G*Power (Erdfelder, Faul, & Buchner, 1996) was designed as a general stand-alone power analysis program for statistical tests commonly used in social and behavioral research. G*Power 3 is a major extension of, and improvement over, the previous versions. It runs on widely used computer platforms (i.e., Windows XP, Windows Vista, and Mac OS X 10.4) and covers many different statistical tests of thet, F, and χ2 test families. In addition, it includes power analyses forz tests and some exact tests. G*Power 3 provides improved effect size calculators and graphic options, supports both distribution-based and design-based input modes, and offers all types of power analyses in which users might be interested. Like its predecessors, G*Power 3 is free.

https://link.springer.com/content/pdf/10.3758/BF03193146.pdf

G*Power 3: A flexible statistical power analysis program for the social, behavioral, and biomedical sciences

THE DESIGN AND ANALYSIS OF EXPERIMENTS. By Oscar Kempthorne. New York, John Wiley and Sons, Inc., 1952. 631 pp. $8.50. This book by a teacher of statistics (as well as a consultant for \"experimenters\") is a comprehensive study of the philosophical background for the statistical design of experiment. It is necessary to have some facility with algebraic notation and manipulation to be able to use the volume intelligently. The problems are presented from the theoretical point of view, without such practical examples as would be helpful for those not acquainted with mathematics. The mathematical justification for the techniques is given. As a somewhat advanced treatment of the design and analysis of experiments, this volume will be interesting and helpful for many who approach statistics theoretically as well as practically. With emphasis on the \"why,\" and with description given broadly, the author relates the subject matter to the general theory of statistics and to the general problem of experimental inference. MARGARET J. ROBERTSON

The Design and Analysis of Experiments

The R package mice imputes incomplete multivariate data by chained equations. The software mice 1.0 appeared in the year 2000 as an S-PLUS library, and in 2001 as an R package. mice 1.0 introduced predictor selection, passive imputation and automatic pooling. This article documents mice, which extends the functionality of mice 1.0 in several ways. In mice, the analysis of imputed data is made completely general, whereas the range of models under which pooling works is substantially extended. mice adds new functionality for imputing multilevel data, automatic predictor selection, data handling, post-processing imputed values, specialized pooling routines, model selection tools, and diagnostic graphs. Imputation of categorical data is improved in order to bypass problems caused by perfect prediction. Special attention is paid to transformations, sum scores, indices and interactions using passive imputation, and to the proper setup of the predictor matrix. mice can be downloaded from the Comprehensive R Archive Network. This article provides a hands-on, stepwise approach to solve applied incomplete data problems.

/pdf/mice-multivariate-imputation-by-chained-equations-in-r-2cffzza5jj.pdf

mice: Multivariate Imputation by Chained Equations in R

An essential textbook for any student or researcher in biology needing to design experiments, sample programs or analyse the resulting data The text begins with a revision of estimation and hypothesis testing methods, covering both classical and Bayesian philosophies, before advancing to the analysis of linear and generalized linear models Topics covered include linear and logistic regression, simple and complex ANOVA models (for factorial, nested, block, split-plot and repeated measures and covariance designs), and log-linear models Multivariate techniques, including classification and ordination, are then introduced Special emphasis is placed on checking assumptions, exploratory data analysis and presentation of results The main analyses are illustrated with many examples from published papers and there is an extensive reference list to both the statistical and biological literature The book is supported by a website that provides all data sets, questions for each chapter and links to software

/pdf/experimental-design-and-data-analysis-for-biologists-8ybva8d53x.pdf

Experimental Design and Data Analysis for Biologists

Summary

The use of both linear and generalized linear mixed-effects models (LMMs and GLMMs) has become popular not only in social and medical sciences, but also in biological sciences, especially in the field of ecology and evolution. Information criteria, such as Akaike Information Criterion (AIC), are usually presented as model comparison tools for mixed-effects models.


The presentation of ‘variance explained’ (R2) as a relevant summarizing statistic of mixed-effects models, however, is rare, even though R2 is routinely reported for linear models (LMs) and also generalized linear models (GLMs). R2 has the extremely useful property of providing an absolute value for the goodness-of-fit of a model, which cannot be given by the information criteria. As a summary statistic that describes the amount of variance explained, R2 can also be a quantity of biological interest.


One reason for the under-appreciation of R2 for mixed-effects models lies in the fact that R2 can be defined in a number of ways. Furthermore, most definitions of R2 for mixed-effects have theoretical problems (e.g. decreased or negative R2 values in larger models) and/or their use is hindered by practical difficulties (e.g. implementation).


Here, we make a case for the importance of reporting R2 for mixed-effects models. We first provide the common definitions of R2 for LMs and GLMs and discuss the key problems associated with calculating R2 for mixed-effects models. We then recommend a general and simple method for calculating two types of R2 (marginal and conditional R2) for both LMMs and GLMMs, which are less susceptible to common problems.


This method is illustrated by examples and can be widely employed by researchers in any fields of research, regardless of software packages used for fitting mixed-effects models. The proposed method has the potential to facilitate the presentation of R2 for a wide range of circumstances.

https://besjournals.onlinelibrary.wiley.com/doi/epdf/10.1111/j.2041-210x.2012.00261.x

A general and simple method for obtaining R2 from generalized linear mixed-effects models

1. CONCEPTS AND EXAMPLES OF RESEARCH. Concepts. Examples. Concluding Remarks. References. 2. CLASSIFICATION OF VARIABLES AND THE CHOICE OF ANALYSIS. Classification of Variables. Overlapping of Classification Schemes. Choice of Analysis. References. 3. BASIC STATISTICS: A REVIEW. Preview. Descriptive Statistics. Random Variables and Distributions. Sampling Distributions of t, ?O2, and F. Statistical Inference: Estimation. Statistical Inference: Hypothesis Testing. Error Rate, Power, and Sample Size. Problems. References. 4. INTRODUCTION TO REGRESSION ANALYSIS. Preview. Association versus Causality. Statistical versus Deterministic Models. Concluding Remarks. References. 5. STRAIGHT-LINE REGRESSION ANALYSIS. Preview. Regression with a Single Independent Variable. Mathematical Properties of a Straight Line. Statistical Assumptions for a Straight-line Model. Determining the Best-fitting Straight Line. Measure of the Quality of the Straight-line Fit and Estimate ?a2. Inferences About the Slope and Intercept. Interpretations of Tests for Slope and Intercept. Inferences About the Regression Line ?YY|X = ?O0 + ?O1X . Prediction of a New Value of Y at X0. Problems. References. 6. THE CORRELATION COEFFICIENT AND STRAIGHT-LINE REGRESSION ANALYSIS. Definition of r. r as a Measure of Association. The Bivariate Normal Distribution. r and the Strength of the Straight-line Relationship. What r Does Not Measure. Tests of Hypotheses and Confidence Intervals for the Correlation Coefficient. Testing for the Equality of Two Correlations. Problems. References. 7. THE ANALYSIS-OF-VARIANCE TABLE. Preview. The ANOVA Table for Straight-line Regression. Problems. 8. MULTIPLE REGRESSION ANALYSIS: GENERAL CONSIDERATIONS. Preview. Multiple Regression Models. Graphical Look at the Problem. Assumptions of Multiple Regression. Determining the Best Estimate of the Multiple Regression Equation. The ANOVA Table for Multiple Regression. Numerical Examples. Problems. References. 9. TESTING HYPOTHESES IN MULTIPLE REGRESSION. Preview. Test for Significant Overall Regression. Partial F Test. Multiple Partial F Test. Strategies for Using Partial F Tests. Tests Involving the Intercept. Problems. References. 10. CORRELATIONS: MULTIPLE, PARTIAL, AND MULTIPLE PARTIAL. Preview. Correlation Matrix. Multiple Correlation Coefficient. Relationship of RY|X1, X2, !KXk to the Multivariate Normal Distribution. Partial Correlation Coefficient. Alternative Representation of the Regression Model. Multiple Partial Correlation. Concluding Remarks. Problems. References. 11. CONFOUNDING AND INTERACTION IN REGRESSION. Preview. Overview. Interaction in Regression. Confounding in Regression. Summary and Conclusions. Problems. References. 12. DUMMY VARIABLES IN REGRESSION. Preview. Definitions. Rule for Defining Dummy Variables. Comparing Two Straight-line Regression Equations: An Example. Questions for Comparing Two Straight Lines. Methods of Comparing Two Straight Lines. Method I: Using Separate Regression Fits to Compare Two Straight Lines. Method II: Using a Single Regression Equation to Compare Two Straight Lines. Comparison of Methods I and II. Testing Strategies and Interpretation: Comparing Two Straight Lines. Other Dummy Variable Models. Comparing Four Regression Equations. Comparing Several Regression Equations Involving Two Nominal Variables. Problems. References. 13. ANALYSIS OF COVARIANCE AND OTHER METHODS FOR ADJUSTING CONTINUOUS DATA. Preview. Adjustment Problem. Analysis of Covariance. Assumption of Parallelism: A Potential Drawback. Analysis of Covariance: Several Groups and Several Covariates. Comments and Cautions. Summary Problems. Reference. 14. REGRESSION DIAGNOSTICS. Preview. Simple Approaches to Diagnosing Problems in Data. Residual Analysis: Detecting Outliers and Violations of Model Assumptions. Strategies of Analysis. Collinearity. Scaling Problems. Diagnostics Example. An Important Caution. Problems. References. 15. POLYNOMIAL REGRESSION. Preview. Polynomial Models. Least-squares Procedure for Fitting a Parabola. ANOVA Table for Second-order Polynomial Regression. Inferences Associated with Second-order Polynomial Regression. Example Requiring a Second-order Model. Fitting and Testing Higher-order Model. Lack-of-fit Tests. Orthogonal Polynomials. Strategies for Choosing a Polynomial Model. Problems. 16. SELECTING THE BEST REGRESSION EQUATION. Preview. Steps in Selecting the Best Regression Equation. Step 1: Specifying the Maximum Model. Step 2: Specifying a Criterion for Selecting a Model. Step 3: Specifying a Strategy for Selecting Variables. Step 4: Conducting the Analysis. Step 5: Evaluating Reliability with Split Samples. Example Analysis of Actual Data. Issues in Selecting the Most Valid Model. Problems. References. 17. ONE-WAY ANALYSIS OF VARIANCE. Preview. One-way ANOVA: The Problem, Assumptions, and Data Configuration. for One-way Fixed-effects ANOVA. Regression Model for Fixed-effects One-way ANOVA Fixed-effects Model for One-way ANOVA. Random-effects Model for One-way ANOVA. -comparison Procedures for Fixed-effects One-way ANOVA. a Multiple-comparison Technique. Orthogonal Contrasts and Partitioning an ANOVA Sum of Squares. Problems. References. 18. RANDOMIZED BLOCKS: SPECIAL CASE OF TWO-WAY ANOVA. Preview. Equivalent Analysis of a Matched-pairs Experiment. Principle of Blocking. Analysis of a Randomized-blocks Experiment. ANOVA Table for a Randomized-blocks Experiment. Models for a Randomized-blocks Experiment. Fixed-effects ANOVA Model for a Randomized-blocks Experiment. Problems. References. 19. TWO-WAY ANOVA WITH EQUAL CELL NUMBERS. Preview. Using a Table of Cell Means. General Methodology. F Tests for Two-way ANOVA. Regression Model for Fixed-effects Two-way ANOVA. Interactions in Two-way ANOVA. Random- and Mixed-effects Two-way ANOVA Models. Problems. References. 20. TWO-WAY ANOVA WITH UNEQUAL CELL NUMBERS. Preview. Problem with Unequal Cell Numbers: Nonorthogonality. Regression Approach for Unequal Cell Sample Sizes. Higher-way ANOVA. Problems. References. 21. THE METHOD OF MAXIMUM LIKELIHOOD. Preview. The Principle of Maximum Likelihood. Statistical Inference Using Maximum Likelihood. Summary. Problems. 22. LOGISTIC REGRESSION ANALYSIS. Preview. The Logistic Model. Estimating the Odds Ratio Using Logistic Regression. A Numerical Example of Logistic Regression. Theoretical Considerations. An Example of Conditional ML Estimation Involving Pair-matched Data with Unmatched Covariates. Summary. Problems. References. 23. POLYTOMOUS AND ORDINAL LOGISTIC REGRESSION. Preview. Why Not Use Binary Regression? An Example of Polytomous Logistic Regression: One Predictor, Three Outcome Categories. An Example: Extending the Polytomous Logistic Model to Several Predictors. Ordinal Logistic Regression: Overview. A "Simple" Hypothetical Example: Three Ordinal Categories and One Dichotomous Exposure Variable. Ordinal Logistic Regression Example Using Real Data with Four Ordinal Categories and Three Predictor Variables. Summary. Problems. References. 24. POISSON REGRESSION ANALYSIS. Preview. The Poisson Distribution. Example of Poisson Regression. Poisson Regression: General Considerations. Measures of Goodness of Fit. Continuation of Skin Cancer Data Example. A Second Illustration of Poisson Regression Analysis. Summary. Problems. References. 25. ANALYSIS OF CORRELATED DATA PART 1: THE GENERAL LINEAR MIXED MODEL. Preview. Examples. General Linear Mixed Model Approach. Example: Study of Effects of an Air Polluion Episode on FEV1 Levels. Summary!XAnalysis of Correlated Data: Part 1. Problems. References. 26. ANALYSIS OF CORRELATED DATA PART 2: RANDOM EFFECTS AND OTHER ISSUES. Preview. Random Effects Revisited. Results for Random Effects Models Applied to Air Pollution Study Data. Second Example!XAnalysis of Posture Measurement Data. Recommendations about Choice of Correlation Structure. Analysis of Data for Discrete Outcomes. Problems. References. 27. SAMPLE SIZE PLANNING FOR LINEAR AND LOGISTIC REGRESSION AND ANALYSIS OF VARIANCE. Preview. Review: Sample Size Calculations for Comparisons of Means and Proportions. Sample Size Planning for Linear Regression. Sample Size Planning for Logistic Regression. Power and Sample Size Determination for Linear Models: A General Approach. Sample Size Determination for Matched Case-control Studies with a Dichotomous Outcome. Practical Considerations and Cautions. Problems. References. Appendix A. Appendix B. Appendix C. Solutions to Exercises. Index.

/pdf/applied-regression-analysis-and-other-multivariable-methods-2gj8f32ss1.pdf

Applied Regression Analysis and Other Multivariable Methods

Applied regression analysis and other multivariable methods, 3rd ed.

The purpose of this project was to determine whether Contrast Limited Adaptive Histogram Equalization (CLAHE) improves detection of simulated spiculations in dense mammograms Lines simulating the appearance of spiculations, a common marker of malignancy when visualized with masses, were embedded in dense mammograms digitized at 50 micron pixels, 12 bits deep Film images with no CLAHE applied were compared to film images with nine different combinations of clip levels and region sizes applied A simulated spiculation was embedded in a background of dense breast tissue, with the orientation of the spiculation varied The key variables involved in each trial included the orientation of the spiculation, contrast level of the spiculation and the CLAHE settings applied to the image Combining the 10 CLAHE conditions, 4 contrast levels and 4 orientations gave 160 combinations The trials were constructed by pairing 160 combinations of key variables with 40 backgrounds Twenty student observers were asked to detect the orientation of the spiculation in the image There was a statistically significant improvement in detection performance for spiculations with CLAHE over unenhanced images when the region size was set at 32 with a clip level of 2, and when the region size was set at 32 with a clip level of 4 The selected CLAHE settings should be tested in the clinic with digital mammograms to determine whether detection of spiculations associated with masses detected at mammography can be improved

Contrast limited adaptive histogram equalization image processing to improve the detection of simulated spiculations in dense mammograms.

Statisticians most often use the linear mixed model to analyze Gaussian longitudinal data. The value and familiarity of the R2 statistic in the linear univariate model naturally creates great interest in extending it to the linear mixed model. We define and describe how to compute a model R2 statistic for the linear mixed model by using only a single model. The proposed R2 statistic measures multivariate association between the repeated outcomes and the fixed effects in the linear mixed model. The R2 statistic arises as a 1–1 function of an appropriate F statistic for testing all fixed effects (except typically the intercept) in a full model. The statistic compares the full model with a null model with all fixed effects deleted (except typically the intercept) while retaining exactly the same covariance structure. Furthermore, the R2 statistic leads immediately to a natural definition of a partial R2 statistic. A mixed model in which ethnicity gives a very small p-value as a longitudinal predictor of blood pressure (BP) compellingly illustrates the value of the statistic. In sharp contrast to the extreme p-value, a very small R2 , a measure of statistical and scientific importance, indicates that ethnicity has an almost negligible association with the repeated BP outcomes for the study. Copyright © 2008 John Wiley & Sons, Ltd.

/pdf/an-r2-statistic-for-fixed-effects-in-the-linear-mixed-model-4ohwxxkfyl.pdf

An R2 statistic for fixed effects in the linear mixed model.

An experiment intended to evaluate the clinical application of contrast-limited adaptive histogram equalization (CLAHE) to chest computer tomography (CT) images is reported. A machine especially designed to compute CLAHE in a few seconds is discussed. It is shown that CLAHE can be computed in 4 s after 5-s loading time using the specially designed parallel engine made from a few thousand dollars worth of off-the-shelf components. The processing appears to be useful for a wide range of medical images, but the limitations of observer calibration make it impossible to demonstrate such usefulness by agreement experiments. >

/pdf/contrast-limited-adaptive-histogram-equalization-speed-and-2310q59joe.pdf

Keith E. Muller

Papers

Applied Regression Analysis and Other Multivariable Methods

Applied regression analysis and other multivariable methods, 3rd ed.

Contrast limited adaptive histogram equalization image processing to improve the detection of simulated spiculations in dense mammograms.

An R2 statistic for fixed effects in the linear mixed model.

Contrast-limited adaptive histogram equalization: speed and effectiveness