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I am looking at differences in dates of maximum counts of geese at 3 sites in the UK.

My data look like these created in R:

df <- data.frame(day.number=c(sample(70:75, 30, replace=T), 
                              sample(77:82, 30, replace=T), 
                              sample(80:84, 30, replace=T)),
                 site=paste0('site', sort(rep(1:3, 30))))

The variable day.number is the day number on which the maximum count of geese was recorded in each year. So day number 70 would be 70 days from 1st January in that year. Each row represents a year and there are 30 years worth of data from each site.

I am considering carrying out an ANOVA to test to see if the date of the maximum count is different among sites. Example R code:

summary(aov(day.number ~ site, data=df))

Is an ANOVA appropriate here? Is there a better way of looking at differences in day number of maximum count among sites?

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An ANOVA would ignore the fact that, for each site, you have successive years. That might be a bad thing to ignore. First, it might (probably would) violate the assumption of independence of the data. Second, it doesn't account for any change over time - this might be important.

The first thing I would do is plot the data. One plot I'd make is one with 3 lines (one for each site), with year on the x axis and day on the y axis. This might reveal something interesting.

Then I'd consider some sort of mixed model to account for the dependence of the data. Another possibility is a time-series analysis, but 30 time points might not be enough.

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