Statistical Methods in Agriculture and Experimental Biology

The third edition of this popular introductory text maintains the character that won worldwide respect for its predecessors but features a number of enhancements that broaden its scope, increase its utility, and bring the treatment thoroughly up to date. It provides complete coverage of the statistical ideas and methods essential to students in agriculture or experimental biology. In addition to covering fundamental methodology, this treatment also includes more advanced topics that the authors believe help develop an appreciation of the breadth of statistical methodology now available. The emphasis is not on mathematical detail, but on ensuring students understand why and when various methods should be used. New in the Third Edition: A chapter on the two simplest yet most important methods of multivariate analysis Increased emphasis on modern computer applications Discussions on a wider range of data types and the graphical display of data Analysis of mixed cropping experiments and on-farm experiments

Table of Contents:
INTRODUCTION The Need for Statistics Types of Data The Use of Computers in Statistics PROBABILITY AND DISTRIBUTIONS Probability Populations and Samples Means and Variances The Normal Distribution Sampling Distributions ESTIMATION AND HYPOTHESIS TESTING Estimation of the Population Mean Testing Hypotheses about the Population Mean Population Variance Unknown Comparison of Samples A Pooled Estimate of Variance A SIMPLE EXPERIMENT Randomization and Replication Analysis of a Completely Randomized Design with Two Treatments A Completely Randomized Design with Several Treatments Testing Overall Variation Between the Treatments CONTROL OF RANDOM VARIATION BY BLOCKING Local Control of Variation Analysis of a Randomized Block Design Meaning of the Error Mean Square Latin Square Designs Multiple Latin Squares Design The Benefit of Blocking and the Use of Natural Blocks PARTICULAR QUESTIONS ABOUT TREATMENTS Treatment Structure Treatment Contrasts Factorial Treatment Structure Main Effects and Interactions Analysis of Variance for a Two-Factor Experiment Partial Factorial Structure Comparing Treatment Means - Are Multiple Comparison Methods Helpful? MORE ON FACTORIAL TREATMENT STRUCTURE More than Two Factors Factors with Two Levels The Double Benefit of Factorial Structure Many Factors and Small Blocks The Analysis of Confounded Experiments Split Plot Experiments Analysis of a Split Plot Experiment Experiments Repeated at Different Sites THE ASSUMPTIONS BEHIND THE ANALYSIS Our Assumptions Normality Variance Homogeneity Additivity Transformations of Data for Theoretical Reasons A More General Form of Analysis Empirical Detection of the Failure of Assumptions and Selection of Appropriate Transformations Practice and Presentation STUDYING LINEAR RELATIONSHIPS Linear Regression Assessing the Regression Line Inferences about the Slope of a Line Prediction Using a Regression Line Correlation Testing Whether the Regression is Linear Regression Analysis Using Computer Packages MORE COMPLEX RELATIONSHIPS Making the Crooked Straight Two Independent Variables Testing the Components of a Multiple Relationship Multiple Regression Possible Problems in Computer Multiple Regression LINEAR MODELS The Use of Models Models for Factors and Variables Comparison of Regressions Fitting Parallel Lines Covariance Analysis Regression in the Analysis of Treatment Variation NONLINEAR MODELS Advantages of Linear and Nonlinear Models Fitting Nonlinear Models to Data Inferences about Nonlinear Parameters Exponential Models Inverse Polynomial Models Logistic Models for Growth Curves THE ANALYSIS OF PROPORTIONS Data in the Form of Frequencies The 2 ´ 2 Contingency Table More than Two Situations or More than Two Outcomes General Contingency Tables Estimation of Proportions Sample Sizes for Estimating Proportions MODELS AND DISTRIBUTIONS FOR FREQUENCY DATA Models for Frequency Data Testing the Agreement of Frequency Data with Simple Models Investigating More Complex Models The Binomial Distribution The Poisson Distribution Generalized Models for Analyzing Experimental Data Log-Linear Models Logit Analysis of Response Data MAKING AND ANALYZING SEVERAL EXPERIMENTAL MEASUREMENTS Different Measurements on the Same Units Interdependence of Different Variables Repeated Measurements Joint (Bivariate) Analysis Indices of Combined Yield Investigating Relationships with Experimental Data ANALYZING AND SUMMARIZING MANY MEASUREMENTS Introduction to Multivariate Data Principal Component Analysis Covariance or Correlation Matrix Cluster Analysis Similarity and Dissimilarity Measures Hierarchical Clustering Comparison of PCA and Cluster Analysis CHOOSING THE MOST APPROPRIATE EXPERIMENTAL DESIGN The Components of Design; Units and Treatments Replication and Precision Different Levels of Variation and Within-Unit Replication Variance Components and Split Plot Designs Randomization Managing with Limited Resources Factors with Quantitative Levels Screening and Selection On-Farm Experiments SAMPLING FINITE POPULATIONS Experiments and Sample Surveys Simple Random Sampling Stratified Random Sampling Cluster Sampling, Multistage Sampling and Sampling Proportional to Size Ratio and Regression Estimates REFERENCES APPENDIX INDEX