STATISTICAL CONCEPTS COVERED ON THE EXAMS

(Spring 2008)

BIVARIATE REGRESSION AND CORRELATION ANALYSES *****************

1. Likely geometry of bivariate trends in natural sample populations.

2. Usefulness and flexibility of the second-degree polynomial (quadratic) regression models and correlation coefficients.

3. Difference between a regression model and a prediction equation.

4. Limitations of polynomial curve fitting.

5. Definition of the Least Squares Criterion.

6. Sources of variation in regression analysis (SST, SSR and SSD), and their relationship to the F statistic and R².

7. Null and alternative hypotheses, and underlying assumptions of the F test (both parametric and randomization) in regression analyses.

8 Rationale behind the F test of individual regression terms as opposed to full models.

9. Advantage of the nonparametric randomization F test relative to the parametric F test.

10. Rationale and practice underlying the random sampling, by graphical means, of sample distributions in the randomization F test.

11. Meaning of statistical significance for the F test (both parametric and randomization) in regression analyses in relation to the hyperbolic probability distribution of spurious F statistics.

MULTIVARITE REGRESSION AND CORRELATION ANALYSES **************

12. Relationship between and meaning of bivariate partial and total correlations (and regression coefficients) for multivariate data sets.

13. Interaction terms and dummy variables in multivariate regression.

14. Definition of the Least Squares Criterion.

15. Calculation of R².

16. Rationale for seeking a parsimonious multivariate regression model.

17. Multivariate regression models and strategies for finding the best prediction equation and for establishing the relative contributions of predictor variables.

18. General strategies of forward, backward, ‘stepwise’, and all-possible-subsets selection in stepwise regression.

19. Meaning of multicollinearity in multivariate data sets.

20. Standardized regression coefficients (beta weights) and the relative contributions of predictor variables.

21. Rationales and strategies in trend surface analysis for surface modeling (pseudo-contouring), and for separating regional trends and local anomalies.

MATRIX ALGEBRA *****************************************************

There will be no questions on matrix algebra.

CLUSTER ANALYSIS ****************************************************

22. Objectives of Q- and R-mode cluster analyses.

23. Characteristics of natural, homeostatic, and segregate clusters.

24. General strategies of agglomerative hierarchical clustering and k-means clustering.

25. Inter-sample distances for similarity matrices in Q-mode cluster analysis.

26. Inter-variable correlations for similarity matrices in R-mode cluster analysis.

27. Characteristics of the various clustering methods: single, complete and group average linkages; centroid; and Ward's.

28. Cophenetic correlation in cluster analysis.

29. Distinguishing characteristics of real and spurious clusters.

30. Ordination as an alternative to cluster analysis.

PRINCIPAL COMPONENTS AND FACTOR ANALYSES **********************

31. Objectives of principal components and factor analyses.

32. Conceptualization of the component axes, and the logic behind their sequential positioning and extraction.

33. Conceptualization and meaning of the eigenvalues and eigenvectors for component axes.

34. Conceptualization and meaning of component scores.

35. Meaning of component loadings, and what they say about the variance explained by variables and components.

36. Meaning and identification of 'principal' components.

37. Use of principal components for Q-mode ordination and other applications.

38. Meaning of common and unique factors in factor analysis.

39. Concept of communality and the reasoning behind communality estimates in factor analysis.

40. Vector representation of variables.

41. Conceptualization and purpose of factor rotation.

42. General approach to factor interpretation.

CORRESPONDENCE ANALYSIS ******************************************

43. Objectives of correspondence analysis.

44. Meaning and construction of contingency tables.

45. Use of principal components analysis as a step in correspondence analysis.

CANONICAL CORRELATION ANALYSIS **********************************

46. Objectives of canonical correlation analysis.

47. The meaning of eigenvalues, eigenvectors and, canonical scores.

48. Interpreting the results of canonical correlation analysis.

DISCRIMINANT ANALYSIS **********************************************

49. Objectives and applications of discriminant analysis.

50. General strategy of two-group discriminant analysis.

51. General strategy of parametric Bayesian multiple-group discriminant analysis.

52. General strategy of parametric Factorial multiple-group discriminant analysis.

53. General strategy of K-groups non-parametric discriminant analysis.