Extra_sol - STA4502/STA5507 Extra Credit Homework Solutions...

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Unformatted text preview: STA4502/STA5507 Extra Credit Homework Solutions 1. Johnson (1984) sampled the young-of-year (YOY) gizzard shad (Dorosoma cepedianum) pop- ulation at four different sites in Kokosing Lake (Ohio) in summer 1984. The data are lengths (mm) of the YOY gizzard shad and a subset is given: Site 1 Site 2 Site 3 Site 4 46 42 38 31 28 60 33 30 46 32 26 27 37 42 25 29 32 45 28 30 41 58 28 25 42 27 26 25 45 51 27 24 38 42 27 27 44 52 27 30 Test whether there are any differences between the lengths for the YOY gizzard shad popula- tions in the four Kokosing Lake sites. What specific sites, if any, are different? Use the all possible analysis you can think of, and be sure to be clearly stating HYPOTHESIS and what your assumptions are. (10 pts) 4-sample testing with multiple comparisons Overall test: hypothesis H : 1 = 2 = 3 = 4 H a : i negationslash = j at least one pair ( i, j ) assumptions: the experimental units are assigned to the 4 sites in a completely ran- dom design 1 ANOVA F-test: assume that the observations are selected at random from normally distributed populations with equal variances _______________________________________________________ ANOVA Table: DF SS MS F p-value Treatment 3 2196.88 732.29 17.14 4.420668e-07 Error 36 1537.90 42.72 NA NA Total 39 3734.78 NA NA NA _______________________________________________________ Under the normality assumption, we reject H at significant level = 0 . 05. Permutation F-test: unwilling to assume that the population distributions are normal-------------------------------------------------------- Permutation F-Test-------------------------------------------------------- F_obs: 17.14188 SSX_obs: 52111.1 Number of Permutation: 5000 p-value based on SSX 0 p-value based on F 0-------------------------------------------------------- With permutation F-test, we reject H at significant level = 0 . 05....
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Extra_sol - STA4502/STA5507 Extra Credit Homework Solutions...

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