Description Usage Arguments Details Value Author(s) References See Also Examples
The data input consists of a sequence of independent realizations observations of each random variable, observations of the different sequences also being independent.
1 2 3  npStochinUnpaired(x1, x2, d = 0, alternative = "two.sided",
iterations = 5000, alpha = 0.05, epsilon = 1 * 10^(6),
ignoreNA = FALSE, max.iterations = 100000)

x1, x2 
the (nonempty) numerical data vectors which contain the variables to be tested. 
d 
the maximal difference in probabilities assumed H_0 : P(X_2 > X_1)  P(X_2 < X_1) <= d. Default is 0. 
alternative 
a character string describing the alternative
hypothesis. Default is "greater". If "less" is given, 
iterations 
the number of iterations used, should not be changed if the exact solution should be derived. 
alpha 
the type I error. 
epsilon 
the tolerance in terms of probability of the Monte Carlo simulations. 
ignoreNA 
if 
max.iterations 
the maximum number of iterations that should be
carried out. This number could be increased to achieve greater accuracy in
cases where the difference between the threshold probability and theta is
small. Default: 
Given 1 < d < 1 it is a test of the null hypothesis H_0 : P(X_2 > X_1) ≤ P(X_2 < X_1) + d against the alternative hypothesis H_1 : P(X_2 > X_1) > P(X_2 < X_1) + d.
The data is randomly matched into pairs and then treats them as matched
pairs. The number of pairs is equal to the number of observations in the
smaller sequence. The exact randomized test is then used to determine if
sufficiently many occurrences of x_2 > x_1 occur when compared to how
often x_2 < x_1 occurs, using level theta
*alpha
. The
matching into pairs is repeated iterations
times. The test gives a
rejection of the average rejection probability in these iterations lies
above theta
. If the average rejection probability lies too close to
theta then the number of iterations is increased.
theta
is determined to maximize the set of differences
P(X_2>X_1)  P(X_2<X_1) belonging to the alternative hypothesis in
which the type II error probability lies below 0.5. For more details see
the paper.
A list with class "nphtest" containing the following components:
method 
a character string indicating the name and type of the test that was performed. 
data.name 
a character string giving the name(s) of the data. 
alternative 
a character string describing the alternative hypothesis. 
estimate 
an estimate of P(x_2 > x_1)  P(x_2 < x_1). 
probrej 
numerical estimate of the
rejection probability of the randomized test, derived by taking an average
of 
bounds 
the lower and upper bounds of the variables. 
null.value 
the specified hypothesized value of the correlation between the variables. 
alpha 
the type I error. 
theta 
the parameter that minimizes the type II error. 
pseudoalpha 

rejection 
logical indicator for whether or not the null hypothesis can be rejected. 
iterations 
the number of iterations that were performed. 
Karl Schlag, Peter Saffert and Oliver Reiter
Schlag, Karl H. 2008, A New Method for Constructing Exact Tests without Making any Assumptions, Department of Economics and Business Working Paper 1109, Universitat Pompeu Fabra. Available at https://ideas.repec.org/p/upf/upfgen/1109.html.
https://homepage.univie.ac.at/karl.schlag/statistics.php
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