mwtie_xy {EQUIVNONINF} | R Documentation |
Distribution-free two-sample equivalence test for tied data: test statistic and critical upper bound
Description
Implementation of the asymptotically distribution-free test for
equivalence of discrete distributions in terms of the Mann-Whitney-Wilcoxon functional
generalized to the case that ties between observations from different distributions may
occur with positive probability. For details see Wellek S (2010) Testing statistical hypotheses of
equivalence and noninferiority. Second edition, 6.4.
Usage
mwtie_xy(alpha,m,n,eps1_,eps2_,x,y)
Arguments
alpha |
significance level |
m |
size of Sample 1 |
n |
size of Sample 2 |
eps1_ |
absolute value of the left-hand limit of the hypothetical equivalence range for
|
eps2_ |
right-hand limit of the hypothetical equivalence range for |
x |
row vector with the |
y |
row vector with the |
Details
Notation: and
stands for the functional defined by
and
, respectively,
with
cdf of Population 1 being independent of
cdf of Population 2.
Value
alpha |
significance level |
m |
size of Sample 1 |
n |
size of Sample 2 |
eps1_ |
absolute value of the left-hand limit of the hypothetical equivalence range for
|
eps2_ |
right-hand limit of the hypothetical equivalence range for |
WXY_TIE |
observed value of the |
SIGMAH |
square root of the estimated asymtotic variance of |
CRIT |
upper critical bound to |
REJ |
indicator of a positive [=1] vs negative [=0] rejection decision to be taken with the data under analysis |
Author(s)
Stefan Wellek <stefan.wellek@zi-mannheim.de>
Peter Ziegler <peter.ziegler@zi-mannheim.de>
References
Wellek S, Hampel B: A distribution-free two-sample equivalence test allowing for tied observations. Biometrical Journal 41 (1999), 171-186.
Wellek S: Testing statistical hypotheses of equivalence and noninferiority. Second edition.
Boca Raton: Chapman & Hall/CRC Press, 2010, 6.4.
Examples
x <- c(1,1,3,2,2,3,1,1,1,2)
y <- c(2,1,2,2,1,1,2,2,2,1,1,2)
mwtie_xy(0.05,10,12,0.10,0.10,x,y)