| dc.description.abstract | Tests Comb and Comb II are used to test the equality of means in a mixed design
which is a combination of randomized complete block design and completely
randomized design. The powers of Comb and Comb II for a mixed design have already
been compared with Page's test (Magel, Terpstra, Wen (2009)) when there was little or
no block effect added to the portion that was analyzed as a completely randomized
design. In this paper, we wish to compare the tests when the portion of the design
analyzed as a completely randomized design actually has a block effect.
A Monte Carlo simulation study was conducted to compare the power of the three
tests where Page's test was used only on data from the randomized complete block
portion. A variety of situations were considered. Three underlying distributions were
included in the simulation study. These included the normal distribution, exponential
distribution, and t distribution with degree of freedom equal to 3. For every distribution,
16, 32 and 40 blocks were used in the randomized complete block design portion where
the equal sample size of completely randomized data portion was 1/8, 1/4 and 1/2 the
number of blocks considered. Unequal sample sizes for the completely randomized
design portion were also considered. Powers were estimated for different location
parameter arrangements for 3, 4 and 5 populations. Two variances, 0.25 and I, for the
block effect were used. The block factor added into the completely randomized design portion didn't
change the test with highest rejection percentage for the equal sample size cases,
although the powers of the two tests for the mixed design decreased. For most of
unequal sample size cases, Page's test has the highest rejection percentage. Overall, it
was concluded that it was better to use one of the two tests for mixed design instead of
Page's test when there were equal sample sizes for portion analyzed as a completely
randomized design. When there were not equal size samples, but the first sample size
was twice the size of the others, it was generally better to use Comb over Page's unless
the number of populations became very large or there was a large block effect variance. | en_US |
