Download Statistics and Data Analysis in Geology (3rd_ed.) PDF

TitleStatistics and Data Analysis in Geology (3rd_ed.)
TagsGeology Experiment Quantitative Research Statistical Hypothesis Testing
File Size11.0 MB
Total Pages257
Table of Contents
                            Cover
Front Matter
Preface
Table of Contents
1. Introduction
	1.1 The Book and the Course it Follows
	1.2 Statistics in Geology
	1.3 Measurement Systems
	1.4 A False Feeling of Security
2. Elementary Statistics
	2.1 Probability
	2.2 Continuous Random Variables
	2.3 Statistics
	2.4 Summary Statistics
3. Matrix Algebra
	3.1 The Matrix
	3.2 Elementary Matrix Operations
	3.3 Matrix Multiplication
	3.4 Inversion and Solution of Simultaneous Equations
	3.5 Determinants
	3.6 Eigenvalues and Eigenvectors
		3.6.1. Eigenvalues
		3.6.2 Eigenvectors
	3.7 Exercises
4. Analysis of Sequences of Data
	4.1 Geologic Measurements in Sequences
	4.2 Interpolation Procedures
	4.3 Markov Chains
		4.3.1 Embedded Markov Chains
	4.4 Series of Events
	4.5 Runs Tests
	4.6 Least-Squares Methods and Regression Analysis
5. Spatial Analysis
	5.1 Geologic Maps, Conventional and Otherwise
	5.2 Systematic Patterns of Search
	5.3 Distribution of Points
		5.3.1 Uniform Density
		5.3.2 Random Patterns
		5.3.3 Clustered Patterns
		5.3.4 Nearest-Neighbor Analysis
	5.4 Distribution of Lines
	5.5 Analysis of Directional Data
6. Analysis of Multivariate Data
	6.1 Multiple Regression
	6.2 Discriminant Functions
		6.2.1 Tests of Significance
	6.3 Multivariate Extensions of Elementary Statistics
		6.3.1 Equality of Two Vector Means
		6.3.2 Equality of Variance-Covariance Matrices
	6.4 Cluster Analysis
Appendix
	Table A.1 Cumulative Probabilities for the Standardized Normal Distribution
	Table A.2 Critical Values of t for v Degrees of Freedom and Selected Levels of Significance
	Table A.3 Critical Values of F for v_1 and v_2 Degrees of Freedom and Selected Levels of Significance
	Table A.4 Critical Values of chi^2 for v Degrees of Freedom and Selected Levels of Significance
	Table A.5 Probabilities of Occurrence of Specified Values of the Mann-Whitney W_x Test Statistic
	Table A.6 Critical Values of Spearman's rho for Testing the Significance of a Rank Correlation
	Table A.7 Critical Values of D in the Kolmogorov-Smirnov Goodness-of-Fit Test
	Table A.8 Critical Values of the Lilliefors Test Statistic, T , for Testing Goodness-of-Fit to a Normal Distribution
	Table A.9 Maximum Likelihood Estimates of the Concentration Parameter kappa for Calculated Values of R
	Table A.10 Critical Values of R for Rayleigh's Test for the Presence of a Preferred Trend
	Table A.11 Critical Values of R for the Test of Uniformity of a Spherical Distribution
Index
	A
	B
	C
	D
	E
	F
	G
	H
	I
	J
	K
	L
	M
	N
	O
	P
	Q
	R
	S
	T
	U
	V
	W
	X
	Y
	Z
                        
Document Text Contents
Page 2

Statistics and Data Analysis

Third Edition

John C. Davis
Kansas Geological Survey
The University of Kansas

John Wiley & Sons
New York Clxchester Brisbane Toronto Singapore

Page 128

Spatial Analysis

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Figure 5-5. Locations of 123 exploratory holes drilled to top of Ordovician rocks (Arbuckle
Group) in central Kansas. Map has been divided into 12 cells of equal size.

orientation of subareas. However, the test is most efficient if the number of subar-
eas is a maximum (this increases the degrees of freedom), subject to the restriction
that no subarea contain fewer than five points. The expected number of points in
each subarea is

N
k (5 .8)

E = -

where N is the total number of data points and k is the number of subareas. A
x 2 test of goodness of fit of the observed distribution to the expected (uniform)
distribution is

where Oi is the observed number of data points in subarea i and E is the expected
number. The test has v = k - 2 degrees of freedom, where k is the number of
subareas.

As an example of the application of this test, consider the data-point distribu-
tion shown in Figure 5-5. These are the locations of 123 holes drilled in the search
for oil in the Ordovician Arbuckle stratigraphic succession in central Kansas. These
data are listed in file ARBUCKLE.TXT. In Figure 5-5, the map area has been divided
into 12 equal subareas, each of which we expect to contain about ten points, if the
points are uniformly distributed. The observed number of points in each subarea
and the computations necessary to find the test value are given in Table 5-1. This
test has v = 10 degrees of freedom, so the critical value of x 2 at the 5% (a = 0.05)
significance level is 18.3. The computed test value of x 2 = 17.0 does not exceed

301

Page 129

Statistics and Data Analysis in Geology - Chapter 5

this, so we conclude that there is no evidence suggesting that the quadrats are
unevenly populated. Note that the test applies only to the uniformity of point den-
sities between areas of a specified size and shape. It is possible that we could
select quadrats of different sizes or shapes that might not be uniformly populated,
especially if they were smaller than those used in this test.

Table 5-1. Number of wells in 12 subareas of central Kansas.

Observed Number (0 - E ) *
of Points E

10 0.006
5 2.689
5 2.689

11 0.055
13 0.738

5 2.689
12 0.299
16 3.226
16 3.226
9 0.152

13 0.738
8 0.494

TOTAL = 123
aTest value is not significant at the a = 0.05 level.

x 2 = 16.995"

Random patterns
Establishing that a pattern is uniform does not specify the nature of the unifor-
mity, for both regular and random patterns are expected to be homogeneous. For
many purposes, verifying uniformity is sufficient; but, if we desire more informa-
tion about the pattern, we must turn to other tests. If points are distributed at
random across a map area, even though the coverage is uniform, we do not expect
exactly the same number of points to lie within each subarea. Rather, there will
be some preferred number of points that occur in most subareas and there will
be progressively fewer subareas that contain either more points or fewer. This is
apparent in the example we just worked: although our hypothesis of uniformity
specified that we expect about ten observations in each subarea, we actually found
some areas that contained more than ten and some that contained fewer.

You will recall that the Poisson probability distribution is the limiting case
of the binomial distribution when p , the probability of a success, is very small
and (1 - p ) approaches 1.0. The Poisson distribution can be used to model the
occurrence of rare, random occurrences in time, as it was used in Chapter 4, or
it can be used to model the random placement of points in space. Although the
Poisson distribution, like the binomial, uses the numbers of successes, failures,
and trials in the calculation of probabilities, it can be rewritten so that neither the
number of failures nor the total number of trials is required. Rather, it uses the
number of points per quadrat and the density of points in the entire area to predict
how many quadrats should contain specified numbers of points. These predicted

302

Page 256

Index Terms Links

This page has been reformatted by Knovel to provide easier navigation.

West Texas (USA) 36

WHITE.TXT 93

Whitewater Bay 93 96 111

whorl 502

Wilburton gas field (Oklahoma) 391

Wilcoxon test 105

Williston Basin (North Dakota) 239

Windfall Reef (Devonian) 406

Wind River Basin 73

Wisconsinan 274

Wishart’s modification 498

witherite 494

within-cluster similarity 498

within-groups covariance matrix 573 576

WLYONS.TXT 113

Wolf River (Kansas) 350

Woodford shale (Devonian) 282

Wulff net 338 446

Wyoming (USA) 70 72 125 153 279 286 397

406 446

X

xenocryst 286

Xian province (China) 113

X-ray fluorescence 206

Y

Yellowcraigs (Scotland) 108

Yuma (Arizona) 446

YUMA.PIC 447

YUMA.TIF 447

Z

Page 257

Index Terms Links

This page has been reformatted by Knovel to provide easier navigation.

zeolites, sedimentary 114 592

ZEOLITES.TXT 592

zero isopach problem 391 449

zircon 102

zonation 234

z-score 57 95 110 476

z-statistic 57 61 63 66 310

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