REFERENCES

Acton, F. S. (1966). Analysis of Straight-Line Data, Dover, New York. Ager, D. V. (1973). The Nature of the Stratigraphical Record, Macmillan, London;

Halsted Press, New York. Ahrens, L. H. (1954). The log-normal distribution of the elements. Geochim. cosmo­

chim. Acta, 6, 121-31 Aitchison, J. and Brown, J. A. C. (1957). The Log-normal Distribution, with Special

Reference to its Use in Economics, Cambridge University Press, Cambridge Allen, J. R. L. (1970). Studies in fluviatile sedimentation: a comparison of fining­

upwards cyclothems with special reference to coarse-member composition and interpretation. J. sedim. Petrol., 40, 298-323

Barford, N. C. (1967). Experimental Measurements: Precision, Error and Truth, Addison-Wesley, London

Bates, R. C. (1959). An application of statistical analysis to exploration for uranium on the Colorado plateau. Econ. Geol., 54, 449-66

Batsche1et, E. (1965). Statistical Methods for the Analysis of Problems in Animal Orientation and Certain Biological Rhythms, American Institute of Biological Sciences, Washington

Batten, D. J. (1973). Use of palynologic assemblage types in Wealden correlation. Palaeontology, 16, 1-40.

Bayly, B. (1968). Introduction to Petrology, Prentice-Hall, Englewood Cliffs, N.J. Billings, G. K. and Ragland, P. C. (1968). Geochemistry and mineralogy of the recent

reef and lagoonal sediments south of Belize (British Honduras). Chem. Geol., 3, 135-53

Bonham-Carter, G. F. (1967). FORTRAN IV program for Q-mode cluster analysis of nonquantitative data using IBM 7090/7094 computers. Computer Contribution No. 17, Kansas Geological Survey

Bozdar, L. B. and Kitchenham, B. A. (1972). Statistical appraisal of the occurrence of lead mines in the northern Pennines. Trans. Inst. Min. Metall. Section B, 81. B183-88

Chayes, F. (1956). Petrographic Modal Analysis, Wiley, New York Chayes, F. (1960). On correlation between variables of constant sum. J. geophys.

Res. 65, 4185-93 Chayes, F. (1970). Another last look at G-l/W-l. Math. Geol., 2, 207-9 Chayes, F. (1971). Ratio Correlation: A Manual for Students of Petrology and

Geochemistry, University of Chicago Press, Chicago Clifford, A. A. (1973). Multivariate Error Analysis, Applied Science Publishers,

Barking Crozier, M. J. (1973). Techniques for morphometric analysis of land slips. Z. Geo­

morpho N.F., 17, 78-101

145

146 STATISTICAL METHODS FOR THE EARTH SCIENTIST

Curl, R. C. (1966). Caves as a measure of karst. J. Geol., 74, 798-830 Curtis, C. D. (1969). Trace element distribution in some British Carboniferous sedi­

ments. Geochim. cosmochim. Acta, 33, 519-23 Davis, 1. C. (1973). Statistics and Data Analysis in Geology, Wiley, New York Dixon, W. 1. and Massey, F. 1. (1957). IntroductIOn to Statistical Analysis, McGraw­

Hill, New York Doornkamp, 1. C. and King, C. A. M. (1971). Numerical Analysis in Geomorphology:

An Introduction. Arnold, London Draper, N. R. and Smith, H. (1966). Applied Regression Analysis, Wiley, New York Fairbairn, H. W. (1951). A co-operative investigation of precision and accuracy in

chemical, spectrochemical and modal analysis of silicate rocks. Bull. U.S. geol. Surv., 980, 1-24

Feller, W. (1968). An Introduction to Probability Theory and its Applications. Volume I, Wiley, New York

Fisher, R. A. (1956). Statistical Methods and Scientific Inferences, Oliver & Boyd, Edinburgh

Fisher, R. A. and Yates, F. (1948). Statistical Tablesfor Biological, Agricultural and Medical Research, Oliver & Boyd, Edinburgh

Flanagan, F. 1. (1973). 1972 values for international geochemical reference samples. Geochim. cosmochim. Acta, 37, 1189-200

Fleischer, M. (1965). Summary of new data on rock samples G-l and W-l, 1962-1965. Geochim. cosmochim. Acta, 29, 1263-83

Fleischer, M. and Stevens, R. E. (1962). Summary of new data on rock samples G-l and W-l. Geochim. cosmochim. Acta, 26, 525-43

Fryer, H. C. (1966). Concepts and Methods of Experimental Statistics, Allyn & Bacon, Rockleigh, N.J.

Ghosh, A. K. (1965). A statistioal approach to the exploration of copper in the Singhbhum shear zone, Bihar, India. Econ. Geol., 60, 1422-30

Gray, A. and Matthews, G. B. (1922). A Treatise on Bessel Functions and Their Applications to Physics, Macmillan, London

Griffiths, 1. C. (1967). Scientific Method in Analysis of Sediments, McGraw-Hill, New York

Gunatilaka, H. A. and Till, R. (1971). A precise and accurate method for the quanti­tative determination of carbonate minerals by X-ray diffraction using a spiking technique. Min. Mag., 38, 481-7

Harbaugh, J. W. and Bonham-Carter, G. (1970). Computer Simulation in Geology, Wiley, New York

Harbaugh, J. W. and Merriam, D. F. (1968). Computer Applications in Stratigraphic Analysis, Wiley, New York

Hayami, I. (1973). Discontinuous variation in an evolutionary species, Cryptopecten vesiculosus, from Japan. J. Palaeont., 47, 401-20

Hellewell, E. G. and Myers, J. O. (1973). Measurement and analysis of in situ rock densities in British Carboniferous and Permo-Triassic. Trans. Inst. Min. Metall. Section B, 82, B51-60

Howarth, R. J. and Lowenstein, P. L. (1971). Sampling variability of stream sediments in broad-scale regional geochemical reconnaissance. Trans. Inst. Min. Metall. Section B, 80, B363-72

Kahn, J. S. (1956). The analysis and distribution of the properties of packing in sand size sediments. 2. The distribution of the packing measurements and an example of packing analysis. J. Geol., 64, 578-606

Kendall, M. G. (1970). Rank Correlation Methods, Griffin, London Kermack, K. A. and Haldane, J. B. S. (1950). Organic correlation and allometry.

Biometrika, 37,30-41

REFERENCES 147

Koch, G. S. and Link, R. F. (1963). Distribution of metals in the Don Tomas vein, Frisco Mine, Chihuahua, Mexico. Econ. Geol., 58, 1061-70

Koch, G. S. and Link, R. F. (1970). Statistical Analysis of Geological Data, Wiley, New York

Koch, G. S. and Link, R. F. (1971). Statistical Analysis of Geological Data. Volume II, Wiley, New York

Krinsley, D. (1960). Magnesium, strontium and aragonite in the shells of certain littoral gastropods. J. Palaeont., 34, 744-55

Krumbein, W. C. (1967). FORTRAN IV computer programs for Markov chain experiments in geology. Computer Contribution No. 13, Kansas Geological Survey

Krumbein, W. C. and Graybill, F. A (1965). An Introduction to Statistical Models in Geology, Wiley, New York

Krumbein, W. C. and Pettijohn, F. J. (1938). Manual of Sedimentary Petrography, Appleton-Century Crofts, New York

Lees, A, Buller, A. T. and Scott, J. (1969). Marine carbonate sedimentation processes, Connemara, Eire. An interim report. Reading University Geological Report No.2

Li, J. C. R. (1964). Statistical inference, I, Edwards Brothers, Ann Arbor MacDonald, R. and Bailey, D. K. (1973). The chemistry of the peralkaline over-

saturated obsidians. Prof Pap. U.S.geol. Surv., 44O-N-l Mandel, J. (1964). The Statistical Analysis of Experimental Data, Wiley, New York Mardia, K. V. (1972). Statistics of Directional Data, Academic Press, London Miall, A D. (1973). Markov chain analysis applied to an ancient alluvial plain

succession. Sedimentology, 20, 347-64 Miller, R. L. and Kahn, J. S. (1962). Statistical Analysis in the Geological Sciences,

Wiley, New York Moroney, M. J. (1970). Factsfrom Figures, Penguin, Harmondsworth Murdoch, J. and Barnes, J. A (1974). Statistical Tables for Science, Engineering,

Management and Business Studies, 2nd revised edition, Macmillan, London Murray, J. W. (1965). The foraminiferida of the Persian Gulf. 2. The Abu Dhabi

Region, Palaeogeog, Palaeoclim. Palaeoecol., 1. 307-32 Parkinson, D. (1954), Quantitative studies of brachipods from the lower Carboni­

ferous reef limestones of England. I. Schizophonia resupinata (Martin). J. Palaeont. 28, 367-81

Peach, P. A. and Renault, J. R. (1965). Statistical analysis of some characteristics of British Columbia molybdenite occurrences. Econ. Geol., 60, 1510-15

Pearson, E. S. and Hartley, H. O. (1969). Biometrika Tablesfor Statisticians, Cam­bridge University Press, Cambridge

Raup, D. M. and Stanley, S. M. (1971). Principles of Palaeontology, Freeman, San Francisco

Read, W. A (1969). Analysis and simulation of Namurian sediments in Central Scotland using a Markov-process model. Math. Geol., 1, 199-219

Read, W. A. and Dean, J. M. (1967). A quantitative study of a sequence of coal­bearing cycles in the Namurian of central Scotland, 1. Sedimentology, 9, 137-56

Read, W. A. and Dean, J. M. (1968). A quantitative study of a sequence of coal­bearing cycles in the Namurian of central Scotland, 2. Sedimentology, 10,121-36

Reyment, R. A. (1966). Preliminary observations on gastropod predation in the western Niger delta. Palaeogeog. Palaeoclim. Palaeoecol., 2, 81-102

Reyment, R. A (1971). Introduction to Quantitative Palaeoecology, Elsevier, Amster­dam

Royal Society (1971). Quantities, Units and Symbols, Royal Society, London Selley, R. C. (1969). Studies of sequence in sediments using a simple mathematical

device. Q. Jl geol. Soc. Lond., 125, 557-81

148 STATISTICAL METHODS FOR THE EARTH SCIENTIST

Siegel, S. (1956). Non-parametric Statistics for the Behavioural Sciences, McGraw­Hill, New York

Sneath, P. H. A. and Sokal, R. R. (1973). Numerical Taxonomy: The Principles and Practice of Numerical Classification, Freeman, San Francisco

Sokal, R. R. and Sneath, P. H. A. (1963). Principles of Numerical Taxonomy, Freeman, San Francisco

Spiegel, M. R. (1961). Schaum's Outline of Theory and Problems of Statistics, McGraw­Hill, New York

Stevens, R. E. and Niles, W. M. (1960). Second report on a co-operative investigation of the composition of two silicate rocks. Bull. U.S. geol. Surv., 1113, 3-43

Taylor, R. K. (1973). Compositional and geotechnical characteristics of a 100-year old colliery spoil heap. Trans. Inst. Min. Metall. Section A, 82, A1-14

Till, R. (1971). Are there geochemical criteria for differentiating reef and non-reef carbonates? Bull. Am. Ass. Petrol. Geol., 55, 523-8

Till, R. (1973). The use of linear regression in geomorphology. Area 5, 303-8 Till, R. and Colley, H. (1973). Thoughts on the use of principal component analysis

in petrogenetic problems. Math. Geol., 5, 341-50 Till, R., Hopkins, D. T. and McCann, C. (1972). A collection of computer programs

in BASIC for use in geology and geophysics. Reading University Geological Report No.5

Vistelius, A. B. (1970). Statistical models of silicate analysis and results of investiga­tion ofG-1 and W-1 samples. Math. Geol., 2,1-14

Vistelius, A. B., Ivanov, D. N., Kuroda, Y. and Ruiz Fuller, C. (1970). Variations of modal composition of granitic rocks in some regions around the Pacific. Math. Geol., 2, 63-80

Von Mises, R. (1939). Probability, Statistics and Truth, Hodge, London Von Mises, R. (1964). Mathematical Theory of Probability and Statistics, Academic

Press, New York Wadati, K. (1967). Earthquake, Depth of (Deep-focus earthquake), in International

Dictionary of Geophysics (ed. S. K. Runcorn), Pergamon, London p. 389-92 Watson, G. S. (1966). The statistics of orientation data. J. Geol., 74, 786-97 Webster, R. and Burrough, P. A. (1972). Computer based soil mapping of small

areas from sample data. J. Soil Sci., 23, 210-34 Yevjevich, V. (1971). Probability and Statistics in Hydrology, Water Resources

Publications, Colorado Yule, G. U. and Kendall, M. G. (1953). An Introduction to the Theory of Statistics,

Griffin, London

FURTHER READING

Allen, P. and Krumbein, W. C. (1962). Secondary trend components in the Top Ashdown Pebble Bed: A case history. J. Geol., 70, 507-38

Anderson, A. J. B. (1971). Numerical examination of multivariate soil samples. Math. Geol., 3, 1-14

Anderson, T. N. (1968). An Introduction to Multivariate Statistical Analysis, Wiley, New York

Berry, B. J. L. and Marble, D. F. (1968). Spatial Analysis, A Reader in Statistical Geography, Prentice-Hill, Englewood Cliffs, N.J.

Cattell, R. B. (1965a). Factor analysis: An introduction to essentials: I. Biometrics, 21, 190-215

Cattell, R. B. (1965b). Factor analysis: An introduction to essentials: II. Biometrics, 21, 405-35

Chayes, F. (1970). On deciding whether trend surfaces of progressively higher order are meaningful. Geol. Soc. Am. Bull., 81, 1273-78

Chorley, R. J. (1972). Spatial Analysis in Geomorphology, Methuen, London Cooley, W. W. and Lohnes, P. R. (1962). Multivariate Procedures for the Behavioural

Sciences, Wiley, New York Cooley, W. W. and Lohnes, P. R. (1971). Multivariate Data Analysis, Wiley, New

York Davis, J. C. (1973). Statistics and Data Analysis in Geology, Wiley, New York Davis, J. C. and Sampson, R. J. (1966). FORTRAN II program for multivariate

discriminant analysis using an IBM 1620 computer. Computer Contribution No.4, Kansas Geological Survey

Draper, N. R. and Smith, H. (1966). Applied Regression Analysis, Wiley, New York Harbaugh, J. W. and Merriam, D. F. (1968). Computer Applications in Stratigraphic

Analysis, Wiley, New York Harman, H. H. (1967). Modern Factor Analysis, University of Chicago Press, Chicago Howarth, R. J. (1970). Principal component analysis of the geochemistry and mineral­

ogy of the Portaskaig tillite and Kiltyfanned Schist (Dalradian) of Co. Donegal, Eire, Math. Geol., 2, 285-302

Hsu, H. P. (1970). Fourier Analysis, Simon & Schuster, New York Imbries, J. and Purdy, E. G. (1963). Classification of modern Bahamian carbonate

sediments, in Classification of Carbonate Rocks, a Symposium (ed. W. E. Ham), American Association of Petroleum Geologists, Memoir 1, 253-72

Klovan, J. E. (1966). The use of factor analysis in determining depositional environ­ments from grain size distributions. J. Sedim. Petrol., 36, 115-25

Koch, G. S. and Link, R. F. (1970). Statistical Analysis of Geological Data, Wiley, New York

Koch, G. S. and Link, R. F. (1971). Statistical Analysis of Geological Data. Volume II, Wiley, New York

149

150 STATISTICAL METHODS FOR THE EARTH SCIENTIST

Krumbein, W. C. (1959). The 'sorting out' of geological variables illustrated by regression analysis of factors controlling beach firmness. J. Sedim. Petrol., 29, 575-87

Krumbein, W. C. and Graybill, F. A. (1965). An Introduction to Statistical Models in Geology, Wiley, New York

Le Maitre, R. W. (1968). Chemical variation within and between volcanic rock series-a statistical approach. J. Petrol., 9, 220-52

Li, J. C. R. (1964). Statistical inference, II, Edwards Brothers, Ann Arbor Matalas, N. C. and Reiher, B. J. (1967). Some comments on the use offactor analysis.

Wat. Resour. Res., 3, 213-23 Mather, P. M. (1969). Cluster analysis. Computer Applications No.1, Nottingham Matheron, G. (1971). The theory of region ali sed variables and its applications.

Cah. Cent. Morph. Math. No.5 Miller, R. L. and Kahn, J. S. (1962). Statistical Analysis in the Geological Sciences,

Wiley, New York Overall, J. E. and Klett, C. J. (1972). Applied Multivariate Analysis, McGraw-Hill,

New York Parks, J. M. (1966). Cluster analysis applied to multivariate geological problems.

J. Geol., 74, 703-15 Potter, P. E., Shimp, N. F. and Witters, J. (1963). Trace elements in marine and

fresh-water argillaceous sediments. Geochim. cosmochim. Acta, 27, 669-94 Purdy, E. G. (1963). Recent calcium carbonate facies of the Great Bahama Bank.!.

Petrography and reaction groups. J. Geol., 71, 415-25 Siegel, S. (1956). Non-parametric Statistics for the Behavioural Sciences. McGraw­

Hill, New York Spencer, D. W., Degens, E. T. and Kulbicki, G. (1968). Factors affecting element

distributions in sediments, in Origin and Distribution of the Elements (ed. L. H. Ahrens), Pergamon, London, 981-98

Till, R. and Colley, H. (1973). Thoughts on the use of principal component analysis in petrogenetic problems. Math. Geol., 5 341-50

Wahlstedt, W. C. and Davis, J. C. (1968). FORTRAN IV program for computation and display of principal components. Computer Contribution No. 21, Kansas Geological Survey

Watson, G. S. (1971). Trend-surface analysis. Math. Geol., 3, 215-26 Whitten, E. H. T. (1959). Compositional trends in a granite: Modal variation and

ghost stratigraphy in part of the Donegal granite, Eire. J. geophys. Res., 64, 835-48

Whitten, E. H. T. (1963). Application of quantitative methods in the geochemical study of granite massifs. R. Soc. Can. Spec. Pubis No.6, 76--123

Whitten, E. H. T. (1970). Orthogonal polynomial trend surfaces for irregularly spaced data. Math. Geol., 2, 141-52

Wollenben, J. A., Pauken, R. J. and Dearien, J. A. (1968). FORTRAN IV program for multivariate palaeontologic analysis using an IBM system/360 model 40 computer. Computer Contribution No. 20, Kansas Geological Survey, 1-12

INDEX

Figure and table page references are printed in bold type

IX-level probability 63--6 (see also Significance level)

Accuracy 3, 77-8, 80, precision and 3 Allometric growth line 103 Alternative hypothesis 62-3 Analysis of variance 104ff, 110, 108ff, I13ff,

applications of 116, arcsin transformation in 113, degrees of freedom for 109-10, F-test in 110, logarithmic transformation in 113, null hypothesis for 108, 114, power 105, 107

Arcsin transformation 113 Attributes 5

~-leveI probability 63---6 Bartlett's test 105 Bias 77-8, null hypothesis for 77, I-test for 78 Binomial distribution 25ff, 30, applications of

29-30, formula for 29, mean and standard deviation of 29

Central limit theorem 53--4 Chi-square (X 2 ) distribution 68ff, 69, 73, 74,

129,130, applications of 70-5, 81-2, degrees of freedom for 69-70, 73

Chi-square (X2) test 69ff, 121--4, 129-30, applications of 75, degrees offreedom of73, expected values of 69, 73--4, null hypothesis for 71, 72, 74, 121, observed value in 69, 72, 74, power of 124, use of 124, Yates's correction for continuity of 123

Circular normal distribution 38ff, 38, appli­cations of 42, formula for 38, properties of 39,41-2

Classical regression 91ff, applications of 103, dependent and independent variable in 92, intercept of 92, 95, 97, population line of 92, slope of 92, 95, 97

Closed number systems 90-1, correlation of 90-1

Cluster analysis 141-2, applications of 141-2, dendrogram for 137, coefficients of simila­rity from 136-7, 141

Cochran's test 107, null hypothesis for 107

Coefficient of similarity 134ff, cluster analysis from 136-7, 141, Jaccard's 135, Sokal and Michener's 134

Coefficient of variation 76-7,79 Combinations 10-11 Comparison of two means 61ff Confidence interval, of properties of classical

regression 96-7, greatest lower bound on 60, least upper bound on 61, of reduced major axis line 102, I-test and I-value for 56--63

Confidence level (see Significance level) Contingency tables 118ff, 118, applications of

138, chi-square test for 121--4, expected frequency in 121-2, observed frequency in 121-2

Correlation 83ff, enhancement of, by constant sum 91, non-parametric 130ff

Correlation coefficient (r) 84--8, degrees of freedom of 87, 88, graphing of 88-90, matrix of 90, 103, non-prametric (see Spearman's rank correlation coefficient), null hypothesis for 87, 88, partial 140, population (p) and sample (r) 84, 87-8, significant values of 87-8, t-test for significance of 87, z-values for comparison of 87-8

Correlation matrix 90, applications of 103 Critical regions 36 (see also Significance level) Critical values of sample mean 64 Cumulative frequency distribution 21 Cyclic sequences, analysis of 11-15, 74--5, 143

Degrees of freedom (v), definition of 56, use of 56, 63, 66-8, 69-70, 73, 87, 88, 105---6, 109-10, Ill, 115, 122-3, 129-30, 133--4

Dendrogram 137, applications of 138 Dependent variable 92, 99, 140 Directional data, analysis of 38ff Discriminant analysis 141, applications of 142 Discrete distribution 25-30, 30-1, 45, 46

Error mean square 11 0, 111 Error theory 75ff Error values, distribution of 76-7, 79, 92 Errors 75---6, laws of propagation of 78-9,

random 75-6. n, systematic 77, type I and type II 63---6

Event 7

151

152 INDEX

Expected frequency or value 69, 72, 121-2 Experimental errors 751T

F-distribution 66ff, 67, degrees of freedom 66-7, formula for 66

F-test 68, applications of 116, assumptions of 112-3, Hartley's maximum 105ff, in analysis of variance 108, 11 0, 115, in multiple regres­sion 140, null hypothesis for 108

Factor analysis 142-3, applications of 142-3, comparison of principal component analy­sis with 142

Factorial 10, 119-20 Fisher's least significant difference test III ff,

degrees of freedom of III, formula for III Fisher's exact probability test 119ff, null

hypothesis for 119, power of 122 Fourier analysis 143, applications of 143 Frequency, absolute 19, relative 19 Frequency chart 21, curve 21, diagram 17-19 Frequency distribution, 21

GI and WI inter-laboratory experiment 80-1 Gaussian distribution (see Normal distri­

bution) Geochemical data, analysis of 18ff, 57ff, 62ff,

89ff, 104ff, 113ff, I 24ff, 126ff Geomorphological data, analysis of 86ff, 131ff Geotechnical data, analysis of 70ff, 91ff GLB (see Confidence interval, greatest lower

bound) Goodness-of-fit test 691T, degrees offreedom of

69-70, for normal distribution 70-4 Grain size, log-normal distribution 44

Hartley's maximum-F test 105ff, degrees of freedom of 105-6, null hypothesis for 105

Histogram 17-19, 17, 19 Homogeneity of variance 105ff, Cochran's

test for 107, Hartley's maximum-F test for 105ff

Independent variable 92, 140 Inter-laboratory equipment 80--1 Intercept of regression line, 91, 92, 95, 97, 100,

102

Kolmogorov-Smirnov two-sample test I 26ff, applications of 138, chi-square test for 129-30, degrees of freedom of 129-30, graphical solution of 129

Kriging 141, applications of 141, comparison of trend surface analysis with 141

Kurtosis 25

A-statistic for Markov property 75 Law of propagation of errors 78-9, first and

second 79 Least-squares best-fit, in classical regression

91, 95, in multiple regression 140, in trend­surface analysis 140-1

Linear regression, applications of 103 (see also Classical regression and Reduced major axis line)

Log-normal distribution 43ff, 44, applications of 44, formula for 43, properties of 43

Log transformation 113 LSD (see Fisher'o least significant difference

test) LUB (see Confidence interval, least upper

bound)

Markov chain 15, applications of 15 Markov process 14-15 Markov property, test for 74-5 Mean 22-3, 23, of distribution 24, 29, 32, 36,

39, 43, 45, 48, 52, 53, 54, 108, 109, 126, of population (/I) 48, of sample (m) 48, of sample means 53

Mean square error 11 0, III Mean square treatment 110 Means, comparison of two 61ff, null hypo­

thesis for 62, (-test and (-value for 61ff Measurement process 2ff Measurement scales 3ff, classificatory J--4,

interval 4, nominal 3-4, ordinal 4, ranking 4, ratio 5

Median 22,23 Mode 22,23 Moments 25 Multiple regression 140 Multivariate statistics 90, 133ff

Nominal data, coefficients of similarity for 134ff, comparing set of 118ff, contingency tables for 118ff, 118

Non-parametric correlation coefficient (see Spearman's rank correlation coefficient)

Non-parametric statistics 5, 117ff Non-parametric (-test (see Wilcoxon-Mann­

Whitney test) Normal distribution 30ff, 31, 32, 33, appli­

cations of 32, critical regions of 36, formula for 32, mean and standard deviation of 32

Null hypothesis 62-3, acceptance of 62, 6J-5, 68, 74, 78, 103, 106, 120, 123, rejection of 62, 6J-5, 73, 87,88,110,116, 120, 126, 130, 133

Observed values in chi-square test 69, 71 One-way analysis of variance 108ff

INDEX 153

Ordinal data 4, Kolmogorov-Smirnov test for I 26ff, Spearman's rank correlation coefficient for 13 Iff, Wilcoxon-Mann­Whitney test for 124ff

Palaeontological data, analysis of 53ff, 99ff, 119ff, 134ff

Parameters (see Sample, properties of) Parametric statistics 5, assumptions and power

of 117 Partial correlation 140 Pearson's product moment correlation coeffi­

cient (see Correlation coefficient) Permutations 10-11 Physical properties data, analysis of 33ff,

70ff, 91ff Poisson distribution 45ff, 46, applications of

45-6, mean and variance of 45 Population, definition of 47, sample estimates

of 48, target 48 Population parameters, sample estimates of

48, 531T, 92, 96 Population variance (CT 2 ) 48, 52-3, 54 Population variances, equality of 105 Power of a test 63ff, 105, 107, 117 Precision 3, 76-7 Precision and accuracy 3, 76ff Prediction using classical regression 97 Presence/absence data 117, 134-8 Principal component analysis I 42ff, appli­

cations of 142 -3, comparison of factor analysis with 142

Probability 7ff, continuous distribution 30ff, definition of concept of 7 -8, discrete 25ff, 45ff

Probability density function 25 Probability matrix 13-14 Probability, rules of 8ff Propagation of errors 78ff

Random numbers 48-50, tables of 49 Random sample 48, collection of 48-51 Ranking procedures 124-6, 131--4 Reduced major axis line 99ff, applications of

103, intercept of 100-2, slope of 100-2, z-values for comparing slopes of 102-3

Regression, classical 91ff, linear 91ff, multiple 140 (see also Classical regression)

Replicates 76

Sample 47, properties of 48, 50, 52ff Sample grid 50 Sample mean (see Mean) Sample means, mean and variance of 52-3,

ordered array of III -12

Sample variance (S2) 55 Sampling procedures 47, 48ff, pseudo-random

50, random 48·-50, systematic 50-I, un­biased 50

Sampling with replacement 52 Scatter diagrams 88 Sedimentological data, analysis of lIlT, 201T,

25ff, 74ff, 118ff Significance level 62-3, 63-6, 68, 74, 78, 87-8,

96--7, 102-3, 106, 110, 111-2, 115-6, 119, 120, 122, 126, 130, 133--4

Similarity, coefficients of 134ff Skewness 25 Slope of regression line 91-2,95-7,100,102-3 Spearman's rank correlation coefficient 133ff,

applications of 138, formula for 132, null hypothesis for 132, standard normal deviate of 133, t-test for 133-4

Square-root transformation 113 Standard deviation 24, 29, 32, 36, 37, 38, 43,

45, 52-3, 100, 133 (see also Variance) Standard normal tables 34-5 Standardised normal distribution 36ff, 37,

formula for 36, mean and standard devia­tion of 36

Standards 77, 80 Statistical inference 48 Statistics I, 16, bivariate 139, descriptive 6, 16,

inferential 6, multivariate 139fT, purpose of 47-8, univariate 139

Stochastic process 14 Student's t-distribution (see t-distribution) Sum of cross-products, corrected 84, 86, 95-6 Sum of squares, between-groups 109-10,

corrected 84, 86, 95, 96, 97, 100, error 115, methods 115, minimised 91, specimens 115, total 109, 114, within-groups 109-10

t-distribution 56ff, 57, formula for 56, one­tailed value of 60, power of 61, 63ff, two­tailed value of 58

t-test 61ff, 87, 97, Ill, 133--4, 140, applications of 81, degrees of freedom of 56, one-tailed 60, 61, two-tailed 59

t-value 61ff, 87, 97, 111, 133-4, 140 Testing hypotheses (see Null hypothesis) Theory of regionalised variables 141 Time-series analysis 143, applications of 143,

Fourier analysis and runs tests in 143, Markov chains in 15, 74-5

Transition probability matrix Ilff Treatment mean square 110 Trend-surface analysis 140ff, applications of

141, residuals in 140

154 INDEX

Trial. definition of 7 Type I and type II error 63-6

V-statistic 125-6, properties of 126 V-test (see Wilcoxon-Mann-Whitney test) Unbiased sample, collection of 48 Universe, definition of 47 Upward-transition probability matrix 11ff

Variable, definition of 5, dependent and independent 92, 99, 140

Variance 24, 29, 45, 48,52-4, 55, 79, 95, 105-8, 126, 133, homogeneity of 105ff

Variance analysis 104ff

von Mises' distribution (see Circular normal distribution)

Wilcoxon-Mann-Whitney test 126ff, appli­cations of 138, formula for 125-6, null hypothesis for 124

Yates's correction for continuity 123

z 33, 36-7, 71-2 (see also Standardised normal distribution)

Z-transformation for r 87-8 z-values, use of 87-8, 102-3