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my background is being an applied mathematician with some basic statistic background.

I have a dataset containing a metric random variable whose value is to be explained by the categorical variable. The dependent variable contains measured values.

The categorical variable has three values A,B,C. Its influence is to be tested; it is nominally scaled. In my data set, I have four repetitions per year for each characteristic and I have the whole thing for 10 years.

My limited knowledge now says that if I only had one year, I would use ANOVA, but due to the four repetitions, I probably don't fulfil the requirements.
Then I would look at one of the many Wilcoxon tests to see if there are differences between A,B and C. More precisely, I need something for unpaired data and three characteristics, i.e. Kruskal-Wallis test?

Now to my questions

-) how do I check the ANOVA assumptions if the year clearly (by eye ;) ) has an influence on the dependent variable. That bends my head a little right now

-) I hope the previous questions and thoughts were understandable. My data looks like the following example (less normally distributed ;) ). How do I test for difference depending on A,B,C

year A,B,C y

1 A 0.456405

1 A 0.848563

1 A 0.925366

1 A 0.962574

1 B 0.0135936

1 B 0.18973

1 B 0.888734

1 B 0.895592

1 C 0.569717

1 C 0.582822

1 C 0.629108

1 C 0.980864

2 A 0.342965

2 A 0.424771

2 A 0.583502

2 A 0.674631

... ... ...

10 C 0.0264971

10 C 0.553408

10 C 0.60247

10 C 0.955483

Many thanks for reading tips/links

Kind regards

PS: the link in that answer is dead ANOVA type for dependent samples through time

PPS: I had a beatiful LaTeX-Table for my data-set but after login in, it displays it in one row :( therefore plain text

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Short answer: it's perfectly OK to just average across the four repititions, so you're left with a year x category (10 x 3) design. You can find plenty of examples of this in the psychology literature, where research participants often perform many repititions of a task, and their data is averaged together for ANOVA.

It's not clear from your question whether your categorical variable is a repeated measure or not, which is another topic.

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  • $\begingroup$ Dear Eoin, thank you for the quick reply! Perhaps I am misunderstanding something! I think I also expressed it wrongly at one point above. I want to have the influence of A,B,C, not that of time. BUT what I wanted to point out is that e.g. in year 2 all three are better, then in year 3 they are all worse again, etc. So the year also has an influence! $\endgroup$
    – Michael Fischer
    Commented Feb 23 at 15:49
  • $\begingroup$ Yes, "two way" ANOVA allows you to separate out the two effects. $\endgroup$
    – Eoin
    Commented Feb 23 at 19:24

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