Hi everyone,
I would like to know if are there any differences in parasitic infection in 3 fish Species from 4 Stations.
To do that, I examined parasitic infection in 10 fish per Species per Station (n = 10 fish x 3 Species x 4 Station=120). The collected data (parasitic infection level) was continuous but not normally distributed.
I wonder if:
1. I can run two separate Kruskal Wallis test (one on the effect of Species and the other on the impact of Station on infection level)? Should I worries if Species and Station can interact and change the statistical analysis?
2. Is there any test I can conduct instead of 2 separated Kruskal Wallis
Thank you very much
I can help.
Answers:
1. You must not run separate tests in case there is an interaction between Species and Station. And anyway, you need the effect of Station since it is your replication!
2. Yes, one big Kruskal Wallis (not separate ones) or ANOVA, since the data is normally distributed.
Always test all of your data together to detect all interactions and reduce statistical error and bias :)
One suggestion is to transform your data and see if they follow a normal distribution. Then you can run a two way ANOVA if they do.
Hi, Mai Dang .
1) The first thing is to understand the assumptions of (two-way, factorial) anova, and general linear models in general. It is not an assumption that the data are normally distributed. If you are using a source that says so, you should probably discard this source entirely.
Instead, I recommend consulting a (real) statistics textbook on analysis of experiments. For example, Montgomery, Design and Analysis of Experiments, is a good one, that is pretty common.
1b) An assumption for these models is usually expressed that the errors are normally distributed. Another way to think about this is that the data have a conditional normal distribution. Usually, we assess this by looking at the residuals from the model with a q-q plot or perhaps a histogram.
At the following presentation, see slide 8, and then slides 19 - 22.
https://staff.emu.edu.tr/adhammackieh/Documents/courses/ieng581/lecture-notes/ch03.pdf .
2) Assuming your data don't meet the assumptions of common, OLS, anova, there's probably a different model that would be more appropriate for your analysis. Depending on the software you are using, applying one of these generalized linear models may be just as easy as running a traditional anova. In the case of your data, I suspect Gamma regression may be appropriate.
To answer your question:
3) If you want to go with the nonparametric, rank-based approach, the test analogous to the two-way factorial anova is the Scheirer–Ray–Hare test. (See, for example, https://rcompanion.org/handbook/F_14.html , with the caveat that I wrote this page).
3b) A more flexible nonparametric apprach is Aligned Ranks Transformation anova. (See, for example, https://rcompanion.org/handbook/F_16.html , with the caveat that I wrote this page).
Thank you for your answer. But is Scheduled Ray Hare test available at Graphpad prism or SPSS
@Salvatore S. Mangiafico
Nashwa Nada , I don't know about GraphPad Prism or SPSS, but it's pretty easy to run the the S-R-H test in R, even online without installing software here: https://rdrr.io/snippets/ . But also, the test is relatively simple to calculate by hand if you need to.
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