Many statistical procedures assume symmetrically distributed data (examples are linear rank tests, estimation of location parameters, two-tailed p-values, and confidence intervalls). Thus, it is important check the assumption of symmetry. Using a simulation study this paper compares the performance of four different tests on symmetry, namely the Randles Fligner Policello Wolfe Test, the Cabilio Masaro Test, the Mira Test, and the Miao Gel Gastwirth Test.

1.
P.
Cabilio
, and
J.
Masaro
,
A simple test of symmetry about an unknown median
,
The Canadian Journal of Statistics
,
24
(
3
),
349
361
(
1996
).
2.
M.
Hollander
,
D. A.
Wolfe
,
E.
Chicken
,
Nonparametric statistical methods
,
Wiley
,
2014
.
3.
E.
Kulinskaya
, On two-sided p-values for non-symmetric distributions,
2008
,
Imperial College London
, https://arxiv.org/pdf/0810.2124.pdf.
4.
N.
Markovich
,
Nonparametric Analysis of Univariate Heavy-Tailed Data: Research and Practice
Wiley
,
2007
.
5.
W.
Miao
,
Y. R.
Gel
,
J. L.
Gastwirth
, “
A new test of symmetry about an unknown median
”, , in
Random Walk, Sequential Analysis and Related Topics
, edited by
A. C.
Hsiung
,
z.
Ying
, and
C.
Zhang
,
2006
, pp.
199
214
,
6.
A.
Mira
,
Distribution-free test for symmetry based on Bonferroni’s Measure
;
Journal of Applied Statistics
,
26
(
8
),
959
972
,
1999
.
7.
R Core Team
:
R: A Language and Environment for Statistical Computing: A graduate course in probability. R Foundation for Statistical Computing
,
Vienna, Austria
(
2018
) https://www.R-project.org/
8.
R. H.
Randles
,
M. A.
Fligner
,
G. E.
Policello
,
D. A.
Wolfe
,
An asymptotically distribution-free test for symmetry versus asymmetry
,
Journal of the American Statistical Association
,
75
(
369
),
168
172
,
1980
.
9.
T.
Zheng
,
J. L.
Gastwirth
,
On Bootstrap Tests of Symmetry About an Unknown Median
,
Journal of Data Ccience
,
8
(
3
),
413
427
,
2010
.
10.
X.-H.
Zhou
,
S.
Gao
,
One-Sided Confidence Intervals for Means of Positively Skewed Distributions
,
The American Statistician
,
54
(
2
),
100
104
,
2000
.
This content is only available via PDF.
You do not currently have access to this content.