Lizard Egg Mass, Clutch Size, and Environment Relationship Exploration - Prof. Gary Mcclel, Exams of Statistics

Download Lizard Egg Mass, Clutch Size, and Environment Relationship Exploration - Prof. Gary Mcclel and more Exams Statistics in PDF only on Docsity! Psych 5741, Fall 1994 9 Dec 1994 Judd & McClelland — 1 — Final Exam (Fall Semester) I. In acknowledgment to the biologists in the class who have suffered through the many psychology examples, this problem is based on a biological study. The following questions are loosely based on: Sinervo, B. (1990). The evolution of maternal investment in lizards: An experimental and comparative analysis of egg size and its effects on offspring performance. Evolution, 44, 279-294. One of the issues in this study concerns factors related to the mean egg mass produced by the lizard Sceloporus occidentalis. The following variables are available for a total of 166 female lizards. • MASS: The average mass (in grams) of the eggs laid by each lizard • SIZE: The snout-vent length was used as an index of the mother's size. • CLUTCH: The total number of eggs laid at one time. • ELEV: The elevation (in meters) of the site where the mother was collected • LAT: The latitude (in degrees north of the Equator) of the site where the mother was collected. Using these variables, specify for each question below the MODEL C and MODEL A one would use to answer the question. Also, specify PA-PC and n-PA. A. Do larger lizards lay eggs with greater average mass? B. Controlling for size of mother, is it the case that the eggs in larger clutches are on average smaller? That is, is there a trade-off between egg mass and number of eggs. [This addresses the first sentence in Sinervo's paper which reads: "The presumed trade-off between the number and the size of offspring a female can produce is a fundamental tenet of life-history theory."] C. Sinervo did not use CLUTCH as defined here. Rather, in the model for the previous question he used "residual clutch size, a measure of the number of eggs in a clutch with female-size effects removed (residuals from the regression of clutch size and snout-vent length. Females laying large clutches for a given body size have large residuals relative to females laying small clutches." p. 281 Why was it unnecessary for him to regress average egg MASS on SIZE and "RESIDUAL CLUTCH SIZE"? D. When these lizards are housed in ideal laboratory conditions, the average egg mass is known to be 0.75g. Assuming that size of mother and clutch size are useful predictors of egg mass, specify the most powerful test of whether the egg mass from the lizards collected in the field differ from the laboratory mean. Psych 5741, Fall 1994 9 Dec 1994 Judd & McClelland — 2 — E. In more adverse conditions (i.e., either further north and/or higher elevations), lizards are supposedly less able to devote resources to reproduction. As a consequence, controlling for mother size and size of clutch, the average egg mass should be lower. What are the models for addressing this question. F. A rule-of-thumb in biology is that increasing elevation by 1000m is like going north by 20 degrees. In the context of the previous question, is there any reason to reject this rule- of-thumb for the model of egg mass? [Note: there is some rule-of-thumb like this, but I just made up the particular numbers for this problem! The answer is easy, but clever. Be sure not to waste to much time on this problem if the clever solution doesn't appear quickly.] G. A researcher believes that increasing elevation isn't quite like going north because not only is there a difference in average temperature [remember, cold-blooded lizards like it hot] but also there is a difference in the amount of oxygen available. This researcher thus argues that, controlling for latitude, mother size, and clutch size, higher and higher elevations should have increasingly adverse effects on average egg mass. That is, controlling for other factors is it the case that the adverse effects of increasing altitude are even greater at higher altitudes? What are the models to address this researcher's hypothesis? H. Another researcher wonders whether the relationship between clutch size and egg mass depends on the adversity of the environmental conditions. In particular, when controlling for mother size, does the relationship between clutch size and egg mass depend on the latitude and the elevation? I. In the context of the previous question, is there an especially adverse effect for sites that are both far north and very high? J. In the article, the author reports a regression for egg mass with n = 1344. What mistake has he probably made. [The variables used above were defined so as to avoid this mistake.] Psych 5741, Fall 1994 9 Dec 1994 Judd & McClelland — 5 — libname stat ''; options ps=60 ls=80; proc corr data=stat.div; var age yrsago bitter prob; data stat.div; set stat.div; yrsago2=yrsago*yrsago; ageb=age*bitter; yrsagob=yrsago*bitter; run; proc reg; model prob=age; model prob=bitter; model prob=yrsago; model prob=age yrsago/pcorr2 ss2 tol; model prob=age yrsago bitter/pcorr2 ss2 tol; model prob=age yrsago bitter ageb/pcorr2 ss2 tol; model prob=age yrsago bitter yrsagob/pcorr2 ss2 tol; model prob=age yrsago bitter yrsago2/pcorr2 ss2 tol; run; Correlation Analysis 4 'VAR' Variables: AGE YRSAGO BITTER PROB Simple Statistics Variable N Mean Std Dev Sum Minimum Maximum AGE 150 11.29333 2.44276 1694 7.00000 15.00000 YRSAGO 150 5.34000 2.89834 801.00000 0 12.00000 BITTER 150 3.96667 1.22292 595.00000 1.00000 6.00000 PROB 150 7.00000 3.08710 1050 0 17.00000 Pearson Correlation Coefficients / Prob > |R| under Ho: Rho=0 / N = 150 AGE YRSAGO BITTER PROB AGE 1.00000 0.82475 0.32007 -0.27590 0.0 0.0001 0.0001 0.0006 YRSAGO 0.82475 1.00000 0.38192 -0.30529 0.0001 0.0 0.0001 0.0001 BITTER 0.32007 0.38192 1.00000 0.05867 0.0001 0.0001 0.0 0.4758 PROB -0.27590 -0.30529 0.05867 1.00000 0.0006 0.0001 0.4758 0.0 Psych 5741, Fall 1994 9 Dec 1994 Judd & McClelland — 6 — Model: MODEL1 Dependent Variable: PROB Analysis of Variance Sum of Mean Source DF Squares Square F Value Prob>F Model 1 108.08764 108.08764 12.194 0.0006 Error 148 1311.91236 8.86427 C Total 149 1420.00000 Root MSE 2.97729 R-square 0.0761 Dep Mean 7.00000 Adj R-sq 0.0699 C.V. 42.53275 Parameter Estimates Parameter Standard T for H0: Variable DF Estimate Error Parameter=0 Prob > |T| INTERCEP 1 10.937644 1.15354432 9.482 0.0001 AGE 1 -0.348670 0.09984996 -3.492 0.0006 Model: MODEL2 Dependent Variable: PROB Analysis of Variance Sum of Mean Source DF Squares Square F Value Prob>F Model 1 4.88706 4.88706 0.511 0.4758 Error 148 1415.11294 9.56157 C Total 149 1420.00000 Root MSE 3.09218 R-square 0.0034 Dep Mean 7.00000 Adj R-sq -0.0033 C.V. 44.17399 Parameter Estimates Parameter Standard T for H0: Variable DF Estimate Error Parameter=0 Prob > |T| INTERCEP 1 6.412565 0.85958967 7.460 0.0001 BITTER 1 0.148093 0.20714508 0.715 0.4758 Model: MODEL3 Dependent Variable: PROB Analysis of Variance Sum of Mean Source DF Squares Square F Value Prob>F Model 1 132.34345 132.34345 15.211 0.0001 Error 148 1287.65655 8.70038 C Total 149 1420.00000 Root MSE 2.94964 R-square 0.0932 Dep Mean 7.00000 Adj R-sq 0.0871 C.V. 42.13773 Parameter Estimates Parameter Standard T for H0: Variable DF Estimate Error Parameter=0 Prob > |T| INTERCEP 1 8.736398 0.50617844 17.260 0.0001 YRSAGO 1 -0.325168 0.08337311 -3.900 0.0001 Psych 5741, Fall 1994 9 Dec 1994 Judd & McClelland — 7 — Model: MODEL4 Dependent Variable: PROB Analysis of Variance Sum of Mean Source DF Squares Square F Value Prob>F Model 2 134.92470 67.46235 7.717 0.0007 Error 147 1285.07530 8.74201 C Total 149 1420.00000 Root MSE 2.95669 R-square 0.0950 Dep Mean 7.00000 Adj R-sq 0.0827 C.V. 42.23841 Parameter Estimates Parameter Standard T for H0: Variable DF Estimate Error Parameter=0 Prob > |T| INTERCEP 1 9.458775 1.42293032 6.647 0.0001 AGE 1 -0.095282 0.17534820 -0.543 0.5877 YRSAGO 1 -0.258937 0.14778549 -1.752 0.0818 Squared Partial Variable DF Type II SS Corr Type II Tolerance INTERCEP 1 386.290236 . . AGE 1 2.581257 0.00200462 0.31978734 YRSAGO 1 26.837065 0.02045645 0.31978734 Model: MODEL5 Dependent Variable: PROB Analysis of Variance Sum of Mean Source DF Squares Square F Value Prob>F Model 3 186.21858 62.07286 7.345 0.0001 Error 146 1233.78142 8.45056 C Total 149 1420.00000 Root MSE 2.90698 R-square 0.1311 Dep Mean 7.00000 Adj R-sq 0.1133 C.V. 41.52835 Parameter Estimates Parameter Standard T for H0: Variable DF Estimate Error Parameter=0 Prob > |T| INTERCEP 1 7.877524 1.53920620 5.118 0.0001 AGE 1 -0.099415 0.17240860 -0.577 0.5651 YRSAGO 1 -0.339724 0.14895522 -2.281 0.0240 BITTER 1 0.519158 0.21072177 2.464 0.0149 Squared Partial Variable DF Type II SS Corr Type II Tolerance INTERCEP 1 221.345794 . . AGE 1 2.809751 0.00227217 0.31975707 YRSAGO 1 43.956938 0.03440214 0.30428990 BITTER 1 51.293871 0.03991507 0.85405611