# Trend significance over time

I am trying to find the correct way to assess a trend for significance over time. This is the data I have: for a 15 year period I have the fate of all nests in a colony as either failed for fledged. So as an example:

2000 - 25 out of 50 nests successful, 2001 - 35 out of 60 nests successful, and so on for the 15 years.

What I hope to do is to show whether or not there is a significant trend, either positive or negative, for numbers of fledged nests over this 15-year period. I don't think linear regression or Poisson error regression is a way to go since the response isn't really a normal distribution. However, I admit I don't really know. Can someone suggest an appropriate approach if indeed there is one? Thanks.

Here are three suggestions. If your total counts are known, then this sounds like binomial regression to me. Say you have for observations $i=1,\ldots, n$ the response count $y_i$ (in this case it's your number of successful nests), and your predictor $x_i$ (in this case it sounds like it's time, so $t$). Binomial regression assumes that each $Y_i$ follows a binomial distribution with known $n_i$ and a parameter $p_i(x_i)$ that depends on your input. Typically people use logistic regression, which is a special case of this, where $n_i = 1$ for all $i$. But this doesn't have to be so. In your case $n_i$ is changing and seems to be around $50$ or $60$.
You can also use a beta regression if you don't want to assume that your total nests $n_i$ are known. In this case your response variables would be proportions.