about the response variable.

Hello,

I want to say some general information.

1. Since in experimental studies sample size is usully small, sample distribution may not be valid (i.e. histogram is sharp). In experimental studies, population is potentially infinite (i.e. we can replicate cells and animals unlimitedly) and also the animal or cell samples have same genetics and are kept in standard conditions (without any confounding effect or sampling bias). Therefore, central limit theory is established even for small sample sizes (even n=2!!!) and sampling distribution is usually normal. In such conditions, we use general linear model (ANOVA) (I know that ANOVA is related to two parameters variance distribution, but I mean from the mean comparison point of view).

2. Sometimes, population distribution is right skewed in biological growth models. In such conditions we should use a generalized linear model (such as Poisson).

3. Non-parametric tests are underpowered in such sample sizes.

4. In experimental studies, sample size calculation is based on "law of diminishing returns" based on ANOVA degrees of freedom. Please find it in bellow sources.

Article How to calculate sample size in animal studies?

Article Sample Size Calculation in Animal Studies Using Resource Equ...

5. Final recommendation (personal opinion): Use ANOVA by default. If lack significance, generalize your model.

6. For before-after design, you can use panel data models (general or generalized).