Assume I have distance values (e.g. how close an animal gets to a city) for each individual in my sample. So, for each individual animal, I will have a minimim distance. Next, say I have 4 categories of individuals. Suppose I want to see if there are differences among these categories in how close individuals get to a city. Is there anything conceptually wrong with calculating the mean of these minimum values (and comparing them among categories)? I suppose if the distribution is skewed rather than normal, then median would be more appropriate that the mean, but other than that, is there something fundamentally wrong with averaging minimum values?
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3$\begingroup$ There is nothing conceptually wrong with mean minimum values. It has a name, block minima statistics. en.wikipedia.org/wiki/Extreme_value_theory#Data_analysis $\endgroup$– user234562Commented Apr 26, 2020 at 18:40
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There is nothing conceptually wrong in computing the mean of minimum values. As you say, minima could have a (very) skewed) distribution, in which case maybe you prefer median or some other measure of location. But otherwise, nothing is wrong.
answered Apr 27, 2020 at 18:40