How to test if turtles are dying mostly at a particular time of year? I have citizen science records of turtle sightings (alive/dead, and if dead what caused its death e.g. car/predator/etc), and the date they were spotted. What would be the most appropriate test to answer the following questions:


*

*are turtles are being killed mostly at a particular time of year (or month, if it is easier)?

*is the way turtles are killed related to time of year?
I have a lot more records of live than dead turtles, and the data of "causes of death" has lots of NAs, unfortunately. I am using R.
 A: Key here is that time of year is a circular scale. The dates of death could be converted to angles on the circle and their vector mean calculated as a summary resultant. With daily dates I tend to use a day of year variable $\text{doy}$ running from 1 to 365 to 366, and then calculate 
$\sin[2 \pi ((\text{doy} - 0.5) / \text{number of days in year})] =: s$ 
$\cos[2 \pi ((\text{doy} - 0.5) / \text{number of days in year)}] =: c$  
and the resultant as $\text{arctan} (\sum s / \sum c)$, converted back to a notional date. The vector mean can be supplemented by a measure of variability most commonly known as the mean resultant length, although several less commonly used names such as consistency are more evocative. Naturally you should plot the data too. Smoothing to get an estimate of the density function on the circle is often especially helpful. 
A logit model of (alive, dead) as a response might be related to sine and cosine as predictors. 
Accounts of circular statistics aimed at biologists include 
Batschelet, E. 1981. Circular statistics in biology. 
London: Academic Press. 
Zar, J.H. 2010. 
Biostatistical analysis. 
Upper Saddle River, New Jersey: Pearson Prentice Hall. 
Despite its supposed updating, the text by Zar encapsulates a very old-fashioned style of statistics. For density estimation, see more readily 
Fisher, N.I. 1993. Statistical analysis of circular data. 
Cambridge: Cambridge University Press.
For R support, see Pewsey, A., M. Neuhäuser and G.D. Ruxton. 2013. 
Circular statistics in R. 
Oxford: Oxford University Press. 
A: To find out whether turtles are killed more in e.g. spring than at other times, you could do a t test. See ?t.test. 
This is assuming that your data has no selection bias - for example, that people go to the beach more at certain times of year, and spot turtles. A strong assumption!
To find out whether causes of death are related to seasons, you could use a chi-squared test - see ?chisq.test.
