Page 12 - Statistics and Data Analysis in Geology

Con tents

Introduction to Eigenvector Methods. Including Factor Analysis ........ 500
Eckart-Young theorem .................................................... 502
Principal Component Analysis .............................................. 509
Closure effects on principal components ................................ 523
R-Mode Factor Analysis .................................................... 526
Factor rotation ............................................................. 533
Maximum likelihood factor analysis ..................................... 538
Q-Mode Factor Analysis .................................................... 540
A word about closure ..................................................... 546
Principal Coordinates Analysis ............................................. 548
Correspondence Analysis .................................................... 552
Multidimensional Scaling ................................................... 560
Simultaneous R- and Q-Mode Analysis ................................... 566
Multigroup Discriminant Functions ........................................ 572
Canonical Correlation ....................................................... 577
Exercises ..................................................................... 584
Selected Readings ........................................................... 594

Appendix ................................................................... 601

Table A.l. Cumulative probabilities for the standardized normal
distribution ............................................................. 601

Table A.2. Critical values of t for v degrees of freedom and
selected levels of significance ......................................... 602

Table A.3. Critical values of F for v1 and v2 degrees of freedom
and selected levels of significance .................................... 603

Table A.4. Critical values of x2 for v degrees of freedom and
selected levels of significance ......................................... 607

Table A.5. Probabilities of occurrence of specified values
of the Mann-Whitney Wx test statistic .............................. 608

Table A.6. Critical values of Spearman's p for testing the significance
of a rank correlation ................................................... 613

Table A.7. Critical values of D in the Kolmogorov-Smirnov
goodness-of-fit test .................................................... 614

Table A.8. Critical values of the Lilliefors test statistic, T, for
testing goodness-of-fit to a normal distribution ..................... 617

Table A.9. Maximum likelihood estimates - of the concentration
parameter K for calculated values of R .............................. 618

xv