Is it apporpriate to use two way ANOVA test if I have paired data linked to single individual?

Question

[srdjanmasirevic2]

I am new in statistics. I wanted to do some statistical test to determine whether there is a difference between two samples and over the individuals.

So if I have data that looks like this:

Animal type   Numbers_method_1  Numbers_method_2

Tiger         28                 32
Lion          15                 19
Turtle        187                165
Giraffe       311                233  
Leopard       123                321
...

And I have 25 animal types like this. If possible I wanted to do two way comparison, between the methods, but also between the Animals. But since I have paired data linked to single animal, is it possible to use two-way ANOVA comparison, and if not, why? Do I have to link them into categories? Or in other words, is it impossible to do two way ANOVA with pairs linked only to a single case?

Also, this data is raw data, do I have to normalize it before performing such comparison between animals? ... because each animal is different of course.

Answer 1

[Kevin Blighe]

Before doing anything like this, you have to understand how the data was produced; so, how was it produced? - a manual survey?; some lab instrument? In which sense is it comprised of "raw" data?

You also have to check the distribution of the data - does it follow a normal distribution via a histogram and are your samples 'representative' of the larger population? If the answer to this is 'yes', then you need a parametric test. Otherwise, a non-parametric test should be used. In terms of ANOVA, the typical ANOVA about which we usually think is a parametric test, while, the non-parametric equivalent is a Kruskal-Wallis test. Both assume that your groups are independent.

Given your data, which seems 'unusual', for want of a better word, you most likely want to use the Wilcoxon signed-rank test, which assumes that your groups are related ('paired'), somehow, and which is also a non-parametric test. For example, it looks like you could employ a Wilcoxon signed-rank test to compare Method 1 vs Method 2.

If you want p-values comparing, for example, Tigers versus Lions, then a Chi square test may be appropriate.

For all intents and purposes, you may not have to normalise the data, but, please elaborate on how it was produced if you want further help.

Kevin