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I have a data set comprising the diet composition of seabirds. For each individual sampled, I have the proportion of the diet that is comprised of sand lance. I have many zero values (sand lance is not found in the diet) and many 1 values (sand lance makes up the entire diet). I also have values in between (0,1). How can I compare whether the overall proportion of sand lance is different between years 1 and 2?

Can I simply use a t-test (with or without an arcsine transformation of the data)? Or does the distribution of my data require a more sophisticated modelling techniques?

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  • $\begingroup$ What is it you want to learn from these data? $\endgroup$
    – gung - Reinstate Monica
    Commented Sep 5, 2017 at 19:12
  • $\begingroup$ Why don't you know the name of the species? $\endgroup$
    – Kodiologist
    Commented Sep 5, 2017 at 19:16
  • $\begingroup$ @gung I want to know whether there is a difference between the years in the prevalence of sand lance in the diet $\endgroup$
    – Splash1199
    Commented Sep 5, 2017 at 19:17
  • $\begingroup$ So all all the birds one species? What "years"? Is this a time-series? Are you comparing some years when something happened to years when it didn't? $\endgroup$
    – gung - Reinstate Monica
    Commented Sep 5, 2017 at 19:39
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    $\begingroup$ About how many observations? Can you show us a plot of the data, or better, post the data (or some subset, or a mackup resembling the data)? $\endgroup$
    – kjetil b halvorsen ♦
    Commented Sep 5, 2017 at 21:48

2 Answers 2

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After some consultation, I decided to use a logistic regression. I performed one regression using a binary response (presence or absence of sand lance in the diet), and another using success/failures (# sand lance in the diet vs. # of other fish in the diet). For this, I had to use a quasibinomial distribution due to over-dispersion.

Both models gave similar answers.

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There are specific tests for comparing proportions between two groups! Let us take a random sample of $m$ observations from group A and $n$ observations from group B.

Let $\hat{a}$ be the observed propotion for group A, $\hat{b}$ for group B and $\hat{c}$ the observed overall propotion. Under the assumption that the population proportions are equal:

$\frac{\hat{a}-\hat{b}} {\sqrt{\hat{c}(1-\hat{c}) (\frac{1}{m} + \frac{1}{n})}}$ follows a standard normal distribution.

For more detailed information and an example, check Comparing Two Independent Population Proportions

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