Dear Mehmet!

First of all you wrote "Normality and equal variance assumptions were not violated for parametric tests" - this means you CAN use ANOVA.

I assume you wanted to write they were violated. In this case, you actually CAN run ANOVA, becasue SPSS carry out other tests too. In the output the top row always states "Sphericity assumed" , the next row is Greenhous- Geisser - you want to read this line, and write down the results form here (same applies to every variable)

IF you happen to have nominal variables, you will have to carry out a Log-linear analysis, but that's a whole new storry.

Best regards,

Andrew

Dear Mehmet!

First of all you wrote "Normality and equal variance assumptions were not violated for parametric tests" - this means you CAN use ANOVA.

I assume you wanted to write they were violated. In this case, you actually CAN run ANOVA, becasue SPSS carry out other tests too. In the output the top row always states "Sphericity assumed" , the next row is Greenhous- Geisser - you want to read this line, and write down the results form here (same applies to every variable)

IF you happen to have nominal variables, you will have to carry out a Log-linear analysis, but that's a whole new storry.

Best regards,

Andrew

Since you have before-after data, you likely want an alternative to ANCOVA, not ANOVA (see discussion of Lord's paradox, in particular Wainer 1991 Psych Bull and http://ftp.cs.ucla.edu/pub/stat_ser/r436.pdf). There are several alternatives for ANCOVA. One is allowing a flexible curve (like a spline) for the relationship between the pre and post score. Also, Rand Wilcox discusses a lot of "distribution-free" tests in his books. His ANCOVA based on trimmed means might be what you are looking for, and this is implemented in the ancova function in the R package WRS2 (and there is a bootstrap function with this which may also be useful).

One approach that I often use is to first transform all data to normal quantiles, or z-scores. Then, you use any parametric statistical method that suits your needs.

SO, If the data is not normally distributed, and we want to do MANOVA, does the transformation to normal quantiles affects the results?

or any other alternative to MAONA?

I have 2 independent variabls (Site and Season) and may dependent variables(Salinity, SPM, POM, NH4 etc)

Which non parametric test should I use?

Transforming to z-scores is a linear transformation (x'

Here is a tiny article using a non-parametric approach rather than MANOVA:

• https://odajournal.com/2016/11/11/novometric-analysis-vs-manova-mmpi-codetype-gender-setting-and-the-macandrew-alcoholism-scale/

Here is a short review article that discusses the non-parametric method

• https://odajournal.com/2017/04/18/what-is-optimal-data-analysis/