What statistical analysis to use on a list of dates? I suffer from migraines and for many years I've kept a log of each attack.  I now want to do some analysis on the dates of each attack to see if there are any patterns.
I intend to check the frequency of different days of the week - but how can I tell if any variations are statistically significant?
How about mean time between attack?  Can I use this to tell if the distribution of attacks is truly random?
What other approaches can I use on this dataset?
 A: If you want to detect periodicity, you should examine the autocorrelation (and here )plot of your migrane data. Periodicity will show up as modes in the autocorrelation chart.
As for time between attacks, if they are not all the same, then yes, they are random (and the autocorrelation plot will look uninteresting) However, what kind of randomness? In general, for point-events (headaches, earthquakes, etc) you would use a Poisson model with an unknown rate parameter $\lambda$. 
Now, if your headaches occur at a fixed average rate, then you can fit a poisson model to your data and then do a goodness of fit test to see how well that worked (there will be some bias here because you are testing after fitting). If your p-value is, lets say, <0.01 (to adjust for bias), then your headaches probably occur at random.
A more rigorous method would be to divide your data into two equal-duration group (e.g., years 1-3, and 4-6) and then test for a difference in the ratio of the poisson means. Here is a paper to do this.
