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So we have a dataset with birdspecies (factor, 4 levels) and activity time (in minutes after sunrise). We want to know if the birds have a heterogeneous use of time. So do they come into our garden at all times of the morning (after sunrise-12pm), or do they have certain peaks. Our histogram shows for some birds that they are active around 1-2 hours after sunrise, but others do not. Is there an actual easy test to check this? The Kolmogorov-Smirnov was suggested, but in a one-sample test, it checks our distribution against a normal distribution. But is there a uniform continuous distribution to check against?

Thanks in advance!

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    $\begingroup$ Perhaps you mean a uniform distribution? The normal distribution is also continuous (i.e. opposite of discrete). Unrelatedly, could you show those histograms? Your question is clear without it, but it sounds interesting :) $\endgroup$
    – mkt
    Jul 13 '17 at 12:06
  • $\begingroup$ You could check against a uniform (instead of normal) distribution!? $\endgroup$
    – hplieninger
    Jul 13 '17 at 12:07
  • $\begingroup$ yes, sorry, I meant a uniform distribution $\endgroup$
    – Franciska
    Jul 13 '17 at 12:07
  • $\begingroup$ I'm not sure I understand what you're trying to achieve. A normal distribution is a type of continuous distribution. Can you specify what the goal of your research question is? Are you trying to compare the 4 different bird species or are you wanting to make statements about each species seperately? $\endgroup$
    – Tami
    Jul 13 '17 at 12:09
  • $\begingroup$ we want to know per species of bird if they have an equal distribution and come at all times during the morning or if they have activity peaks where they appear more often at certain times $\endgroup$
    – Franciska
    Jul 13 '17 at 12:11
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I would use a quantile quantile plot to get a sense of how far the two distributions are from each other.

If you need a statistical test, the Kolmogorov-Smirnov can be used for continuous normal distributions (as well as normal distributions) but, like all statistical tests, the p value will be partly due to sample size. Given that you are talking about birds visiting your own garden, I would guess that N is going to be pretty small and it will be hard to find significance for any pattern that doesn't pass the IOTT (Interocular Trauma Test - it hits you between the eyes).

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  • $\begingroup$ This solution does not seem to address the fundamental problem that the endpoints of the distribution are not well-defined. Indeed, a better model might be that the visiting times are a point process whose intensity is the convolution of a uniform with a Normal-like density to model the gradual awakening of the birds in the morning and their gradual going to sleep in the evening. The very nature of the question is much more exploratory than formal: the OP is looking for "activity peaks." A formal test of uniformity isn't going to address that. $\endgroup$
    – whuber ♦
    Jul 13 '17 at 14:16

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