Nested Designs - Scholar

3. F-Tests
F = MSA/MSB tests the null hypothesis that the mean transpiration rate is the same for all five
hybrids versus the alternative that the mean transpiration rate is different for some hybrids.
Alternatively, this could be stated as: F = MSA/MSB tests the null hypothesis (7) that the effects
of all of the hybrids on mean transpiration rate are zero, versus the alternative that the effects of
some of the hybrids are non-zero.
F = MSB/MSC test the null hypothesis that there is no variation in mean transpiration rate
among pots within each hybrid, versus the alternative that there is some variation among pots
within some hybrids:
2
2
H0: 0 , versus HA: 0
(9)
B
B
Finally, F = MSC/MSE tests the null hypothesis that there is no variation in mean transpiration
rate among plants within each pot, versus the alternative that there is some variation among
plants within some pots:
2
2
H0: 0,
versus HA: 0
(8)
C
C
As explained above, the latter two sets of hypotheses are stated in terms of "variation" rather than
in terms of "means" or of "effects" because the effects of pots and plants are assumed to be
random variables rather than fixed constants. Since the effects are random, we cannot assume
they sum to zero as we would if they were fixed. Therefore it would be meaningless to test the
hypothesis that all the random effects are zero. On the other hand, the assumption that the effects
are random variables does make it reasonable to test the hypothesis that the variance of those
random variables is zero, and that is what we are doing. An effect is random rather than fixed
when the levels tested are a random sample from the set of all levels of interest.
nested01.docx 10 4/5/2012