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I have a crossed experimental design with two fixed effects: Neighbour/Stranger and Female/Male.

The response variable is counts. Actually, the counts are background subtracted and some are negative.

Sample sizes are fairly large and balanced = 30 x 4 = 120.

Boxplots of counts are symmetrical for the different fixed effects N/S and F/M.

Counts range from -2 to +10.

The magnitude of median differences is 1 for both effects (n.b. integer data)

Boxplots are a bit wider for N and for M.

I want to test: is the difference between average counts for N/S or F/M significant?

Is ANOVA suitable, followed by t-tests for the significant effects?

Strictly, ANOVA is for continuous, normal variables.

Is there a non-parametric equivalent for two-way ANOVA?

Or perhaps a generalised linear model?

The data are not Poisson because there are negative results.

I am also interested in testing for interactions between N/S and F/M., which is why I chose two-way ANOVA.

What more should I do?

The could be some unequal variance between groups.

I use R for statistical computing

and can try more sophisticated analyses.

Thanks.