Statistically speaking. IX. The nonparametric statistics.
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Biometry↗
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Note on score transformation and nonparametric statistics.
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Humans↗
The basics of nonparametric statistics.
This article introduces readers to the data analytic sub-paradigm of nonparametric statistics. The authors begin with an explanation of how and under what circumstances nonparametric statistics are used, then describe specific nonparametric techniques which are commonly used in social science research. Examples from the contemporary rehabilitation literature are provided throughout the article.
Journal Article↗
A simple nonparametric statistical thresholding for MEG spatial-filter source reconstruction images.
This paper proposes a simple statistical method for extracting target source activities from spatio-temporal source activities reconstructed from MEG measurements. The method requires measurements in a control condition, which contains only non-target source activities. The method derives, at each pixel location, an empirical probability distribution of the non-target source activity using the time course reconstruction obtained from the control period. The statistical threshold that can extract the target source activities is derived from the empirical distributions obtained from all pixel locations. Here, the multiple comparison problem is addressed with a two-step procedure involving standardizing these empirical distributions and deriving an empirical distribution of the maximum pseudo T value at each pixel location. The results of applying the proposed method to auditory-evoked measurements are presented to demonstrate the method's effectiveness.
Algorithms↗
Comparison of nonparametric statistics for detection of linkage in nuclear families: single-marker evaluation.
We have evaluated 23 different statistics, from a total of 10 popular software packages for model-free linkage analysis of nuclear-family data, by applying them to single-marker data simulated under several two-locus disease models. The statistics that we examined fall into two broad categories: (1) those that test directly for increased identity-by-state or identity-by-descent sharing (by use of the programs APM, Genetic Analysis System [GAS] SIBSTATE and SIBDES, SAGE SIBPAL, ERPA, SimIBD, and Genehunter NPL) and (2) those that are based on likelihood-ratio tests and that report LOD scores (by use of the programs Splink, SIBPAIR, Mapmaker/Sibs, ASPEX, and GAS SIBMLS). For each of eight two-locus disease models, we analyzed six data sets; the first three data sets consisted of two-child families with both sibs affected and zero, one, or both parents typed, whereas the other three data sets consisted of four-child families with at least two affected sibs and zero, one, or both parents typed. We report false-positive rates, overall rank by power, and the power for each statistic. We give rough recommendations regarding which programs provide the most powerful tests for linkage, as well as the programs to be avoided under certain conditions. For the likelihood-ratio-based statistics, we examined the effects of various treatments of sibships with multiple affected individuals. Finally, we explored the use of some simple two-of-three composite statistics and found that such tests are of only marginal benefit over the most powerful single statistic.
Adult↗
Nonparametric statistical methods for cost-effectiveness analyses.
Two measures often used in a cost-effectiveness analysis are the incremental cost-effectiveness ratio (ICER) and the net health benefit (NHB). Inferences on these two quantities are often hindered by highly skewed cost data. In this article, we derive the Edgeworth expansions for the studentized t-statistics for the two measures and show how they could be used to guide inferences. In particular, we use the expansions to study the theoretical performance of existing confidence intervals based on normal theory and to derive new confidence intervals for the ICER and the NHB. We conduct a simulation study to compare our new intervals with several existing methods. The methods evaluated include Taylor's interval, Fieller's interval, the bootstrap percentile interval, and the bootstrap bias-corrected acceleration interval. We found that our new intervals give good coverage accuracy and are narrower compared to the current recommended intervals.
Biometry↗
[EEG as a non-stationary signal: an approach to analysis based on nonparametric statistics].
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Brain Mapping↗
The use of nonparametric statistics in quantitative electron microscopy.
Parametric statistical methods assume samples that have a normal distribution and representative sample sizes (i.e. n >20). Quantitative electron microscopy is inherently restricted to small sample sizes and a priori there is no way to know if the expression of the ligand being studied has a normal distribution. Thus to make statistical inferences based on data generated by quantitative electron microscopy using parametric methods may not be justified. Nonparametric statistical methods offer a tool for the evaluation of data that do not meet the criteria for analysis by parametric methods. In this report I show the utility of using nonparametric statistical methods for the analysis of data generated by quantitative electron microscopy.
Animals↗
Reading a research article part II: parametric and nonparametric statistics.
Researchers often try to use a randomization technique in an attempt to reduce bias and ensure that treatment and control groups are as similar as possible. This article has provided an overview of how researchers might use parametric and nonparametric statistics when analyzing data and looking for differences between groups. Researchers must consider the types of data and choose the tests that are appropriate for the variable types to draw appropriate conclusions. The next article in this series will address comparison of more than two groups and repeated measures and other design issues.
Age Distribution↗
A confirmation of Rexed's laminar hypothesis using the Sholl linear method complemented by nonparametric statistics.
Images of Golgi-impregnated neurons from laminae I to VI in the dorsal horn of the cat spinal cord were subjected to the linear Sholl analysis of concentric circles to support Rexed's hypothesis on the laminar organization of spinal gray matter in mammals. Since Rexed's determination of the laminae is based upon size, location, and grouping of cell bodies, neglecting one of the principal morphologic attributes of the neuron-the dendritic tree, the purpose of the present study was to evaluate Rexed's hypothesis testing the structure of dendritic arborization patterns of neurons. The differences in the complexity of dendritic trees between the groups of neurons from different laminae were evaluated by nonparametric statistics. Data obtained using Sholl's method is not always subjected to complete statistical analysis. The problem becomes particularly apparent in the quantitative examination of dendritic structures. Our aim was also to perform a careful analysis of our data for normality, in order to choose the appropriate statistical method for data processing. In the linear Sholl analysis, it is important to properly represent and interpret the frequency functions. The objective of this study was also to investigate the problems of determining the frequency functions, plotting the corresponding lines of regression, and measuring the degree of fluctuation of experimental data points around these lines. The main result of our testing is a confirmation of Rexed's laminar scheme: we have proved that there are 6 out of 10 possible pairs of samples where one member significantly differs from the other, i.e. one lamina is significantly distinguishable from the other.
Algorithms↗
Nonparametric statistical snake based on the minimum stochastic complexity.
We propose a nonparametric statistical snake technique that is based on the minimization of the stochastic complexity (minimum description length principle). The probability distributions of the gray levels in the different regions of the image are described with step functions with parameters that are estimated. The segmentation is thus obtained by minimizing a criterion that does not include any parameter to be tuned by the user. We illustrate the robustness of this technique on various types of images with level set and polygonal contour models. The efficiency of this approach is also analyzed in comparison with parametric statistical techniques.
Algorithms↗
[Use of nonparametric statistical criteria in epidemiological research].
The article deals with the possibility of using two nonparametric statistical methods (sign criterion, Wilkonson's paired criterion) in epidemiological investigations. Examples illustrating the use of these methods are presented and their advantages in comparison with commonly used methods are shown.
Dysentery, Bacillary↗
Utilizing nonparametric statistical techniques: evaluating management effectiveness of an alcoholic treatment center.
A system of measures was designed to evaluate the effect of a change in management of an alcoholic treatment center. The measures also were used to indicate the causes for the changes in performance. Because the treatment center's physical plant is to be replaced in the near future, regression techniques, using one of the evaluation measures, were used to predict the size of the replacement facility and when it should become operational. The evaluation was made approximately a year after the management change occurred. Because only a limited amount of data was available, it was necessary to use nonparametric statistical techniques.
Alcoholism↗
fMRI bold signal analysis using a novel nonparametric statistical method.
We present in this article a novel analytical method that enables the application of nonparametric rank-order statistics to fMRI data analysis, since it takes the omnipresent serial correlations (temporal autocorrelations) properly into account. Comparative simulations, using the common General Linear Model and the permutation test, confirm the validity and usefulness of our approach. Our simulations, which are performed with both synthetic and real fMRI data, show that our method requires significantly less computation time than permutation-based methods, while offering the same order of robustness and returning more information about the evoked response when combined with/compared to the results obtained with the common General Lineal Model approach.
Algorithms↗
Voxel-based morphometry of comorbid schizophrenia and learning disability: analyses in normalized and native spaces using parametric and nonparametric statistical methods.
We employed voxel-based morphometry (VBM) to compare the distributions of grey matter found in structural magnetic resonance imaging (MRI) brain scans of patients with comorbid learning disability with schizophrenia, schizophrenia alone, learning disability alone, and normal controls. Our primary aim was to replicate a previous region of interest (ROI) finding that comorbids and schizophrenics belong to the same population. Nonparametric analysis in normalized space showed no significant differences in grey matter distribution between the comorbid and schizophrenia groups. Furthermore, this analysis showed significant grey matter reductions in the comorbid and schizophrenia groups when compared to the learning-disabled or the normal controls. Parametric analysis localized the significant grey matter reductions between the normal controls and the comorbid and schizophrenia groups to the prefrontal and temporal lobes. It also identified an area of increased grey matter, on the inferior aspect of the postcentral gyrus, in the learning-disabled alone compared to the other groups. Native space parametric and nonparametric analyses, based on modulation of the normalized scans, confirmed the similarity in grey matter distribution of the comorbid and schizophrenia groups. Results confirm the ROI finding that in native space the learning-disabled group possesses the least and normal controls the most grey matter for the cohort. An increase in the basal ganglia of patients with schizophrenia vs. the learning-disabled, probably attributable to antipsychotic medication, was identified in the native space analysis. The native space results did not however register statistically significant temporal lobe reductions found under normalized analysis between schizophrenics and normal controls. This may be attributable to minor physical anomalies (MPA) in the schizophrenic cranium. Overall, these VBM results replicate previous ROI findings and are compatible with the view that comorbid learning disability with schizophrenia is a severe form of schizophrenia, rather than a consequence of learning disability. VBM has the facility to compare grey matter distributions in this structurally diverse cohort.
Adult↗
Adjustment of young adults with mental retardation in community settings: comparison of parametric and nonparametric statistical techniques.
The impact of four different statistical techniques on the interpretive process using data obtained from young adults with mental retardation in applied settings was evaluated. Our hypothesis was that no difference exists across levels of mental retardation for four dependent variables, jointly or separately, using (a) parametric multivariate analysis of variance, (b) nonparametric multivariate analysis of variance, (c) multiple nonparametric analyses of variance, and (d) multinomial logistic regression. The pattern of significance remained the same across the three classical and quasi-classical designs. Substantive differences were found using the fourth technique, multinomial logistic regression. The four techniques were compared using interpretational as well as statistical criteria.
Adult↗
A nonparametric statistical method for image segmentation using information theory and curve evolution.
In this paper, we present a new information-theoretic approach to image segmentation. We cast the segmentation problem as the maximization of the mutual information between the region labels and the image pixel intensities, subject to a constraint on the total length of the region boundaries. We assume that the probability densities associated with the image pixel intensities within each region are completely unknown a priori, and we formulate the problem based on nonparametric density estimates. Due to the nonparametric structure, our method does not require the image regions to have a particular type of probability distribution and does not require the extraction and use of a particular statistic. We solve the information-theoretic optimization problem by deriving the associated gradient flows and applying curve evolution techniques. We use level-set methods to implement the resulting evolution. The experimental results based on both synthetic and real images demonstrate that the proposed technique can solve a variety of challenging image segmentation problems. Futhermore, our method, which does not require any training, performs as good as methods based on training.
Algorithms↗
Segmentation of thrombus in abdominal aortic aneurysms from CTA with nonparametric statistical grey level appearance modeling.
This paper presents a new method for deformable model-based segmentation of lumen and thrombus in abdominal aortic aneurysms from computed tomography (CT) angiography (CTA) scans. First the lumen is segmented based on two positions indicated by the user, and subsequently the resulting surface is used to initialize the automated thrombus segmentation method. For the lumen, the image-derived deformation term is based on a simple grey level model (two thresholds). For the more complex problem of thrombus segmentation, a grey level modeling approach with a nonparametric pattern classification technique is used, namely k-nearest neighbors. The intensity profile sampled along the surface normal is used as classification feature. Manual segmentations are used for training the classifier: samples are collected inside, outside, and at the given boundary positions. The deformation is steered by the most likely class corresponding to the intensity profile at each vertex on the surface. A parameter optimization study is conducted, followed by experiments to assess the overall segmentation quality and the robustness of results against variation in user input. Results obtained in a study of 17 patients show that the agreement with respect to manual segmentations is comparable to previous values reported in the literature, with considerable less user interaction.
Algorithms↗