# Is a chi square test appropriate?

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.

• 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. Mar 19, 2021 at 1:06
• 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. Mar 19, 2021 at 13:30
• 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.
– whuber
Mar 19, 2021 at 13:32
• @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. Mar 19, 2021 at 13:41
• 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.) Mar 19, 2021 at 13:46