Drosophila melanogaster you could take multiple

Drosophila melanogaster ). You could take multiple
tissue samples per fly and make multiple observations per tissue sample, but because
raising 100 flies doesn’t cost any more than raising 10 flies, it will be better to take one
tissue sample per fly and one observation per tissue sample, and use as many flies as you
can afford; you’ll then be able to analyze the data with one-way anova. The variation
among flies in this design will include the variation among tissue samples and among
observations, so this will be the most statistically powerful design. The only reason for
doing a nested anova in this case would be to see whether you’re getting a lot of variation
among tissue samples or among observations within tissue samples, which could tell you
that you need to make your laboratory technique more consistent.

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Unequal sample sizes
When the sample sizes in a nested anova are unequal, the P values corresponding to
the F statistics may not be very good estimates of the actual probability. For this reason,
you should try to design your experiments with a “balanced” design, meaning equal
sample sizes in each subgroup. (This just means equal numbers at each level; the rat
example, with three subgroups per group and 10 observations per subgroup, is balanced).
Often this is impractical; if you do have unequal sample sizes, you may be able to get a
better estimate of the correct P value by using modified mean squares at each level, found
using a correction formula called the Satterthwaite approximation. Under some situations,
however, the Satterthwaite approximation will make the P values less accurate. If you
cannot use the Satterthwaite approximation, the P values will be conservative (less likely
to be significant than they ought to be), so if you never use the Satterthwaite
approximation, you’re not fooling yourself with too many false positives. Note that the
Satterthwaite approximation results in fractional degrees of freedom, such as 2.87; don’t
be alarmed by that (and be prepared to explain it to people if you use it). If you do a
nested anova with an unbalanced design, be sure to specify whether you use the
Satterthwaite approximation when you report your results.
Assumptions
Nested anova, like all anovas, assumes that the observations within each subgroup are
normally distributed and have equal standard deviations.
Example
Keon and Muir (2002) wanted to know whether habitat type affected the growth rate
of the lichen Usnea longissima . They weighed and transplanted 30 individuals into each of
12 sites in Oregon. The 12 sites were grouped into 4 habitat types, with 3 sites in each
habitat. One year later, they collected the lichens, weighed them again, and calculated the
change in weight. There are two nominal variables (site and habitat type), with sites
nested within habitat type. You could analyze the data using two measurement variables,
beginning weight and ending weight, but because the lichen individuals were chosen to