Hello Emanuele,

If each of the birds you observe could be matched across both winters, that would be ideal, as you'd know that the 2022-23 birds were exactly one year older than the 2021-22 birds; no significance test is required!

If bird age can be considered a continuous variable and it's reasonable to assume that, for any given winter, ages of birds are approximately normally distributed, then you could possibly use an independent groups t-test. Each year would represent one group. You can opt to test separately by species.

If the normality assumption seems unreasonable, you could opt for a Mann-Whitney U test.

What to do about the same birds observed in both years? My suggestion is to omit them from the analysis, as age will be confounded with year/batch/group. It's really the unique, unmatched birds that will allow you any insight.

Good luck with your work.

I think you should know all the birds that are wearing rings. You sample only from the population of these birds wearing rings (if you catch a bird without a ring, you don't know its age, I suppose). These may not be so many individuals to assume that you sample from an infinite population, an that should be considered in the analysis. Since you know the (finite) population, I'd suggest to bootstrap the p-values. I also advice against omitting "duplicate" birds, as both samples are taken independently from the (presumably same) population. It is possible and valid to get the same birds in both years, and this should be considered, especially when the population is not very large.

Example:

Your (initial) population is N birds (with rings). Consider you cought a sample of n1 birds in 2022 and a sample of n2 birds in 2023. You can calculate the observed mean difference in age between the two samples. Then you generate many (thousands) of random samples from your initial population with n1 and (after replacement!) n2 and calculate their mean age differences. Under the assumption (null hypothesis) that the initial distribution is unchanged, the p-value is estimated as the proportion of the simulated mean differences that are larger (more extreme) than your observed mean difference.

Another possible assumption is that the population is relevantly different to the known initial population in some unknown way. If nothing else is specified, then you have information only on the samples birds, which are surely still part of the actual population. So you can do the same as before, but re-sampling only from the union set of sampled birds. This will result in a coarser sampling distribution and a lower power, but this might be important when the assumption that the 2022/23 population can reasonably well resemble the initial population is unbearable (for whatever reason).

Hello Emanuele Crepet

you can use paired sample t-test if your data for both periods follow the normal distribution assumption,

https://statistics.laerd.com/statistical-guides/dependent-t-test-statistical-guide-2.php

If not met the normal distribution assumption and with outliers' implication use can use Wilcoxon Signed-Rank Test

https://statistics.laerd.com/spss-tutorials/wilcoxon-signed-rank-test-using-spss-statistics.php

David Morse points out, if you compare birds captured on both occasions the birds are one year older. Not very interesting – we are all one year older than this time last year. In this, I disagree with Issam S. Ismail – this isn't a paired analysis situation.

One thorny problem is the limitation to birds that had been captured and ringed. You have to assume that the probability of a bird being ringed remained constant over the time period represented by the rings. however, if fewer birds were ringed in a particular time period (lockdown, for example) then the subsample of birds whose age you can determine will be biased.

You can use two-sample t-test of independent samples t-test from the parametric test side.

You can check the normality of your data is not normally distributed then use non parametric test like runksum ie Kullasikol Wallis test else use parametric tests like T-Test