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Reflections on distributions

Always consider the biological or ecological implications of your statistical assumptions.

In the introductory lesson on data distributions, we used data from this paper on raptor responses to prescribed fire to demonstrate how using the gamma distribution produces evidence that Swainson’s Hawks are attracted to prescribed fires, but using the normal distribution does not indicate a non-zero effect.

Although I did the statistics for that paper, I have mixed thoughts on whether I took the proper approach. When applying the gamma distribution, one makes a big assumption: No negative values. In this case, that means that we assumed that there would never be fewer Swainson’s Hawks during a burn than before it:

  • On one hand, this seems fair, since the observed data never showed an instance of fewer SWHA during than before:

  • On the other hand, other species did:

It is clearly biologically possible that negative values can occur, just as the normal distribution predicts.

The data don’t include many observations, and it is a bold claim to suggest that no amount of additional sampling would turn up the few slightly negative values the normal distribution predicts should be out there. By applying the gamma distribution, we (I) effectively made this claim.