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I am using to Excel to analyze a dataset I have. I'm looking at bird migration. I have the date the birds were seen and the number of birds (abundance). I have a dataset of 10 years and I am trying to see if there is a shift in arrival time from year to year. What would be the best way to approach this?

tiffany2022
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  • Could you explain how "arrival time" might be related to dates of observation and counts? – whuber Jul 30 '22 at 15:14
  • Birds migrate in the spring and fall. I'm trying to see if their average arrival date has shifted earlier or has stayed the same over the years. So I have data on observation for the spring migration and the number of birds seen during the months March-May. – tiffany2022 Jul 30 '22 at 20:13
  • That's getting closer to something that can be analyzed. But what is a meaningful sense of "average"? It's not clear that it ought to be an arithmetic mean. Maybe a median? A minimum (first arrival time)? A quantile? Knowing a little about bird migration, I would suggest an exploratory study of the distribution of arrival times, rather than limiting your look to some kind of average. Changes in the spread and even the shape of that distribution could provide insight not afforded by any average. – whuber Jul 31 '22 at 12:23

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An idea is split the 10 years of data into 10 separate datasets which span a single year. Then, only use the portion of each year where the bird population is increasing. Perhaps you just select a date range to use in each year. With these 10 sectioned data sets, divide them by their maximum value such that they are normalized (only range from 0 to 1). Now, use logistic regression (fitting tool may be available in excel) to fit the 10 data sets separately. The function you are fitting looks like this: $$ a(d) = \frac{1}{1 + e^{-(d-\mu)/s}}. $$ The fitting tool should provide a $\mu$ and $\sigma$ to make the above function fit each of your data sets.

$\mu$ roughly indicates the value of $d$ where your bird behavior has "transitioned". You can plot $\mu$ for each of the 10 years to see how it has changed!

SeanBrooks
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  • The applicability of this approach is murky. The counts will rise and then fall over time, a pattern obviously not fit by your function $a.$ But logistic regression is entirely wrong for fitting the cumulative population due to the very strong serial correlation in the counts. – whuber Jul 31 '22 at 12:25