Parametric statistics

Abstract: Preface. Introduction. Data Sets. Tests of Statistical Significance of Combined Results. Vote-Counting Methods. Estimation of a Single Effect Size: Parametric and Nonparametric Methods. Parametric Estimation of Effect Size from a Series of Experiments. Fitting Parametric Fixed Effect Models to Effect Sizes: Categorical Methods. Fitting Parametric Fixed Effect Models to Effect Sizes: General Linear Models. Random Effects Models for Effect Sizes. Multivariate Models for Effect Sizes. Combining Estimates of Correlation Coefficients. Diagnostic Procedures for Research Synthesis Models. Clustering Estimates of Effect Magnitude. Estimation of Effect Size When Not All Study Outcomes Are Observed. Meta-Analysis in the Physical and Biological Sciences. Appendix. References. Index.

Abstract: + Abstract: Statistical parametric maps are spatially extended statistical processes that are used to test hypotheses about regionally specific effects in neuroimaging data. The most established sorts of statistical parametric maps (e.g., Friston et al. (1991): J Cereb Blood Flow Metab 11:690-699; Worsley et al. 119921: J Cereb Blood Flow Metab 12:YOO-918) are based on linear models, for example ANCOVA, correlation coefficients and t tests. In the sense that these examples are all special cases of the general linear model it should be possible to implement them (and many others) within a unified framework. We present here a general approach that accommodates most forms of experimental layout and ensuing analysis (designed experiments with fixed effects for factors, covariates and interaction of factors). This approach brings together two well established bodies of theory (the general linear model and the theory of Gaussian fields) to provide a complete and simple framework for the analysis of imaging data. The importance of this framework is twofold: (i) Conceptual and mathematical simplicity, in that the same small number of operational equations is used irrespective of the complexity of the experiment or nature of the statistical model and (ii) the generality of the framework provides for great latitude in experimental design and analysis.

Abstract: Requiring only minimal assumptions for validity, nonparametric permutation testing provides a flexible and intuitive methodology for the statistical analysis of data from functional neuroimaging experiments, at some computational expense. Introduced into the functional neuroimaging literature by Holmes et al. ([1996]: J Cereb Blood Flow Metab 16:7-22), the permutation approach readily accounts for the multiple comparisons problem implicit in the standard voxel-by-voxel hypothesis testing framework. When the appropriate assumptions hold, the nonparametric permutation approach gives results similar to those obtained from a comparable Statistical Parametric Mapping approach using a general linear model with multiple comparisons corrections derived from random field theory. For analyses with low degrees of freedom, such as single subject PET/SPECT experiments or multi-subject PET/SPECT or fMRI designs assessed for population effects, the nonparametric approach employing a locally pooled (smoothed) variance estimate can outperform the comparable Statistical Parametric Mapping approach. Thus, these nonparametric techniques can be used to verify the validity of less computationally expensive parametric approaches. Although the theory and relative advantages of permutation approaches have been discussed by various authors, there has been no accessible explication of the method, and no freely distributed software implementing it. Consequently, there have been few practical applications of the technique. This article, and the accompanying MATLAB software, attempts to address these issues. The standard nonparametric randomization and permutation testing ideas are developed at an accessible level, using practical examples from functional neuroimaging, and the extensions for multiple comparisons described. Three worked examples from PET and fMRI are presented, with discussion, and comparisons with standard parametric approaches made where appropriate. Practical considerations are given throughout, and relevant statistical concepts are expounded in appendices.

Abstract: With more than 500 pages of new material, the Handbook of Parametric and Nonparametric Statistical Procedures, Fourth Edition carries on the esteemed tradition of the previous editions, providing up-to-date, in-depth coverage of now more than 160 statistical procedures. The book also discusses both theoretical and practical statistical topics, such as experimental design, experimental control, and statistical analysis. New to the Fourth Edition Multivariate statistics including matrix algebra, multiple regression, Hotellings T2, MANOVA, MANCOVA, discriminant function analysis, canonical correlation, logistic regression, and principal components/factor analysis Clinical trials, survival analysis, tests of equivalence, analysis of censored data, and analytical procedures for crossover design Regression diagnostics that include the Durbin-Watson test Log-linear analysis of contingency tables, Mantel-Haenszel analysis of multiple 2 2 contingency tables, trend analysis, and analysis of variance for a Latin square design Levene and Brown-Forsythe tests for evaluating homogeneity of variance, the Jarque-Bera test of normality, and the extreme studentized deviate test for identifying outliers Confidence intervals for computing the population median and the difference between two population medians The relationship between exponential and Poisson distribution Eliminating the need to search across numerous books, this handbook provides you with everything you need to know about parametric and nonparametric statistical procedures. It helps you choose the best test for your data, interpret the results, and better evaluate the research of others.

Abstract: 1 probability 2 Random variables, distribution functions, and expectation 3 Special parametric families of univariate distributions 4 Joint and conditional distributions, stochastic independence, more expectation 5 Distributions of functions of random variables 6 Sampling and sampling distributions 7 Parametric point estimation 8 Parametric interval estimation 9 Tests of hypotheses 10 Linear models 11 Nonparametric method Appendix A Mathematical Addendum Appendix B tabular summary of parametric families of distributions Appendix C References and related reading Appendix D Tables