I have an array of 50,972 household incomes for a small metro area, and I want to measure how much the so-called top "one-percent" make (e.g., the 99th percentile). As you'd expect, it's a power curve:
To start, I just sorted the array and took the last 510 values, which begin at \$385,244 and go up to \$1,070,357.
First question: To be in the top 1%, do you have to make AT LEAST the cutoff or MORE than the cutoff? It makes very little difference in this case, but I'm curious whether the percentile values are considered inclusive.
R has a
quantile function that can find the cutoffs with less effort:
distribution = quantile(income_array, prob = seq(0, 1, length = 101))
(The 101 is to account for the 0% up to the 100%, I believe.) If you look at the 99% value, it matches my manual calculation of \$385,244 exactly, while the 100%, naturally, matches \$1,070,357.
So we know how much you have to make to be in the vaunted 1%. But in terms of expressing how MUCH richer that 1% are than the median--which is an important policy consideration--I'm not certain if it makes sense to use the lower bound of \$385K or some median value within that top slice.
In other words, the top one-percent themselves are also weighted to the richest of the rich.
For example, would it be more accurate to take the median of the 1%? (\$584,438, which I realize is the same as cutoff to be in the top 0.5%).
I'm not sure if this is relevant, but the R
percentile function optionally takes a
type argument that specifies which of 9 different algos to use, documented here. This is beyond my level of stats prowess. The default is 7.
I should note that the data has many repeat values because it comes from a carefully weighted sample of households. Each income is repeated in the array a number of times equal to the household's weight, such that the outcome is equivalent to the number of households.