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D 7 pts independence of measurements across and

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(d) (7 pts) Independence of measurements across and within groups: trees were sampled randomly, and were experimentally chosen to be burnt and in- vaded by beetles. It can be pointed out that if trees are located in regions that are far apart, then the region might affect the genetic background or the presence/absence of beetles and raise con- cerns about this independence assumption. But this assumption seems to be met from the avail- able information. Normality of measurements within each group: Having a qq-plot of residuals would make it easy to see, but the dotplots show no outlier, no appar- ent skew, and makes us think normality probably holds here. Equal variances: seems okay. Sample standard deviations are quite similar (the largest is no larger than twice the smallest). Furthermore, Levene’s test supports this assumption: F = 0 . 21 on 3 and 34 df gives p > 0 . 25 and leads us to accept σ 1 = σ 2 = σ 3 = σ 4 . Frequency 20 40 60 80 100 0 10 20 30 Summary of grades 68 77 88 2
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