# How to remove inter-year variation from my assessment of seasonal varriation

I have a 30 year dataset of fish sampling. I know from previous analyses that there is a huge amount of variation between years in catch rates. What I would like to do is create a descriptive plot that shows the average catch rate for each month that was sampled for a single species after removing this inter-year variation.

I started by just taking the average for each month and using that, but the amount of inter-year variation creates huge error bars, so it's not clear that anything is happening. I thought about scaling everything so that all within year catch data was presented as a proportion of the maximum monthly catch rate, so trends would appear as percentage changes rather than the absolute value, but in a given year samples weren't collected for every single month; so I don't think this would work.

Is there a statistical test which would allow me to do this? I thought about a GLMM with year as a random effect, but I don't anticipate there being a linear increase in catch rates over time. Would an ANOVA with year as a random effect and month as a categorical variable work?

Edit: To clarify this is less about hypothesis testing and more about providing descriptive plots that show how the abundance of a given species is changing seasonally. For example I'm interested in showing how species exhibit seasonal changes in their preference for sites with artificial reefs (see attached plot for rough examples). I'd like to remove the noise resulting from inter-year variation so that I can shrink those error bars and make the seasonal trend more obvious.

• If I run an ANOVA with year included as a random effect I'm left with an output that includes an estimate for each month and a standard error. Can I then plot the estimates for each month and use the standard errors as my error bars? Feb 3, 2021 at 20:21
• Having a bit more of an idea of what the actual data looks like (a plot?) might make it easier to suggest an appropriate model. It would also be great to know what you would like to do; just a plot?, predictions for the future? p-values? Some suggestions for modeling the time series: Facebook Prophet / Gaussian Processes with well selected kernel functions / splines.
– MJW
Feb 5, 2021 at 14:10
• @MJW thanks, I've edited the question to provide more detail. I'm not interested in fitting the best line/spline (not hypothesis testing), just trying to show the seasonal variation and provide a descriptive plot that shows how preference for reef sites might be changing over time. Feb 5, 2021 at 14:34