Nonparametric statistical

A first evaluation of the data can be done by running nonparametric statistical estimation techniques like, for example, the Nadaraya-Watson kernel regression estimate [2]. These techniques have the advantage of being relatively cost-free in terms of assumptions, but they do not provide any possibility of interpreting the outcome and are not at all reliable when extrapolating. The fact that these techniques do not require a lot of assumptions makes them... 

S. Siegel. Nonparametric Statistics for the Behavioral Sciences. McGraw-Hill, Tokyo, 1956. 

Statistical methods are based on specific assumptions. Parametric statistics, those most familiar to the majority of scientists, have more stringent underlying assumptions than do nonparametric statistics. Among the underlying assumptions for many parametric statistical methods (such as the analysis of variance) is that the data are continuous. The nature of the data associated with a variable (as described previously) imparts a value to that data, the value being the power of the statistical tests which can be employed. 

Rank transformations Depends on nature of samples As a bridge between parametric and nonparametric statistics... 

The analysis of rank data, what is generally called nonparametric statistical analysis, is an exact parallel of the more traditional (and familiar) parametric methods. There are methods for the single comparison case (just as Student s t-test is used) and for the multiple comparison case (just as analysis of variance is used) with appropriate post hoc tests for exact identification of the significance with a set of groups. Four tests are presented for evaluating statistical significance in rank data the Wilcoxon Rank Sum Test, distribution-free multiple comparisons, Mann-Whitney U Test, and the Kruskall-Wallis nonparametric analysis of variance. For each of these tests, tables of distribution values for the evaluations of results can be found in any of a number of reference volumes (Gad, 1998). 

Conover, J.W. and Inman, R.L. (1981). Rank transformation as a bridge between parametric and nonparametric statistics. Am. Statistician 35 124-129. 

Hollander, M. and Wolfe, D.A. (1973). Nonparametric Statistical Methods. Wiley, New York, pp. 124-129. 

Nonparametric statistics (NPS) differs primarily from its traditional, distribution-based counterpart by dealing with data of unknown probability distributions. Its principal attractiveness lies, in fact, in not requiring the knowledge of a probability distribution. NPS is especially inviting when the assumption of normal distribution of small data sets is hazardous (if at all admissible), even if NPS-based calculations are more time consuming than in traditional statistics. The steadily growing importance of NPS has been amply demonstrated by numerous textbooks and monographs published within the last few decades, e.g. [1-7],... 

Hollander, M., Wolfe, D. Nonparametric Statistical Methods Wiley New York, NY, 1973. 

Lehman, E. Nonparametrics Statistical Methods Based on Ranks Holden Day San Francisco, CA, 1975. 

Daniel, W. Applied Nonparametric Statistics Houghton, Miffin Boston, MA, 1978. 

Higgins, J. J. An Introduction to Modern Nonparametric Statistics Duxbury, Thomson Brooks/Cole Belmont, CA, 2004. 

Conover, W.J., Practical Nonparametric Statistics (Second Edition), John Wiley Sons, page 223ff, 1980. 

In such a case the solution could be to apply one of the nonparametric statistical procedures. Even in this case, nonparametric statistics is characterized by less rigorous assumptions than those for parametric one, and it is relatively less efficient. There are different forms of transformation. We shall present here the most widely applied ones in research studies. 

Note The branch of statistics concerned with measurements that follow the normal distribution are known as parametric statistics. Because many types of measurements follow the normal distribution, these are the most common statistics used. Another branch of statistics designed for measurements that do not follow the normal distribution is known as nonparametric statistics.)... 

The McGrath-Lin nonparametric statistic finds a number of dispersion effects in the dyestuffs experiment. The strongest effects are the main effect of F and the CEF interaction, which have p-values of 0.003 and 0.001, respectively. In addition, the main effect of B and the BC, BF, BDF, and ABCF interactions all... 

McGrath, R. N. and Lin, D. K. J. (2002). A nonparametric dispersion test for unreplicated two-level fractional factorial designs. Journal of Nonparametric Statistics, 14, 699-714. 

In general, a regularization parameter should be chosen for each voxel. Since there may be thousands of voxels, the use of graphical or other methods requiring intervention is prohibitive. In the present work, an automatic, data-driven method is utilized to obtain a reliable estimate of the regularization parameter for each voxel. It is based on nonparametric statistical theory, which can incorporate a number of performance criteria, including unbiased prediction risk (UBPR),9 cross-validation (CV),15 and generalized cross-validation (GCV).16... 

Analysis of the data for correlation, separability, etc. using techniques drawn from statistics, nonparametric statistics, and pattern recognition. Testing of discriminants for predictive ability. 

Zinc and scandium. The nonnormality of the distributions of Zn and Sc can be seen in the plots of residuals versus factors (Figure 4.5.5). Under these circumstances it is necessary to either apply a normalizing transformation, or to use nonparametric statistical procedures. Since the data distributions for Zn and Sc both demonstrate deviation from normality the statistical analyses of these two elements have been dealt with in the same paragraph. The box and whisker plots for these elements are presented in Figure 4.5.6 to provide further insight into their distributions. 

Data analyses included data visualization, nonparametric statistical analysis on observations (data from study 1 only), and parametric analysis with nonlinear mixed effects modeling. 

Conover WJ (1999) Practical nonparametric statistics, John Wiley Sons, ISBN 0-471-16068-7... 

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