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I need some help choosing the statistical test to calculate if the bee families have a preference for a straw size.

To summarize the project, I am looking at 4 bee families Osmia-Megachile-Chelostoma-Vespidae. Those nest in straws of three different sizes: small, medium, and large.

The data collected from the field looks like this:

        -Osmia-Megachile-Chelostoma-Vespidae
-Small   92      45       5          10
-medium  52      2        17         4
-large   14      0        2          0

It seems simple enough to say that megachile prefers small, but I have no idea how to test for it.

$\chi^2$ only says that the distribution is different than random but no preference.

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  • $\begingroup$ A properly applied $\chi^2$ test will demonstrate that there are preferences. (The null hypothesis of no preference is not the same as no difference in patterns among the species, and has different expected values.) But why do that? You have four species and four tests to conduct. Is there any aspect of your data collection that suggests the results among the species are interdependent (such as competition among them for available nests)? $\endgroup$
    – whuber
    Commented Apr 14, 2017 at 20:47
  • $\begingroup$ From the data collection (Trap nest ) there should not be any competition for nest because availability is high hence competition for nesting spot with risk of predation is highly unlikely $\endgroup$
    – Philippe T
    Commented Apr 14, 2017 at 22:30
  • $\begingroup$ Then the preferences are perfectly clear, aren't they: Osmia, Megachile, and Vespidae prefer "Small" while Chelostoma prefer "Medium". Chi-square testing will confirm this if you feel it's really necessary--but only the Vespidae even deserve a test due to the small counts. (You will find a p-value around 0.33% for that. The usual $\chi^2$ approximation is suspect but it's not too bad: it will give you a p-value of 0.44%.) $\endgroup$
    – whuber
    Commented Apr 14, 2017 at 22:46
  • $\begingroup$ That what I had in mind thank you very much this was very helpful $\endgroup$
    – Philippe T
    Commented Apr 14, 2017 at 23:26

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