Firstly, my apologies for the basic nature of this question. I am numerate but stats has always befuddled me. I have had a look through earlier questions.

I have installed a red mason bee box. It has 174 tubes of 3 different types - sleeved 87, empty 44 and plugged 43. Currently the occupied tubes number, sleeved 7, empty 12 and plugged 7. The nesting season continues.

I also have installed a similar box where there are currently only 2 occupied tubes and instinctively know that this must be insignificant but would like to understand where the transition is so that I can improve my chances next year.

I am conscious that early on the bees have a high degree of choice in selecting a specific tube but that as more tubes are taken that choice will become more restricted. I guess that this is a secondary conundrum - when is bees choice so restricted that the preference cannot be effectively determined?

I have looked at ANOVA and plugged the data into a tool as 3 groups with 1,1,1,0,0,0,0 etc but frankly even the output is not clear to me. I would be very grateful for advice on testing the data to be clear on the best choice for next year’s box.

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    $\begingroup$ Hi Russ, welcome to the site. Its not completely clear what your question is. What do you mean by "where the transition is"? $\endgroup$ Commented May 24, 2023 at 11:57
  • $\begingroup$ Hi George. Thanks for replying. My overall question is which test or tests should I use to determine which type of tube works best. By “transition” I suppose threshold might be a better term? I mean that at a certain point there will be enough data from the second box (currently only two tubes occupied) to be confident that the answer to the question - which type of tube is preferred - can be ascertained. $\endgroup$
    – Russ
    Commented May 24, 2023 at 12:38
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    $\begingroup$ It's unclear what "works best" might mean. Shouldn't we trust the bees to decide which type is most suitable? If so, then the counts you observe tell you something about the relative sizes of the local bee population. There are secondary issues to consider, too. For instance, if the types are not randomly distributed throughout the box, their occupancy will be confounded with location within the box. Consequently, it's not plausible that simply applying some statistical test could reliably answer your question. $\endgroup$
    – whuber
    Commented May 24, 2023 at 17:21
  • $\begingroup$ Really? The bees are deciding. The question is which of the three tubes types are optimal for next year? They are randomly distributed within the box. Reliably? $\endgroup$
    – Russ
    Commented May 24, 2023 at 21:05
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    $\begingroup$ This comes down to what question you are asking and what you will do with that information. You could test whether one tube is more popular than another, but I don't think that would tell you a lot about what to do next year. Eg a grocery store could test what was the most popular brand of washing powder but they would still stock a wide range, since they know people vary in their preferences. If all your tubes except one type get filled then maybe reduce that next time, but its not necessarily a statistical question. $\endgroup$ Commented May 25, 2023 at 10:43