Logging in the rain forest: contrasts. Figure 29.2 (page 29-5) gives basic ANOVA output for the study of the effects of logging described in Example 29.1. We might describe the overall effect of logging by comparing the mean species count for unlogged plots (Group A) with the average of the mean counts for the two groups of logged plots (Groups B and C).
(a) What population contrast L expresses this comparison?
(b) Starting from the output in Figure 29.2, give the sample contrast that estimates L and its standard error.
(c) Is there good evidence that the mean species count in unlogged plots is higher than the average for the two groups of logged plots? State hypotheses in terms of the population contrast L and carry out a test.
(d) How much higher is the mean count in unlogged plots than the average for the two groups of unlogged plots? Give a 95% confidence interval.
Example 29.1:
STATE: How does logging in a tropical rain forest affect the forest in later years? Researchers compared forest plots in Borneo that had never been logged (Group A) with similar plots nearby that had been logged 1 year earlier (Group B) and 8 years earlier (Group C). Although the study was not an experiment, the authors explain why we can consider the plots to be randomly selected. Table 29.1 displays data on the number of tree species found in each plot.1 Is there evidence that the mean numbers of species in the three groups differ?