1st Edition
Statistics with Applications in Biology and Geology
The use of statistics is fundamental to many endeavors in biology and geology. For students and professionals in these fields, there is no better way to build a statistical background than to present the concepts and techniques in a context relevant to their interests. Statistics with Applications in Biology and Geology provides a practical introduction to using fundamental parametric statistical models frequently applied to data analysis in biology and geology.
Based on material developed for an introductory statistics course and classroom tested for nearly 10 years, this treatment establishes a firm basis in models, the likelihood method, and numeracy. The models addressed include one sample, two samples, one- and two-way analysis of variance, and linear regression for normal data and similar models for binomial, multinomial, and Poisson data. Building on the familiarity developed with those models, the generalized linear models are introduced, making it possible for readers to handle fairly complicated models for both continuous and discrete data. Models for directional data are treated as well. The emphasis is on parametric models, but the book also includes a chapter on the most important nonparametric tests.
This presentation incorporates the use of the SAS statistical software package, which authors use to illustrate all of the statistical tools described. However, to reinforce understanding of the basic concepts, calculations for the simplest models are also worked through by hand. SAS programs and the data used in the examples and exercises are available on the Internet.
Data
Model Specification
Model Checking
Statistical Inference
Concluding Remarks
PRELIMINARY INVESTIGATIONS
Dot Diagrams and Bar Charts
Histograms
Fractile Diagrams
Fractile Diagrams for the Normal Distribution
Transformation
Concluding Remarks
Annex to Chapter 2
NORMAL DATA
One Sample
Annex to Section
Main Points in Section
Two or More Samples
Main Points in Section
Linear Regression
Annex to Section
Main Points in Section
Supplement to Chapter
The Normal Distribution and Related Distributions
Multivariate Normal Distributions
LINEAR NORMAL MODELS
The Linear Normal Model
Main Points in Section
Comparison of Regression Lines
Annex to Section
Two-way Analysis of Variance
Annex to Section 4
AN INTRODUCTION TO POWER OF TESTS AND DESIGN OF EXPERIMENTS
Power of Tests
Reduction of s 2- An Example of Blocking
Control Plot for the Paired t-Test
The Paired t--Test and Two-Way Analysis of Variance
Annex to Chapter
Supplement to Chapter 5
Non-Central t-, c, and F-Distributions
CORRELATION
Introduction
Definitions
Examples
The Bivariate Normal Distribution
Model Checking
Inference on r Based on a Single Bivariate Normal Sample
Inference on r Based on Several Bivariate Normal Samples
Correlation and Regression
Interpretation of Correlation
Further Topics in the Bivariate Normal Distribution
Annex to Chapter 6
Main Points in Section 6
THE MULTINOMIAL DISTRIBUTION
Examples
Inference in One Multinomial Distribution
Inference in Several Multinomial Distributions
Fisher's Exact Test
Test for Goodness of Fit
Sequence of Models
Annex to Chapter 7
Main Points in Chapter 7
THE POISSON DISTRIBUTION
Examples
Probabilistic Results for the Poisson Distribution
One Sample
Several Samples
Transformation
Annex to Chapter 8
Main Points in Chapter 8
GENERALIZED LINEAR MODELS
Classes of Distributions
The Generalized Linear Model
Examples
MODELS FOR DIRECTIONAL DATA
Notation
Examples
The Circular Normal Distribution
One Sample
Several Samples
Annex to Chapter 10
Supplement to Chapter 10
Descriptive Measures for Directional Data
Further Analogies
THE LIKELIHOOD METHOD
Likelihood Inference
Concepts from General Test Theory
Approximative Likelihood Theory
SOME NONPARAMETRIC TESTS
Sign Test
Rank Tests
Annex to Chapter 12
Main Points in Chapter 12
APPENDICES
Simulated Fractile Diagrams
The Newton-Raphson Procedure
REFERENCES
INDEX
Biography
Preben Blaesild, Jorgen Granfeldt
"The authors provide a useful website for the book [which] contains the many data sets used in the examples and exercises, as well as the SAS jobs. … [T]his book could be a very good source of supplementary, applied material … [or] an excellent book for a second course in practical applications."
- Computers & Geosciences
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