First time using mad() Median Absolute Deviation on a vector, mostly 4 and 5, some NA.
Am I mistaken, but why would the mad function not return a positive value for
mad(c(4,5,5,5))
? Instead, I get a 0. I would only expect 0 if all values in the vector are the same, not if there is variation in value.
Please enlighten me. I am using R version 4.05.
According to the documentation the function will return the "median of the absolute deviations from the median"
So in the case of
x <- c(4,5,5,5)
The median is
median(x)
# [1] 5
and the differences are
x-median(x)
# [1] -1 0 0 0
which have absolute value
abs(x-median(x))
# [1] 1 0 0 0
And the median value of the vector is just 0
median(abs(x-median(x)))
[1] 0
It seems your expectation is just off. You don't get 0 only when all values are the same, you can get 0 when the median difference is 0. That happens when more than half of your values are actually the median value. Another vector that returns 0 is
mad(c(1, 7, 7, 7, 100))
[1] 0