Description Usage Arguments Details Value Author(s) References See Also Examples
This test requires that the user knows upper and lower bounds before gathering the data such that the properties of the data generating process imply that all observations will be within these bounds. The data input consists of a sequence of observations, each being an independent realization of the random variable. No further distributional assumptions are made.
1 2 3  npVarianceSingle(x, v, lower = 0, upper = 1,
alternative = "two.sided", alpha = 0.05, iterations = 5000,
epsilon = 1 * 10^(6), ignoreNA = FALSE, max.iterations = 100000)

x 
a (nonempty) numeric vector of data values. 
v 
the value of the variance to be tested as H_0: Var(x) ≤ v. 
lower, upper 
the theoretical lower and upper bounds on the data outcomes known exante before gathering the data. 
alternative 
a character string describing the alternative hypothesis, can take values "greater", "less" or "two.sided" 
alpha 
the type I error. 
iterations 
the number of iterations used, should not be changed if the exact solution should be derived. 
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: 
This is a test of the null hypothesis H_0: Var(X) ≤ v against H_1 : Var(X) > v.
This test randomly matches the data into pairs, then computes for each pair the square of the difference and continues with the resulting sequence with half as many observations as npMeanSingle. See the cited paper for more information.
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 
the estimated mean or difference in means depending on whether it was a onesample test or a twosample test. 
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 and Oliver Reiter
Karl Schlag (2008). Exact tests for correlation and for the slope in simple linear regressions without making assumptions. Available at https://ideas.repec.org/p/upf/upfgen/1097.html.
https://homepage.univie.ac.at/karl.schlag/statistics.php
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