# How to analyse separation of events in time?

I want to test whether the breeding periods of several closely related birds is significantly separated in time. What statistical test should I use?

My data consists of several observations per species with the date of breeding initiation (i.e. egg laying dates).

Could I just simply do an ANOVA on the Julian dates of breeding initiation?

I only have data of breeding birds, none of non-breeding ones. We only recorded breeding initiation of birds on nests. Each bird was recorded only once. I don't think survival analysis would fit this type of data. Am I wrong? (I'm not familiar with survival analysis).

Breeding time of different species do not deviate from normality. Variances are equal among species.

Here is what the data looks like. Each type and color of line represents a different species.

• Why not? Is there something about the data that would preclude ANOVA or make you suspect a violation of the ANOVA assumptions?
– whuber
Jan 5, 2014 at 22:42
• I'm not sure I understand what, exactly, you mean by 'significantly separated in time'. What would be the null and alternative hypotheses that would lead to a decision about statistical significance? Jan 5, 2014 at 23:58
• The multimodality of several of these species is intriguing. (The solid black, dashed black, and dashed purple lines in the range 130 - 180 are especially noteworthy.) Do you have an explanation for that--or better yet, data that could discriminate among the modes?
– whuber
Jan 11, 2014 at 19:56
• Some of the species had very small sample sizes. Dashed black had 4, solid black 7, dashed purple 6. They did not deviate from normality (shapiro), yet I excluded them from the analyses due to the small sample size. Jan 12, 2014 at 20:25

Survival models, at least in their common form, look at the hazard rate. In your case, that would be the hazard of breeding. If different species have different hazards, they will have different breeding times. This assumes that each bird breeds only once in the time period covered by your study. However, the main purpose of survival models is to deal with censored data. In your case, that would mean that some birds don't breed at all in the period covered by your study. Is that the case?

If every bird breeds (and maybe even if they don't) there may be better methods, especially since you say you have only a few birds per species. I would first look at the data graphically, or perhaps in a table.

It sounds like you should look into methods of survival analysis. There are many online resources. These methods are for time-to-event data, which it seems like you have. Keep in mind, however, that they are designed to assess differences in occurrence rather than duration. They can help you answer the question of "Does breeding initiate at different times?" but to my knowledge they do not allow you to make inferences about the duration of the breeding periods.

If you use SAS, I can recommend Survival Analysis Using SAS: A Practical Guide, Second Edition.

If you use an ANOVA, you are likely to get nonsense and also have low power. Normal (Gaussian) distributions tend to fit time-to-event data poorly.

• Could you indicate how survival analysis would be applied to these data?
– whuber
Jan 5, 2014 at 22:43
• ANOVA does not have to normal data; it has to have normally distributed errors and I see no reason that a linear model fit to these data would necessarily violate that assumption (you'd have to run the model to see). If there is no censorship, then there is no need for survival models. It isn't clear from the post whether there is or isn't censorship. Jan 5, 2014 at 22:47