148
(3)
yi= 0.5
and
2 =
1.0,
(4)
y i= 1-0
and
i =
1.0,
(5)
y != 0.5
and
22 =
2.0,
(6)
yi= 0.5
and
3.0
(7)
y i= 1*0
and
2 =
3.0.
Tables 5.6-5.8 give the results of the Monte Carlo for each
distribution type with entries corresponding to the number
of times a statistic rejected Hq The twelve statistics are
numbered in accordance with the listing in Table 5.5. The
column headings Null, Scale, Location and Location/Scale
refer to the type of bivariate pairs being generated and the
type of alternative that it reflects. The standard
deviation associated with each entry e can be estimated by
fe(500 e)/500)^2 Covariance estimates between certain
entries were also estimated but are not reported here. The
following discussion refers only to statistics 1 to 10 in
Tables 5.6-5.8. The discussion of statistics 11 and 12 will
follow.
Inspecting Tables 5.6-5.8, we see that as the
correlation increases between the components in the
bivariate pairs that the power increases for all the
tests. Similar results were observed in the Monte Carlo in
Section 5.2. For the null hypothesis (column 1), all the
tests are maintaining the significance level under Hq fairly
well, although, the levels for the tests using CD show more