I have some data on the landings of crab and lobster in Wales from 2002-2019 and I also know whether they were landed into ports in North or South Wales. What statistical test(s) do I need to do to compare landings of both species between North and South? Should I conduct two separate t-tests for each species or is there a test I can do that does it all in one go? Crab and lobster are caught in the same pots so their abundances are linked.
If your question is simply whether the weights differ between N and S, then yes, a separate t test for each species is the way to go.
But if you're wondering whether there is a some sort of relationship between the weights of the landings of crabs and lobsters, then you'll first need to formulate a more precise question or hypothesis.
You need to perform an ANOVA since there is more than one species at two sites and each species may affect the other. You cannot do separate t-tests since it will increase Type 1 errors. But test for normality of data first, otherwise you would perform a Chi square test :)
I agree with Andrew, try an ANOVA at the start - do not use t-tests here. If the data do not conform to the assumptions of normality you will have to resort to chi square tests.
What are you intending to do with the comparison -- fish harvests per unit time tend to vary with the density of the stocks. Thus, if one or both of the stocks are being fish down, the next season's harvest per unit time will be lower. I suggest that you get:
Hilborn, R. & Walter, C.J. 1992.Quantitative Fisheries Stock Assessment: Choice,
Dynamics and Uncertainty. Chapman & Hall, International Thomson
Publishing, New York, NY.
In replaced the old stock evaluation reference of:
Gulland, J.A. 1983. Fish Stock Assessment: A Manual of Basic Methods. Wiley,
New York, NY.
Basically both books are must reads for fisheries managers and researchers and both warn that fisheries always have multiple driving factors and models must be carefully thought through and tested before relying on statistical results.
With set gillnets, by kill may be a major issue -- in the Stikine and Fraser River set gillnet fisheries, I found that when the gear was picked every four hours it killed 5 Sockeye salmon for every four landed but when the gear was picked every 12 hours the gear killed 10 fish for every fish landed.
Thus, you need to consider many variable/conditions when modeling a fishery -- even ridiculously bad models produce results. However, those results tend to be ridiculous when checked against reality.
Good Luck
Every basic course in biometrics teaches t-test, chi-squared and factorial ANOVA, with a warning that the latter is sensitive to normality. Students are rarely taught that it is normality of the error term, not the data, that is relevant (so that a test for normality won't help!), nor that ANOVA is far more sensitive to heterogeneities in variance than to departures from normality (a big problem with most fisheries data). You will need to go far beyond such over-simplifications to make much of your data -- which may well lead you into entirely different kinds of hypothesis tests.
However, I think that Stefan hit the essential point: "you'll first need to formulate a more precise question or hypothesis". Your data are not drawn from a simple two-way experimental design (crab-lobster, crossed with north-south). You have multiple years and multiple months. The spatial variations in availability of the two species will certainly be on a much finer scale than north/south, which might complicate analysis or might suggest more useful questions to ask of the data. That is all a way of saying that the data rows within the north/crab group (or the south/crab, north/lobster or south/lobster) are not replicate measurements of the same thing, differing only because of the value of a random error term.
Meanwhile, most of your data rows appear to be from one boat fishing for one day but some have the catches of multiple days on one row -- whether a combination of many trips or a single long trip isn't clear to me.
And what were the fishermen doing? Crab and lobster may be taken with the same traps but are some set with the aim of taking one species, some the other and some a mix? Does the targeting differ between places or times? Do fishermen from some harbours do one thing and those from another something else, even though both fish in the same times and places at the scales for which you have data? Does targeting change with season? Perhaps more-expensive lobsters more often targeted in the run-up to Christmas (when Canadian lobster are air-freighted to parts of Europe to get the best prices) or in summer (when there are more tourists in Wales and perhaps a higher demand for fresh seafood)?
If you don't know, then you risk asking the wrong questions of the data and you will misunderstand what it is telling you.
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