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I have a dataset which consists of fish density/biomass from two sampling periods (1 and 2) in two locations (A and B). In sampling period 1 locations A and B are both clear, while in sampling period 2 A is clear but B is experiencing very high turbidity. I want to assess whether the increased turbidity has caused a change in how the fish are using the habitat-- i.e. if they are preferentially choosing the clear "A" location at sampling period 2, compared to sampling period 1.

I was thinking I could assess this with a chi-square test, but my measures of biomass and density are continuous, not discrete-- would rounding up to the nearest whole number be valid?/Any other suggestions on how to analyze this? I don't think an ANOVA will work because I really only have one measure of density/biomass per group/time.

*** EDIT ***

I actually have 100's of measures of density and biomass in each sampling of the 4 sampling areas/periods-- density and biomass were obtained using a sonar-like device that pings the fish every minute or so. But these measures obviously won't be independent of each other, so I was planning on just averaging across the sampling period.

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    $\begingroup$ No. Your measurements are not counts and rounding to integers won't make them counts. After all, you could change your units of measurement and get quite different integers after rounding. It sounds as if you have no information about variability in any case. $\endgroup$
    – Nick Cox
    Commented Mar 19, 2021 at 1:06
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    $\begingroup$ It's not clear you can make these independent. They sound like pseudoreplications to me. I think you have 4 data points. You can simply report the four numbers as descriptive. $\endgroup$
    – gung - Reinstate Monica
    Commented Mar 19, 2021 at 13:30
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    $\begingroup$ S. Thompson describes how to analyze such samples in his book Sampling. The later chapters focus on methods to sample ecological systems, such as transect sampling. The idea is that you need to estimate the chances of detecting any individual and any pair of individuals in the population (based, perhaps, on the properties of your sonar); and then you can use those chances in a Hansen-Hurwitz like estimator. $\endgroup$
    – whuber ♦
    Commented Mar 19, 2021 at 13:32
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    $\begingroup$ @MisterMak Imagine there is a camera on the bottom of the boat. The camera takes a picture of all of the fish which are directly under the boat every minute. The boat weaves back and forth over the sampling area and takes 100 pictures in total. There is variation in the number of fish in each picture, but no way to say with any confidence how many of those fish are unique individuals. This is why I was planning on averaging across all of the fish "photos" because the measurements won't be independent from each other. $\endgroup$
    – Dugan
    Commented Mar 19, 2021 at 13:41
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    $\begingroup$ whuber's reference is probably better, but one thing that could be done is you could run an exemplary chi squared test on some fish numbers that make some sense at some point in time. If this gives you a p-value of about zero (really far lower than any reasonable cutoff for significance) you could state that the evidence looks very clear and strong for a change despite the specific test just giving an example calculation rather than being precise for your problem. (Of course still assuming that individual fish are independent.) $\endgroup$
    – Christian Hennig
    Commented Mar 19, 2021 at 13:46

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Would this work (posting as an answer because it's not really a comment)?

I have 100 samples in each of the four sampling groups (A1, A2, B1, and B2). The samples collected within A1 are not independent from each other, but they are independent from the samples collected in A2, B1 and B2.

Therefore, could I take a random sample in sampling group A1, another random sample in sampling group A2, B1 and B2 and perform a Chi-square test on these 4 numbers. Obtain the Chi-square test statistic and then repeat this procedure 10,000 times to obtain an average Chi-square value with a standard error, and then get a p Value from that?

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    $\begingroup$ I think it depends on what statistical rigour you want. You could probably obtain a result that convinces people (and even referees) if the effect exists (or doesn't), though you should explain clearly what you are doing. Also, it is often useful to run simulations (ie generate mock data sets A1, A2, B1 and B2 and push them through your analysis pipeline) ahead of time to see if things behave as expected. $\endgroup$
    – Mister Mak
    Commented Mar 19, 2021 at 19:15
  • $\begingroup$ If observations in A1 are not independent of each other, randomly sampled elements from A1 are not independent either. So no, random sampling from your data doesn't help. $\endgroup$
    – Christian Hennig
    Commented Mar 20, 2021 at 11:02
  • $\begingroup$ @Lewian even if I’m only using one “photo” per group? i.e. one photo of fish numbers from each of groups A1, A2, B1, B2, is hen calculate the chi square, then repeat? $\endgroup$
    – Dugan
    Commented Mar 20, 2021 at 13:57
  • $\begingroup$ Can you show the distribution of counts in A1 for instance, to confirm whether or not if follows a Poisson distribution? $\endgroup$
    – Mister Mak
    Commented Mar 20, 2021 at 14:27
  • $\begingroup$ @Dugan: As I wrote before as a comment to the original question, if you use one number per group a chi squared test can be, let's say, "well motivated", and if that gives you an "about zero" p-value, I'd be fine with the conclusion that something's going on there. However if you repeat this with different photos, you don't add independent information, so I don't see this getting you much further. $\endgroup$
    – Christian Hennig
    Commented Mar 20, 2021 at 15:18

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