Thread: Does the difference between males and females between two groups of species differ?

1. Does the difference between males and females between two groups of species differ?

Background
I have body weight measures from seven rodent species in both northern and southern Europe. For each of the total 14 species, I have measurements for males and females (not always perfectly balanced for sex and sample sizes vary among species).

The data look like that (here given for one exemplary species from the North):
Indiv. Location Species Sex Weight
1 North Species_1 Males 1.25
2 North Species_1 Males 2.12
3 North Species_1 Males 1.67
4 North Species_1 Males 1.25
5 North Species_1 Males 2.32
6 North Species_1 Males 1.27
7 North Species_1 Females 1.15
8 North Species_1 Females 1.81
9 North Species_1 Females 1.57
10 North Species_1 Females 1.35
11 North Species_1 Females 2.32
12 North Species_1 Females 1.52

Question of interest / Working hypothesis
I would like to test whether the difference in body weight between males and females (sexual dimorphism) is increased in the species from northern Europe as opposed to the ones from southern Europe. My hypothesis is that the sexual dimorphism is increased in the northern species.

Analysis
I would like to build a statistical test/model (preferentially in R) in which I can test whether there is any general difference in the extent of sexual dimorphism between the northern and southern European rodent species. And in case there is such a difference, I'd like to know how strong this effect is and whether it is significantly different.

I would very much appreciate if someone could help me with which statistical test/model I can test my research question. Thank you a lot!

2. Re: Does the difference between males and females between two groups of species diffe

So you have 2 origins (animals from the south vs. from the north) and 2 sexes, and an interval scaled dependent variable. You could consider a two-way analysis of variance. The interaction between "origin" and "sex" tells you whether the difference between sexes is different between regions.

With kind regards

Karabiner

3. Re: Does the difference between males and females between two groups of species diffe

Yes, looking at the interaction seems to be the way to go. But what about the fact that these animals are of different species? Probably this should be taken into account, though I'm not quite sure how (mixed model?).

4. Re: Does the difference between males and females between two groups of species diffe

Thank you for these first suggestions.
@Karabiner: So you are thinking of a two-way ANOVA? It's something I had in mind too...
But as Junes points out, I'm not sure about the fact that these are different species. Hence, the weight measures vary quite strongly among the different species. And variance seems to generally scale with the mean. Given that there might actually be an overall difference in weight between the northern and southern species, would that be be a problem for a two-way ANOVA?
Another worry I had is that I'm interested in testing for a difference in sexual dimorphism between northern and southern species *irrespective* of the *direction of the effect*. In other words: it might be that in some species, males might be heavier than females, in other species it might be exactly opposite. Would that be a problem?

5. Re: Does the difference between males and females between two groups of species diffe

A mixed model may be applicable here. See here for examples in R. I'm not sure how this would work in your case. Just to be sure, Species are nested within Region, right? So that there are no species present in both north and south.

A simpler option would be just to compare using a t-test on a per species basis, though you would need some multiple comparisons correction (Bonferroni, or a less conservative alternative).

6. Re: Does the difference between males and females between two groups of species diffe

I thought about the t-test. But there seem to be too many inherent problems in this case. Also, I'm sort of interested whether there is an overall difference in dimorphism between the sexes in the two regions.
To your other question: yes, species occur only once, either in the north or south.

7. Re: Does the difference between males and females between two groups of species diffe

*irrespective* of the *direction of the effect*.
If it is already known which sex is the larger one, you could
substitute the factor sex by "larger versus smaller of the sexes".

I'm not sure about the fact that these are different species. Hence, the weight measures vary quite strongly among the different species.
Are all 14 species found in the north as well as in the south?
You could perform a three-way ANOVA then, using species,
region, larger/smaller-sex as factors.

With kind regards

Karabiner

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