Verfügbarkeit: Statistical methods in biology

Statistical methods in biology: design and analysis of experiments and regression

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Format:	Buch
Sprache:	English
Veröffentlicht:	Boca Raton, Fla. CRC Press 2015
Schlagworte:	Regressionsanalyse Biostatistik Biometrie Datenanalyse Biometry Regression analysis
Online-Zugang:	Inhaltsverzeichnis Klappentext
Beschreibung:	XX, 582 S. graph. Darst.
ISBN:	9781439808788

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Datensatz im Suchindex

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adam_text	Contents Preface .............................................................................................................................................xv Authors .........................................................................................................................................xix 1. Introduction .............................................................................................................................1 1.1 Different Types of Scientific Study .............................................................................1 1.2 Relating Sample Results to More General Populations ...........................................3 1.3 Constructing Models to Represent Reality ...............................................................4 1.4 Using Linear Models ....................................................................................................7 1.5 Estimating the Parameters of Linear Models ...........................................................8 1.6 Summarizing the Importance of Model Terms ........................................................9 1.7 The Scope of This Book ..............................................................................................11 2. A Review of Basic Statistics ...............................................................................................13 2.1 Summary Statistics and Notation for Sample Data ...............................................13 2.2 Statistical Distributions for Populations ..................................................................16 2.2.1 Discrete Data ..................................................................................................17 2.2.2 Continuous Data ............................................................................................22 2.2.3 The Normal Distribution ..............................................................................24 2.2.4 Distributions Derived from Functions of Normal Random Variables .......26 2.3 From Sample Data to Conclusions about the Population ......................................28 2.3.1 Estimating Population Parameters Using Summary Statistics ...............28 2.3.2 Asking Questions about the Data: Hypothesis Testing ...........................29 2.4 Simple Tests for Population Means ..........................................................................30 2.4.1 Assessing the Mean Response: The One-Sample t-Test ...........................30 2.4.2 Comparing Mean Responses: The Two-Sample t-Test. .............................32 2.5 Assessing the Association between Variables ........................................................36 2.6 Presenting Numerical Resulte ...................................................................................39 Exercises ..................................................................................................................................41 3. Principles for Designing Experiments .............................................................................43 3.1 Key Principles ..............................................................................................................43 3.1.1 Replication ......................................................................................................46 3.1.2 Randomization ...............................................................................................48 3.1.3 Blocking ...........................................................................................................51 3.2 Forms of Experimental Structure .............................................................................52 3.3 Common Forms of Design for Experiments ...........................................................57 3.3.1 The Completely Randomized Design .........................................................57 3.3.2 The Randomized Complete Block Design .................................................58 3.3.3 The Latin Square Design ..............................................................................59 3.3.4 The Split-Plot Design .....................................................................................60 3.3.5 The Balanced Incomplete Block Design .....................................................61 3.3.6 Generating a Randomized Design ..............................................................62 Exercises ..................................................................................................................................62 tříí viii Contents 4. Models for a Single Factor ..................................................................................................69 4.1 Defining the Model .....................................................................................................69 4.2 Estimating the Model Parameters ............................................................................73 4.3 Summarizing the Importance of Model Terms ......................................................74 4.3.1 Calculating Sums of Squares .......................................................................76 4.3.2 Calculating Degrees of Freedom and Mean Squares ...............................80 4.3.3 Calculating Variance Ratios as Test Statistics ............................................81 4.3.4 The Summary ANOVA Table .......................................................................82 4.4 Evaluating the Response to Treatments ...................................................................84 4.4.1 Prediction of Treatment Means ....................................................................84 4.4.2 Comparison of Treatment Means ................................................................85 4.5 Alternative Forms of the Model ................................................................................88 Exercises ..................................................................................................................................90 5. Checking Model Assumptions ..........................................................................................93 5.1 Estimating Deviations ................................................................................................93 5.1.1 Simple Residuals ............................................................................................94 5.1.2 Standardized Residuals ................................................................................95 5.2 Using Graphical Tools to Diagnose Problems ........................................................96 5.2.1 Assessing Homogeneity of Variances .........................................................96 5.2.2 Assessing Independence ...............................................................................98 5.2.3 Assessing Normality ...................................................................................101 5.2.4 Using Permutation Tests Where Assumptions Fail ................................102 5.2.5 The Impact of Sample Size ..........................................................................103 5.3 Using Formal Tests to Diagnose Problems ............................................................104 5.4 Identifying Inconsistent Observations ..................................................................108 Exercises ................................................................................................................................110 6. Transformations of the Response ...................................................................................113 6.1 Why Do We Need to Transform the Response? ...................................................113 6.2 Some Useful Transformations .................................................................................114 6.2.1 Logarithms ....................................................................................................114 6.2.2 Square Roots .................................................................................................119 6.2.3 Logits .............................................................................................................120 6.2.4 Other Transformations ................................................................................121 6.3 Interpreting the Results after Transformation ......................................................122 6.4 Interpretation for Log-Transformed Responses ...................................................123 6.5 Other Approaches .....................................................................................................126 Exercises ................................................................................................................................127 7. Models with a Simple Blocking Structure ....................................................................129 7.1 Defining the Model ...................................................................................................130 7.2 Estimating the Model Parameters ..........................................................................132 7.3 Summarizing the Importance of Model Terms ....................................................134 7.4 Evaluating the Response to Treatments .................................................................140 7.5 Incorporating Strata: The Multi-Stratum Analysis of Variance .........................141 Exercises ................................................................................................................................146 Contents ix 8. Extracting Information about Treatments .....................................................................149 8.1 From Scientific Questions to the Treatment Structure ........................................150 8.2 A Crossed Treatment Structure with Two Factors ...............................................152 8.2.1 Models for a Crossed Treatment Structure with Two Factors ...............153 8.2.2 Estimating the Model Parameters .............................................................155 8.2.3 Assessing the Importance of Individual Model Terms ..........................158 8.2.4 Evaluating the Response to Treatments: Predictions from the Fitted Model ..................................................................................................160 8.2.5 The Advantages of Factorial Structure .....................................................162 8.2.6 Understanding Different Parameterizations ...........................................163 8.3 Crossed Treatment Structures with Three or More Factors ...............................164 8.3.1 Assessing the Importance of Individual Model Terms ..........................166 8.3.2 Evaluating the Response to Treatments: Predictions from the Fitted Model .................................................................................................171 8.4 Models for Nested Treatment Structures ..............................................................173 8.5 Adding Controls or Standards to a Set of Treatments .........................................179 8.6 Investigating Specific Treatment Comparisons ....................................................182 8.7 Modelling Patterns for Quantitative Treatments .................................................190 8.8 Making Treatment Comparisons from Predicted Means ...................................195 8.8.1 The Bonferroni Correction .........................................................................196 8.8.2 The False Discovery Rate ...........................................................................197 8.8.3 All Pairwise Comparisons ..........................................................................198 8.8.3.1 The LSD and Fisher s Protected LSD .........................................198 8.8.3.2 Multiple Range Tests ....................................................................199 8.8.3.3 Tukey s Simultaneous Confidence Intervals ............................200 8.8.4 Comparison of Treatments against a Control ..........................................201 8.8.5 Evaluation of a Set of Pre-Planned Comparisons ...................................201 8.8.6 Summary of Issues ......................................................................................205 Exercises ................................................................................................................................206 9. Models with More Complex Blocking Structure .........................................................209 9.1 The Latin Square Design ..........................................................................................209 9.1.1 Defining the Model ......................................................................................211 9.1.2 Estimating the Model Parameters .............................................................211 9.1.3 Assessing the Importance of Individual Model Terms ..........................212 9.1.4 Evaluating the Response to Treatments: Predictions from the Fitted Model ..................................................................................................215 9.1.5 Constraints and Extensions of the Latin Square Design .......................217 9.2 The Split-Plot Design ................................................................................................220 9.2.1 Defining the Model ......................................................................................222 9.2.2 Assessing the Importance of Individual Model Terms ..........................223 9.2.3 Evaluating the Response to Treatments: Predictions from the Fitted Model ..................................................................................................225 9.2.4 Drawbacks and Variations of the Split-Plot Design ................................228 9.3 The Balanced Incomplete Block Design .................................................................232 9.3.1 Defining the Model ......................................................................................235 9.3.2 Assessing the Importance of Individual Model Terms ..........................236 Contents 9.3.3 Drawbacks and Variations of the Balanced Incomplete Block Design .....237 Exercises ................................................................................................................................238 10. Replication and Power .......................................................................................................241 10.1 Simple Methods for Determining Replication ......................................................242 10.1.1 Calculations Based on the LSD ..................................................................242 10.1.2 Calculations Based on the Coefficient of Variation ................................243 10.1.3 Unequal Replication and Models with Blocking ....................................244 10.2 Estimating the Background Variation ...................................................................245 10.3 Assessing the Power of a Design ............................................................................245 10.4 Constructing a Design for a Particular Experiment ............................................249 10.5 A Different Hypothesis: Testing for Equivalence .................................................253 Exercise ..................................................................................................................................256 11. Dealing with Non-Orthogonality ...................................................................................257 11.1 The Benefits of Orthogonality .................................................................................257 11.2 Fitting Models with Non-Orthogonal Terms ........................................................259 11.2.1 Parameterizing Models for Two Non-Orthogonal Factors ....................259 11.2.2 Assessing the Importance of Non-Orthogonal Terms: The Sequential ANOVA Table ...........................................................................265 11.2.3 Calculating the Impact of Model Terms ...................................................269 11.2.4 Selecting the Best Model .............................................................................270 11.2.5 Evaluating the Response to Treatments: Predictions from the Fitted Model ..................................................................................................270 11.3 Designs with Planned Non-Orthogonality ...........................................................272 11.3.1 Fractional Factorial Designs .......................................................................273 11.3.2 Factorial Designs with Confounding ........................................................274 11.4 The Consequences of Missing Data .......................................................................274 11.5 Incorporating the Effects of Unplanned Factors ..................................................277 11.6 Analysis Approaches for Non-Orthogonal Designs ............................................280 11.6.1 A Simple Approach: The Intra-Block Analysis ........................................281 Exercises ................................................................................................................................284 12. Models for a Single Variate: Simple Linear Regression .............................................287 12.1 Defining the Model ...................................................................................................288 12.2 Estimating the Model Parameters ..........................................................................292 12.3 Assessing the Importance of the Model ................................................................296 12.4 Properties of the Model Parameters .......................................................................299 12.5 Using the Fitted Model to Predict Responses .......................................................301 12.6 Summarizing the Fit of the Model .........................................................................305 12.7 Consequences of Uncertainty in the Explanatory Variate ..................................306 12.8 Using Replication to Test Goodness of Fit .............................................................308 12.9 Variations on the Model ...........................................................................................313 12.9.1 Centering and Scaling the Explanatory Variate ......................................313 12.9.2 Regression through the Origin ..................................................................314 12.9.3 Calibration ....................................................................................................320 Exercises ................................................................................................................................321 Contents xi 13. Checking Model Fit ............................................................................................................325 13.1 Checking the Form of the Model............................................................................325 13.2 More Ways of Estimating Deviations ....................................................................328 13.3 Using Graphical Tools to Check Assumptions .....................................................330 13.4 Looking for Influential Observations ....................................................................332 13.4.1 Measuring Potential Influence: Leverage .................................................333 13.4.2 The Relationship between Residuals and Leverages .............................335 13.4.3 Measuring the Actual Influence of Individual Observations ...............336 13.5 Assessing the Predictive Ability of a Model: Cross-Validation ..........................338 Exercises ................................................................................................................................342 14. Models for Several Variâtes: Multiple Linear Regression .........................................345 14.1 Visualizing Relationships between Variâtes .........................................................345 14.2 Defining the Model ...................................................................................................347 14.3 Estimating the Model Parameters ..........................................................................350 14.4 Assessing the Importance of Individual Explanatory Variâtes .........................352 14.4.1 Adding Terms into the Model: Sequential ANOVA and Incremental Sums of Squares .....................................................................353 14.4.2 The Impact of Removing Model Terms: Marginal Sums of Squares ... 356 14.5 Properties of the Model Parameters and Predicting Responses ........................358 14.6 Investigating Model Misspecification ....................................................................359 14.7 Dealing with Correlation among Explanatory Variâtes ......................................361 14.8 Summarizing the Fit of the Model .........................................................................365 14.9 Selecting the Best Model ..........................................................................................366 14.9.1 Strategies for Sequential Variable Selection .............................................369 14.9.2 Problems with Procedures for the Selection of Subsets of Variables ........376 14.9.3 Using Cross-Validation as a Tool for Model Selection ............................377 14.9.4 Some Final Remarks on Procedures for Selecting Models ....................378 Exercises ................................................................................................................................378 15. Models for Variâtes and Factors ......................................................................................381 15.1 Incorporating Groups into the Simple Linear Regression Model ......................382 15.1.1 An Overview of Possible Models ..............................................................383 15.1.2 Defining and Choosing between the Models ..........................................388 15.1.2.1 Single Line Model ........................................................................388 15.1.2.2 Parallel Lines Model ....................................................................388 15.1.2.3 Separate Lines Model ..................................................................390 15.1.2.4 Choosing between the Models: The Sequential ANOVA Table ................................................................................391 15.1.3 An Alternative Sequence of Models ..........................................................396 15.1.4 Constraining the Intercepts ........................................................................398 15.2 Incorporating Groups into the Multiple Linear Regression Model ...................399 15.3 Regression in Designed Experiments ....................................................................406 15.4 Analysis of Covariance: A Special Case of Regression with Groups ................409 15.5 Complex Models with Factors and Variâtes ..........................................................414 15.5.1 Selecting the Predictive Model ..................................................................414 15.5.2 Evaluating the Response: Predictions from the Fitted Model ...............417 xii Contents 15.6 The Connection between Factors and Variâtes ....................................................417 15.6.1 Rewriting the Model in Matrix Notation .................................................421 Exercises ................................................................................................................................423 16. Incorporating Structure: Linear Mixed Models ...........................................................427 16.1 Incorporating Structure ...........................................................................................427 16.2 An Introduction to Linear Mixed Models .............................................................428 16.3 Selecting the Best Fixed Model ...............................................................................430 16.4 Interpreting the Random Model .............................................................................432 16.4.1 The Connection between the Linear Mixed Model and Multi- Stratum ANOVA ..........................................................................................434 16.5 What about Random Effects? ..................................................................................435 16.6 Predicting Responses ...............................................................................................436 16.7 Checking Model Fit ...................................................................................................437 16.8 An Example ................................................................................................................438 16.9 Some Pitfalls and Dangers .......................................................................................444 16.10 Extending the Model ................................................................................................445 Exercises ................................................................................................................................447 17. Models for Curved Relationships ...................................................................................451 17.1 Fitting Curved Functions by Transformation .......................................................451 17.1.1 Simple Transformations of an Explanatory Variate ................................451 17.1.2 Polynomial Models ......................................................................................456 17.1.3 Trigonometric Models for Periodic Patterns ............................................460 17.2 Curved Surfaces as Functions of Two or More Variâtes ......................................463 17.3 Fitting Models Including Non-linear Parameters ...............................................472 Exercises ................................................................................................................................476 18. Models for Non-Normal Responses: Generalized Linear Models ...........................479 18.1 Introduction to Generalized Linear Models .........................................................480 18.2 Analysis of Proportions Based on Counts: Binomial Responses .......................481 18.2.1 Understanding and Defining the Model ..................................................483 18.2.2 Assessing the Importance of the Model and Individual Terms: The Analysis of Deviance ...........................................................................487 18.2.2.1 Interpreting the ANODEV with No Over-Dispersion ............489 18.2.2.2 Interpreting the ANODEV with Over-Dispersion ..................490 18.2.2.3 The Sequential ANODEV Table .................................................493 18.2.3 Checking the Model Fit and Assumptions ..............................................494 18.2.4 Properties of the Model Parameters ..........................................................4% 18.2.5 Evaluating the Response to Explanatory Variables: Prediction ............498 18.2.6 Aggregating Binomial Responses .............................................................500 18.2.7 The Special Case of Binary Data ................................................................501 18.2.8 Other Issues with Binomial Responses ....................................................501 18.3 Analysis of Count Data: Poisson Responses .........................................................502 18.3.1 Understanding and Defining the Model ..................................................503 18.3.2 Analysis of the Model .................................................................................506 183.3 Analysing Poisson Responses with Several Explanatory Variables .....509 18.3.4 Other Issues with Poisson Responses .......................................................512 Contents xiii 18.4 Other Types of GLM and Extensions .....................................................................512 Exercises ................................................................................................................................513 19. Practical Design and Data Analysis for Real Studies .................................................517 19.1 Designing Real Studies ............................................................................................518 19.1.1 Aims, Objectives and Choice of Explanatory Structure ........................518 19.1.2 Resources, Experimental Units and Constraints ....................................519 19.1.3 Matching the Treatments to the Resources ..............................................520 19.1.4 Designs for Series of Studies and for Studies with Multiple Phases. ... 521 19.1.5 Design Case Studies ....................................................................................523 19.2 Choosing the Best Analysis Approach ..................................................................535 19.2.1 Analysis of Designed Experiments ...........................................................536 19.2.2 Analysis of Observational Studies ............................................................537 19.2.3 Different Types of Data ...............................................................................538 19.3 Presentation of Statistics in Reports, Theses and Papers ....................................538 19.3.1 Statistical Information in the Materials and Methods ...........................539 19.3.2 Presentation of Results ................................................................................540 19.4 And Finally. ..............................................................................................................543 References ...................................................................................................................................545 Appendix A: Data Tables .........................................................................................................551 Appendix B: Quantiles of Statistical Distributions ...........................................................559 Appendix C: Statistical and Mathematical Results ............................................................563 Index .............................................................................................................................................569 Statistics Written in simple language with relevant examples, Statistical Methods in Biology: Design and Analysis of Experiments and Regression is a practi¬ cal and illustrative guide to the design of experiments and data analysis in the biological and agricultural sciences. The book presents statistical ideas in the context to which they are being applied, drawing on relevant examples from the authors experience. Taking a practical and intuitive approach, the book includes mathematical for¬ mulae only where this helps to formalise and explain the methods being applied, providing extended discussions of examples based on real data sets arising from scientific research. The authors analyse data in detail to illustrate the use of basic formulae for simple examples white using statistical packages for more complex examples. The associated website (www.stats4bio!.info) shows how to obtain the example analyses in the GenStať . R and SAS; statistical packages. This on¬ line material provides a basic introduction to the facilities in each package, with code for all of the examples and half of the exercises in each chapter. By the time you reach the end of the book and online material you wiil have gained: • A clear appreciation of the importance of a statistical approach to the design of your experiments. • A sound understanding of the statistical methods used to analyse data obtained from designed experiments, and of the regression approaches used to construct simple models to describe the observed response as a function of explanatory variables, • Knowledge of how to use statistical packages to analyse data with the approaches described, and most importantly. • An appreciation of how to interpret the results of these statistical analyses in the context of the biological or agricultural science within which you are working. The book concludes with a practical guide to design and data analysis. Overall, it gives you the statistical understanding required to successfully identify and ap¬ ply these statistical methods to add value to your scientific research.
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isbn	9781439808788
language	English
oai_aleph_id	oai:aleph.bib-bvb.de:BVB01-027515823
oclc_num	894786624
open_access_boolean
owner	DE-11 DE-703 DE-29T
owner_facet	DE-11 DE-703 DE-29T
physical	XX, 582 S. graph. Darst.
publishDate	2015
publishDateSearch	2015
publishDateSort	2015
publisher	CRC Press
record_format	marc
spelling	Statistical methods in biology design and analysis of experiments and regression S. J. Welham ... Boca Raton, Fla. CRC Press 2015 XX, 582 S. graph. Darst. txt rdacontent n rdamedia nc rdacarrier Regressionsanalyse (DE-588)4129903-6 gnd rswk-swf Biostatistik (DE-588)4729990-3 gnd rswk-swf Biometrie (DE-588)4124925-2 gnd rswk-swf Datenanalyse (DE-588)4123037-1 gnd rswk-swf Biometry Regression analysis Biometrie (DE-588)4124925-2 s Regressionsanalyse (DE-588)4129903-6 s DE-604 Biostatistik (DE-588)4729990-3 s Datenanalyse (DE-588)4123037-1 s Welham, Suzanne Jane Sonstige oth Digitalisierung UB Bayreuth - ADAM Catalogue Enrichment application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=027515823&sequence=000003&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis Digitalisierung UB Bayreuth - ADAM Catalogue Enrichment application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=027515823&sequence=000004&line_number=0002&func_code=DB_RECORDS&service_type=MEDIA Klappentext
spellingShingle	Statistical methods in biology design and analysis of experiments and regression Regressionsanalyse (DE-588)4129903-6 gnd Biostatistik (DE-588)4729990-3 gnd Biometrie (DE-588)4124925-2 gnd Datenanalyse (DE-588)4123037-1 gnd
subject_GND	(DE-588)4129903-6 (DE-588)4729990-3 (DE-588)4124925-2 (DE-588)4123037-1
title	Statistical methods in biology design and analysis of experiments and regression
title_auth	Statistical methods in biology design and analysis of experiments and regression
title_exact_search	Statistical methods in biology design and analysis of experiments and regression
title_full	Statistical methods in biology design and analysis of experiments and regression S. J. Welham ...
title_fullStr	Statistical methods in biology design and analysis of experiments and regression S. J. Welham ...
title_full_unstemmed	Statistical methods in biology design and analysis of experiments and regression S. J. Welham ...
title_short	Statistical methods in biology
title_sort	statistical methods in biology design and analysis of experiments and regression
title_sub	design and analysis of experiments and regression
topic	Regressionsanalyse (DE-588)4129903-6 gnd Biostatistik (DE-588)4729990-3 gnd Biometrie (DE-588)4124925-2 gnd Datenanalyse (DE-588)4123037-1 gnd
topic_facet	Regressionsanalyse Biostatistik Biometrie Datenanalyse
url	http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=027515823&sequence=000003&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=027515823&sequence=000004&line_number=0002&func_code=DB_RECORDS&service_type=MEDIA
work_keys_str_mv	AT welhamsuzannejane statisticalmethodsinbiologydesignandanalysisofexperimentsandregression

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