HANDBOOK OFBIOLOGICALSTATISTICS170Unequal sample sizesWhen the sample sizes in a nested anova are unequal, thePvalues corresponding totheFstatistics 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 equalsample sizes in each subgroup. (This just means equal numbers at each level; the ratexample, 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 abetter estimate of the correctPvalue by using modified mean squares at each level, foundusing a correction formula called the Satterthwaite approximation. Under some situations,however, the Satterthwaite approximation will make thePvalueslessaccurate. If youcannot use the Satterthwaite approximation, thePvalues will be conservative (less likelyto be significant than they ought to be), so if you never use the Satterthwaiteapproximation, you’re not fooling yourself with too many false positives. Note that theSatterthwaite approximation results in fractional degrees of freedom, such as 2.87; don’tbe alarmed by that (and be prepared to explain it to people if you use it). If you do anested anova with an unbalanced design, be sure to specify whether you use theSatterthwaite approximation when you report your results.AssumptionsNested anova, like all anovas, assumes that the observations within each subgroup arenormally distributed and have equal standard deviations.ExampleKeon and Muir (2002) wanted to know whether habitat type affected the growth rateof the lichenUsnea longissima. They weighed and transplanted 30 individuals into each of12 sites in Oregon. The 12 sites were grouped into 4 habitat types, with 3 sites in eachhabitat. One year later, they collected the lichens, weighed them again, and calculated thechange in weight. There are two nominal variables (site and habitat type), with sitesnested 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