Two ways to stop a handful of extreme rows dominating a column's centre.
ctrmmean() DISCARDS the floor(n * trim) largest
and smallest values, as mean(x, trim = ) does.
cwinsmean() instead PULLS THEM IN to the most extreme
surviving values, so every observation still contributes weight –
usually the better choice when the extremes are real measurements rather
than errors.
Arguments
- x
Numeric (or logical) vector; coerced with
as.numeric().- trim
Proportion trimmed (or winsorized) at each end, a single number in \([0, 0.5]\) (default 0.1, i.e. 10% at each end). At
0.5both reduce to the median.
Details
With \(g = \lfloor n \cdot \mathrm{trim} \rfloor\) and the sorted values
\(x_{(1)} \le \dots \le x_{(n)}\), the trimmed mean is
\(\frac{1}{n - 2g} \sum_{i=g+1}^{n-g} x_{(i)}\) and the winsorized mean
replaces \(x_{(1)}, \dots, x_{(g)}\) by \(x_{(g+1)}\) and
\(x_{(n-g+1)}, \dots, x_{(n)}\) by \(x_{(n-g)}\) before averaging all
\(n\) values. At trim = 0.5 both return the median, as mean() does.
A trim that is not a single number in \([0, 0.5]\) is an error. An
empty x, or any NA/NaN in x, gives NaN (missing
values are not
removed). A character, factor or list x is refused
("must be numeric"). Both sort a copy of x, so the cost is
\(O(n \log n)\).
Examples
x <- c(1, 2, 3, 4, 5, 6, 7, 8, 9, 100)
mean(x) # dragged up by the 100
#> [1] 14.5
ctrmmean(x, 0.1) # the 100 and the 1 dropped
#> [1] 5.5
cwinsmean(x, 0.1) # the 100 pulled back to 9
#> [1] 5.5
# Agrees with base R's own trimming.
all.equal(ctrmmean(x, 0.2), mean(x, trim = 0.2))
#> [1] TRUE
# trim = 0 is the plain mean; trim = 0.5 is the median.
all.equal(ctrmmean(x, 0), mean(x))
#> [1] TRUE
all.equal(ctrmmean(x, 0.5), cmed(x))
#> [1] TRUE
# A trim past one half is not a trim.
try(cwinsmean(x, 0.7))
#> Error : `trim` must be a single number in [0, 0.5]
try(ctrmmean(letters))
#> Error : ctrmmean: `x` must be numeric, got character