This function carries out an hypothesis test in which the null hypothesis is that the two samples are governed by the same underlying generative probability distribution against the alternative hypothesis that they are governed by two different generative probability distributions.
two_sample_test(
x,
y,
stats = list(stat_t),
B = 1000L,
M = NULL,
alternative = "two_tail",
combine_with = "tippett",
type = "exact",
seed = NULL,
...
)A numeric vector or a numeric matrix or a list representing the 1st
sample. Alternatively, it can be a distance matrix stored as an object of
class dist, in which case test statistics based on
inter-point distances (marked with the _ip suffix) should be used.
A numeric vector if x is a numeric vector, or a numeric matrix if
x is a numeric matrix, or a list if x is a list, representing the second
sample. Alternatively, if x is an object of class
dist, it should be a numeric scalar specifying the
size of the first sample.
A list of functions produced by as_function
specifying the chosen test statistic(s). A number of test statistic
functions are implemented in the package and can be used as such.
Alternatively, one can provide its own implementation of test statistics
that (s)he deems relevant for the problem at hand. See the section
User-supplied statistic function for more information on how these
user-supplied functions should be structured for compatibility with the
flipr framework. Default is list(stat_t).
The number of sampled permutations. Default is 1000L.
The total number of possible permutations. Defaults to NULL, which
means that it is automatically computed from the given sample size(s).
A single string or a character vector specifying whether
the p-value is right-tailed, left-tailed or two-tailed. Choices are
"right_tail", "left_tail" and "two_tail". Default is "two_tail". If
a single string is provided, it is assumed that it should be applied to all
test statistics provided by the user. Alternative, the length of
alternative should match the length of the stats parameter and it is
assumed that there is a one-to-one correspondence.
A string specifying the combining function to be used to
compute the single test statistic value from the set of p-value estimates
obtained during the non-parametric combination testing procedure. For now,
choices are either "tippett" or "fisher". Default is "tippett", which
picks Tippett's function.
A string specifying which formula should be used to compute the
p-value. Choices are exact (default), upper_bound and estimate. See
Phipson & Smith (2010) for details.
An integer specifying the seed of the random generator useful for
result reproducibility or method comparisons. Default is NULL.
Extra parameters specific to some statistics.
A list with three components: the value of the
statistic for the original two samples, the p-value of the resulting
permutation test and a numeric vector storing the values of the permuted
statistics.
A user-specified function should have at least two arguments:
the first argument is data which should be a list of the n1 + n2
concatenated observations with the original n1 observations from the first
sample on top and the original n2 observations from the second sample
below;
the second argument is perm_data which should be an integer vector giving
the indices in data that are considered to belong to the first sample.
It is possible to use the use_stat function with nsamples = 2
to have flipr automatically generate a template file for writing down
your own test statistics in a way that makes it compatible with the flipr
framework.
See the stat_t function for an example.
n <- 10L
mx <- 0
sigma <- 1
# Two different models for the two populations
x <- rnorm(n = n, mean = mx, sd = sigma)
delta <- 10
my <- mx + delta
y <- rnorm(n = n, mean = my, sd = sigma)
t1 <- two_sample_test(x, y)
t1$pvalue
#> [1] 0
# Same model for the two populations
x <- rnorm(n = n, mean = mx, sd = sigma)
delta <- 0
my <- mx + delta
y <- rnorm(n = n, mean = my, sd = sigma)
t2 <- two_sample_test(x, y)
t2$pvalue
#> [1] 0.4335637