APPENDIX 1
TABLES OF CRITICAL VALUES FOR TESTING FOR DIFFERENCES
IN SCALE
The tables in this appendix list the critical values of
T = T + T
nlnc nl nc
(i.e., T with L, = L~ = 1) for .01, .025, .05 and .10
n1nc 12
levels of significance for n^ = 1,2,..., 1 5 and
n2 = 1,2,3,. . 1 0 These tables are also appropriate for
TM since T
n 1 nc
nl nc
= TM
nl nc
or larger values of n^ or
nc, the asymptotic normal distribution of Tn n (and
TMn n ) could be used. When n^= 0 or nc= 0, the critical
values can be obtained from the critical values for the
Wilcoxon signed rank distribution based on n^ or nc
observations (respectively).
The critical values for this test statistic were
derived for each n^ and nc by convoluting two Wilcoxon
signed rank statistics (based on n^ observations and n£
observations). Thus, it follows that the critical values
for a test based on n,= a and n = b are the same as the
1 c
critical values for a test based on n,= b and n = a
1 c
observations. Therefore, the tables can also be viewed as
listing the critical values for n^ = 1,2, . 1 0 and
nc = 1,2 ...,15. These
test H : a,=o0 versus H
o 1 2 a
values are tabled for the
l02 or
Ha: o^o 2, the symmetry of T about
1 nr
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