ad_test | R Documentation |
A two-sample test based on the Anderson-Darling test statistic (ad_stat
).
ad_test(a, b, nboots = 2000, p = default.p, keep.boots = T, keep.samples = F)
ad_stat(a, b, power = def_power)
a |
a vector of numbers (or factors – see details) |
b |
a vector of numbers |
nboots |
Number of bootstrap iterations |
p |
power to raise test stat to |
keep.boots |
Should the bootstrap values be saved in the output? |
keep.samples |
Should the samples be saved in the output? |
power |
power to raise test stat to |
The AD test compares two ECDFs by looking at the weighted sum of the squared differences between them – evaluated at each point in the joint sample. The weights are determined by the variance of the joint ECDF at that point, which peaks in the middle of the joint distribution (see figure below). Formally – if E is the ECDF of sample 1, F is the ECDF of sample 2, and G is the ECDF of the joint sample then
AD = \sum_{x \in k} \left({|E(x)-F(x)| \over \sqrt{2G(x)(1-G(x))/n} }\right)^p
where k is the joint sample. The test p-value is calculated by randomly resampling two samples of the same size using the combined sample. Intuitively the AD test improves on the CVM test by giving lower weight to noisy observations.
In the example plot below, we see the variance of the joint ECDF over the range of the data. It clearly peaks in the middle of the joint sample.
In the example plot below, the AD statistic is the weighted sum of the heights of the vertical lines, where weights are represented by the shading of the lines.
Inputs a
and b
can also be vectors of ordered (or unordered) factors, so long as both have the same levels and orderings. When possible, ordering factors will substantially increase power.
Output is a length 2 Vector with test stat and p-value in that order. That vector has 3 attributes – the sample sizes of each sample, and the number of bootstraps performed for the pvalue.
ad_test()
: Permutation based two sample Anderson-Darling test
ad_stat()
: Permutation based two sample Anderson-Darling test
dts_test()
for a more powerful test statistic. See cvm_test()
for the predecessor to this test statistic. See dts_test()
for the natural successor to this test statistic.
set.seed(314159)
vec1 = rnorm(20)
vec2 = rnorm(20,0.5)
out = ad_test(vec1,vec2)
out
summary(out)
plot(out)
# Example using ordered factors
vec1 = factor(LETTERS[1:5],levels = LETTERS,ordered = TRUE)
vec2 = factor(LETTERS[c(1,2,2,2,4)],levels = LETTERS, ordered=TRUE)
ad_test(vec1,vec2)
Add the following code to your website.
For more information on customizing the embed code, read Embedding Snippets.