Just as titled, I'm curious as to what should you choose to represent a measure of central tendency for a zero-inflated vector or such. My background says go "mean" if normally distributed, "median" if not normally distributed. I wonder if median is a preferred measure of central tendency for a zero-inflated dataset that is not normal of course.
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$\begingroup$ Why not offer a fuller description by using familiar statistics for the nonzero values and report the proportion or number of zeros? $\endgroup$– whuber ♦Commented Sep 21, 2023 at 13:22
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Depending on the degree of zero inflation, I might choose no single measure of central tendency at all. It would also depend on whether the non-zero elements are counts (most zero-inflated measures seem to be counts) or continuous, or something else. There isn't always a useful measure of central tendency. For one thing, if more than 50% are 0, then the median will (of course) be 0. That's not very informative.
If I was forced to give one measure, I might choose a trimmed mean.
(Other situations where any measure of central tendency might have problems are multimodal distributions).
answered Sep 21, 2023 at 9:41