Brief Solutions for Problem 1 - Statistical Methods for Bioscience II | HORT 572, Exams of Data Analysis & Statistical Methods

Download Brief Solutions for Problem 1 - Statistical Methods for Bioscience II | HORT 572 and more Exams Data Analysis & Statistical Methods in PDF only on Docsity! Stat/For/Hort 572 – Midterm II, Spring 2004 — Brief Solutions for Problem 1 First we assess the effect of habitat types on the abundance using a one-way ANOVA approach. From the following output, we conclude that there is strong evidence of a habitat effect (p < 0.0001). Further pairwise comparison using the LSD suggests that the habit types are different from one another, with the exception that the clay disturbed and the sandy undisturbed are not significantly different. The residual plot reveals a possible fan shape but otherwise the 4 model assumptions seem to be satisfied. Dependent Variable: abund Sum of Source DF Squares Mean Square F Value Pr > F Model 3 19643.35000 6547.78333 50.53 <.0001 Error 16 2073.20000 129.57500 Corrected Total 19 21716.55000 t Tests (LSD) for abund Alpha 0.05 Error Degrees of Freedom 16 Error Mean Square 129.575 Critical Value of t 2.11991 Least Significant Difference 15.262 t Grouping Mean N type A 252.400 5 1 B 208.400 5 2 B B 206.000 5 3 C 163.800 5 4 Next we relate the abundance to the environmental variables using MLR. The full model has two ex- planatory variables, namely, soil moisture (p < 0.001) and soil temperature (p = 0.13). Notice poten- tial multicollinearity due to a fairly high negative correlation between soil moisture and soil temperature (r = −0.77). Coefficients: Estimate Std. Error t value Pr(>|t|) (Intercept) 85.0241 37.6017 2.261 0.0372 * moist 7.9440 0.6961 11.412 2.16e-09 *** temp -1.3888 0.8679 -1.600 0.1280 Residual standard error: 7.201 on 17 degrees of freedom Multiple R-Squared: 0.9594, Adjusted R-squared: 0.9546 By a backward elimination, the best model has only soil moisture as the explanatory variable. The residual plot does not reveal any serious departure from the 4 model assumptions. Coefficients: Estimate Std. Error t value Pr(>|t|) (Intercept) 26.6799 9.5891 2.782 0.0123 * moist 8.8063 0.4594 19.168 2.00e-13 *** Residual standard error: 7.506 on 18 degrees of freedom Multiple R-Squared: 0.9533, Adjusted R-squared: 0.9507 Finally we study the effect of soil moisture and soil temperature on the abundance for different habi- tat types using MLR. We create new variables i1,i2,i3 to represent the interaction between moist and w1,w2,w3, and new variables ii1,ii2,ii3 to represent the interaction between temp and w1,w2,w3. For model comparisons, we fit several models assuming equal intercepts and/or equal slopes, in addition to the full model. Using the principle of additional sum of squares, it appears that the intercepts and slopes for the models abund∼moist+temp are different for different habitat types (p = 0.0063) and the difference is likely due to the differences in the slopes (p = 0.029) rather than the differences in the intercepts (p = 0.66). For further understanding of the data, one could compare the regression in a pairwise fashion or for any specific habitat types of particular interest. 1