Abstract:
The likelihood ratio test for testing simultaneous homogeneity of main effects of several
factors against ordered alternatives in multifactor designs has been developed in the
literature. But the level probabilities needed to implement these tests have been computed
only for the 2-way layout. We use these results to calculate critical points for testing
simultaneous homogeneity of main effects against simple order alternatives in 3-way
layout and Latin square design.
Tabulation of critical values requires finding values of c that satisfy
_2 m+n+t
Pr(E (m,n,t);:::: c)= I Q(l;m,n,t)Pr(B1 1 ;:::: c), for 3-way layout
and
l=4 -(/-3) -(mnt-1+2) 2
'
2
_2
3 m
Pr(E (m,m,m);:::: c)= I Q(l;m,m,m)Pr(B1 1 2 ;:::: c), for Latin Square
-(l-3) -(m -/+2)
l=4 2
'
2
-2
Design, where E is the corresponding likelihood ratio test statistic, Q(l;m, n,t) are
convolution of probabilities used in order restricted inference and Ba,b is the Beta
distribution with parameters a, b.
The tables presented here provide critical values for testing at significance level a for
the combinations of m,n,t and a, where
m,n,t = 2(1)10, a= 0.1, 0.05, 0.025, 0.01, 0.005.
An application in the case of Latin Square Design and FORTRAN programs for the
computation of critical values in several layouts are also presented.
