Page 9 - Statistics and Data Analysis in Geology

Con tents

Nested design in analysis of variance ..................................... 88
The x2 Distribution ........................................................... 92
Goodness-of-fit test ......................................................... 93
The Logarithmic and Other Transformations ............................... 97
Other transformations .................................................... 102
Nonparametric Methods .................................................... 102
Mann-Whitney test ........................................................ 103
Kruskal-Wallis test ........................................................ 105
Nonparametric correlation ................................................ 105
Ko I mog o r ov-S m i r n ov tests ............................................... 107
Exercises ..................................................................... 112
Selected Readings ........................................................... 119

3 . Matrix Algebra ................. .......... ....... .... ... ......... .... 123
The Matrix ................................................................... 123
Elementary Matrix Operations ............................................. 125
Matrix Multiplication ........................................................ 127
Inversion and Solution of Simultaneous Equations ....................... 132
Determinants ................................................................ 136
Eigenvalues and Eigenvectors .............................................. 141
Eigenvalues ................................................................ 141
Eigenvectors ............................................................... 150
Exercises ..................................................................... 153
Selected Readings ........................................................... 157

4 . Analysis of Sequences of Data .............................. 159
Geologic Measurements in Sequences ..................................... 159
Inter pol at ion Procedures .................................................... 163
Markov Chains ............................................................... 168
Embedded Markov chains ................................................. 173
Series of Events ............................................................. 178
Runs Tests ................................................................... 185
Least-Squares Methods and Regression Analysis ......................... 191
Confidence belts around a regression ................................... 200
Calibration ................................................................. 204
Curvilinear regression ..................................................... 207

xii