Statistics and Data Analysis in Geology (3rd edition)

Cover......Page 1
Front Matter......Page 2
6.15 Exercises......Page 0
Preface......Page 4
Table of Contents......Page 8
1. Introduction......Page 14
1.1 The Book and the Course it Follows......Page 16
1.2 Statistics in Geology......Page 19
1.3 Measurement Systems......Page 20
1.4 A False Feeling of Security......Page 22
2.1 Probability......Page 24
2.2 Continuous Random Variables......Page 38
2.3 Statistics......Page 42
2.4 Summary Statistics......Page 47
3.1 The Matrix......Page 51
3.2 Elementary Matrix Operations......Page 53
3.3 Matrix Multiplication......Page 55
3.4 Inversion and Solution of Simultaneous Equations......Page 60
3.5 Determinants......Page 64
3.6.1. Eigenvalues......Page 69
3.6.2 Eigenvectors......Page 78
3.7 Exercises......Page 81
4.1 Geologic Measurements in Sequences......Page 87
4.2 Interpolation Procedures......Page 91
4.3 Markov Chains......Page 96
4.3.1 Embedded Markov Chains......Page 101
4.4 Series of Events......Page 106
4.5 Runs Tests......Page 113
4.6 Least-Squares Methods and Regression Analysis......Page 119
5.1 Geologic Maps, Conventional and Otherwise......Page 120
5.2 Systematic Patterns of Search......Page 122
5.3 Distribution of Points......Page 126
5.3.1 Uniform Density......Page 127
5.3.2 Random Patterns......Page 129
5.3.3 Clustered Patterns......Page 134
5.3.4 Nearest-Neighbor Analysis......Page 137
5.4 Distribution of Lines......Page 140
5.5 Analysis of Directional Data......Page 143
6. Analysis of Multivariate Data......Page 148
6.1 Multiple Regression......Page 149
6.2 Discriminant Functions......Page 158
6.2.1 Tests of Significance......Page 164
6.3 Multivariate Extensions of Elementary Statistics......Page 166
6.3.1 Equality of Two Vector Means......Page 170
6.3.2 Equality of Variance-Covariance Matrices......Page 171
6.4 Cluster Analysis......Page 174
Table A.1 Cumulative Probabilities for the Standardized Normal Distribution......Page 180
Table A.2 Critical Values of t for v Degrees of Freedom and Selected Levels of Significance......Page 181
Table A.3 Critical Values of F for v_1 and v_2 Degrees of Freedom and Selected Levels of Significance......Page 182
Table A.4 Critical Values of chi^2 for v Degrees of Freedom and Selected Levels of Significance......Page 186
Table A.5 Probabilities of Occurrence of Specified Values of the Mann-Whitney W_x Test Statistic......Page 187
Table A.6 Critical Values of Spearman's rho for Testing the Significance of a Rank Correlation......Page 192
Table A.7 Critical Values of D in the Kolmogorov-Smirnov Goodness-of-Fit Test......Page 193
Table A.8 Critical Values of the Lilliefors Test Statistic, T , for Testing Goodness-of-Fit to a Normal Distribution......Page 196
Table A.9 Maximum Likelihood Estimates of the Concentration Parameter kappa for Calculated Values of R......Page 197
Table A.10 Critical Values of R for Rayleigh's Test for the Presence of a Preferred Trend......Page 198
Table A.11 Critical Values of R for the Test of Uniformity of a Spherical Distribution......Page 199
A......Page 200
B......Page 203
C......Page 205
D......Page 211
E......Page 215
F......Page 217
G......Page 219
H......Page 221
I......Page 222
K......Page 224
L......Page 225
M......Page 227
N......Page 232
O......Page 233
P......Page 235
Q......Page 239
R......Page 240
S......Page 243
T......Page 250
V......Page 253
W......Page 255
Z......Page 256