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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.

STATISTICAL ANALYSIS

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

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.

STATISTICAL ANALYSIS

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

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.

STATISTICAL ANALYSIS

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

STATISTICAL ANALYSIS

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

STATISTICAL ANALYSIS

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

STATISTICAL ANALYSIS

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