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[email protected]Final Examination.Fall 95 Final Examination Page <6> of 10 Statistical Methods I (360-310a) December 14, 1995, 9:00-12:00 Last Name: Part II (continued) Third episode: Macintosh is conscious that to be in good health, a forest must be managed. This means that a young stand must be submitted to thinning (“éclaircie” in French), which consists in cutting the smallest trees of the stand over years so that only the biggest trees will be left at the end. In this episode, we will assume that “time is running fast” so that we will be able to judge the effect of thinning in a few hours while this usually takes years. (Macintosh will be older by several years at the end of this episode…) Because Macintosh never applied any thinning treatment in the past, he wants to compare two intensities of thinning, low and high, coded respectively “L” and “H” below. His first question, for obvious reasons, is: “Is there a significant difference in the mean tree growth rate in circumference per plot that these two thinning intensities provide”? Thereafter, and because the forest he is working in now is composed of three different tree species located in distinct parts of the forest (see figure), his second question to you is: “Do the differences between the two thinning intensities depend on the tree species that they are applied to?” Tree species 1 Tree species 2 Tree species 3 12) What design would you recommend to Macintosh? This suitable design should allow him to test for the effects sketched above. Justify your answer and describe briefly the field lay-out. /10 Final Examination Page <7> of 10 Statistical Methods I (360-310a) December 14, 1995, 9:00-12:00 Last Name: Part II (continued) Third episode (continued): In accordance with (we hope!) the experimental design you recommended in question 12), Macintosh collected the following data (after normalization) of mean tree growth rate in circumference per plot (after a certain number of years): L L H H L L L L H H H H 5 5 5 5 4 6 5 5 8 6 10 8 13) a) On that basis, do you suspect the differences between the two thinning intensities to be constant, or not, from tree species to tree species? Justify your answer, preferably graphically. 5/ Final Examination Page <8> of 10 Statistical Methods I (360-310a) December 14, 1995, 9:00-12:00 Last Name: Part II (continued) Third episode (last page): b) On the same basis (i.e., the data displayed on page 7), assess by ANOVA the main differences in the mean tree growth rate in circumference per plot between the two thinning intensities and the constancy of the differences between thinning intensities from tree species to tree species. In particular, give the linear model and its assumptions, and build the ANOVA table. How could one increase the power of the two F tests performed? 20/