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I checked my calculations and I am getting a negative number. Can LIFs be negative?

Arryana
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  • I was originally pretty sure there was a duplicate but for the life of me I couldn't find it (and so answered it, thinking I was mistaken). Eventually I had to go through many pages of hits of searches on boxplots in order to find it. – Glen_b Jan 26 '19 at 01:24

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Yes, a lower inner fence can be negative even when all the data are strictly positive. If the data are all positive, then the whisker itself must be positive (since whiskers are only at data values), but the inner fences can extend beyond the data.

It's an easy matter to construct examples where this is the case; you simply need the value of the lower quartile to be less than 60% of the value of upper quartile. One quick example -- samples of size 30 (say) from an exponential distribution will almost always have this property.

Here's some R code by way of an example:

 x <- rexp(30)
 f <- fivenum(x)
 H.Sp <- f[4]-f[2]
 LIF <- f[2]-1.5*H.Sp
 LIF
Glen_b
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