Building Test Batteries Based on Analyzing Random Number Generator Tests within the Framework of Algorithmic Information Theory.

The problem of testing random number generators is considered and a new method for comparing the power of different statistical tests is proposed. It is based on the definitions of random sequence developed in the framework of algorithmic information theory and allows comparing the power of different tests in some cases when the available methods of mathematical statistics do not distinguish between tests. In particular, it is shown that tests based on data compression methods using dictionaries should be included in test batteries.

The quasi-xgamma frailty model with survival analysis under heterogeneity problem, validation testing, and risk analysis for emergency care data.

Frailty models are important for survival data because they allow for the possibility of unobserved heterogeneity problem. The problem of heterogeneity can be existed due to a variety of factors, such as genetic predisposition, environmental factors, or lifestyle choices. Frailty models can help to identify these factors and to better understand their impact on survival. In this study, we suggest a novel quasi xgamma frailty (QXg-F) model for the survival analysis. In this work, the test of Rao-Robson and Nikulin is employed to test the validity and suitability of the probabilistic model, we examine the distribution's properties and evaluate its performance in comparison with many relevant cox-frailty models. To show how well the QXg-F model captures heterogeneity and enhances model fit, we use simulation studies and real data applications, including a fresh dataset gathered from an emergency hospital in Algeria. According to our research, the QXg-F model is a viable replacement for the current frailty modeling distributions and has the potential to improve the precision of survival analyses in a number of different sectors, including emergency care. Moreover, testing the ability and the importance of the new QXg-F model in insurance is investigated using simulations via different methods and application to insurance data.

Response of streamflow and nutrient loads in a small temperate catchment subject to land use change.

The aim of this study was to quantify the effect of land use change (LUC) implemented to meet nutrient load targets for a freshwater lake in New Zealand. We used the Soil and Water Assessment Tool (SWAT) model in combination with a non-parametric statistical test to determine whether afforestation of 15% of a subcatchment area was adequate to meet assigned nutrient load targets. A regional management authority set nutrient load targets of reduction in total nitrogen (TN) by 0.9 t yr-1 and reduction in total phosphorus (TP) by 0.05 t yr-1 to avoid eutrophication in the receiving waters of a freshwater lake. The load reduction was designed to be achieved through 200 ha of LUC from pasture to trees. Analysis of nutrient loads before, during, and following LUC shows that a 15% increase in forest cover decreased the annual flow (7.2%), TP load (33.3%), and TN load (13.1%). As flow and water quality observations were discrete and at irregular intervals, we used a parametric test and the SWAT model as different lines of evidence to demonstrate the effect of afforestation on flow and water quality. Policymakers concerned with decisions about LUC to improve the quality of receiving waters can benefit from applying our findings and using a statistical and numerical modelling framework to evaluate the adequacy of land use change to support improvements in water quality.

Design and Implementation of a Fuzzy Classifier for FDI Applied to Industrial Machinery.

In the present work, the design and the implementation of a Fault Detection and Isolation (FDI) system for an industrial machinery is proposed. The case study is represented by a multishaft centrifugal compressor used for the syngas manufacturing. The system has been conceived for the monitoring of the faults which may damage the multishaft centrifugal compressor: instrument single and multiple faults have been considered as well as process faults like fouling of the compressor stages and break of the thrust bearing. A new approach that combines Principal Component Analysis (PCA), Cluster Analysis and Pattern Recognition is developed. A novel procedure based on the statistical test ANOVA (ANalysis Of VAriance) is applied to determine the most suitable number of Principal Components (PCs). A key design issue of the proposed fault isolation scheme is the data Cluster Analysis performed to solve the practical issue of the complexity growth experienced when analyzing process faults, which typically involve many variables. In addition, an automatic online Pattern Recognition procedure for finding the most probable faults is proposed. Clustering procedure and Pattern Recognition are implemented within a Fuzzy Faults Classifier module. Experimental results on real plant data illustrate the validity of the approach. The main benefits produced by the FDI system concern the improvement of the maintenance operations, the enhancement of the reliability and availability of the compressor, the increase in the plant safety while achieving reduction in plant functioning costs.

Differential Gene Expression Data Analysis of ASD Using Random Forest.

Autism spectrum disorder (ASD) is a developmental disability caused by differences in the brain regions. Analysis of differential expression (DE) of transcriptomic data allows for genome-wide analysis of gene expression changes related to ASD. De-novo mutations may play a vital role in ASD, but the list of genes involved is still far from complete. Differentially expressed genes (DEGs) are treated as candidate biomarkers and a small set of DEGs might be identified as biomarkers using either biological knowledge or data-driven approaches like machine learning and statistical analysis. In this study, we employed a machine learning-based approach to identify the differential gene expression between ASD and Typical Development (TD). The gene expression data of 15 ASD and 15 TD were obtained from the NCBI GEO database. Initially, we extracted the data and used a standard pipeline to pre-process the data. Further, Random Forest (RF) was used to discriminate genes between ASD and TD. We identified the top 10 prominent differential genes and compared them with the statistical test results. Our results show that the proposed RF model yields 5-fold cross-validation accuracy, sensitivity and specificity of 96.67%. Further, we obtained precision and F-measure scores of 97.5% and 96.57%, respectively. Moreover, we found 34 unique DEG chromosomal locations having influential contributions in identifying ASD from TD. We have also identified chr3:113322718-113322659 as the most significant contributing chromosomal location in discriminating ASD and TD. Our machine learning-based method of refining DE analysis is promising for finding biomarkers from gene expression profiles and prioritizing DEGs. Moreover, our study reported top 10 gene signatures for ASD may facilitate the development of reliable diagnosis and prognosis biomarkers for screening ASD.

Value of baseline characteristics in the risk prediction of atrial fibrillation.

Introduction: Atrial fibrillation (AF) is prone to heart failure and stroke. Early management can effectively reduce the stroke rate and mortality. Current clinical guidelines screen high-risk individuals based solely on age, while this study aims to explore the possibility of other AF risk predictors. Methods: A total of 18,738 elderly people (aged over 60 years old) in Chinese communities were enrolled in this study. The baseline characteristics were mainly based on the diagnosis results of electrocardiogram (ECG) machine during follow up, accompanied by some auxiliary physical examination basic data. After the analysis of both independent and combined baseline characteristics, AF risk predictors were obtained and prioritized according to the results. Independent characteristics were studied from three aspects: Chi-square test, Mann-Whitney U test and Cox univariate regression analysis. Combined characteristics were studied from two aspects: machine learning models and Cox multivariate regression analysis, and the former was combined with recursive feature elimination method and voting decision. Results: The resulted optimal combination of risk predictors included age, atrial premature beats, atrial flutter, left ventricular hypertrophy, hypertension and heart disease. Conclusion: Patients diagnosed by short-time ECG machines with the occurrence of the above events had a higher probability of AF episodes, who are suggested to be included in the focus of long-term ECG monitoring or increased screening density. The incidence of risk predictors in different age ranges of AF patients suggests differences in age-specific patient management. This can help improve the detection rate of AF, standardize the management of patients, and slow down the progression of AF.

A Bayesian perspective on severity: risky predictions and specific hypotheses.

A tradition that goes back to Sir Karl R. Popper assesses the value of a statistical test primarily by its severity: was there an honest and stringent attempt to prove the tested hypothesis wrong? For "error statisticians" such as Mayo (1996, 2018), and frequentists more generally, severity is a key virtue in hypothesis tests. Conversely, failure to incorporate severity into statistical inference, as allegedly happens in Bayesian inference, counts as a major methodological shortcoming. Our paper pursues a double goal: First, we argue that the error-statistical explication of severity has substantive drawbacks; specifically, the neglect of research context and the specificity of the predictions of the hypothesis. Second, we argue that severity matters for Bayesian inference via the value of specific, risky predictions: severity boosts the expected evidential value of a Bayesian hypothesis test. We illustrate severity-based reasoning in Bayesian statistics by means of a practical example and discuss its advantages and potential drawbacks.

Guía práctica para seleccionar una prueba estadística a aplicar en una investigación biomédica

Introducción: el análisis estadístico se divide en dos componentes: el análisis descriptivo y el análisis inferencial, las pruebas estadísticas, se fraccionan en paramétricas y no paramétricas. Sin embargo, la elección de una prueba estadística apropiada, representa un reto. Objetivo: proponer una herramienta, que sirva para seleccionar una prueba estadística a aquellos no expertos en bioestadística, para las investigaciones biomédicas. Métodos: se realizó un estudio tipo revisión bibliográfica narrativa. Se partió de una revisión de la literatura sobre las principales pruebas estadísticas que se utilizan en la actualidad, disponibles en la literatura de las bases de datosbibliográficas como Pubmed/Medline, SciELO, SCOPUS, Springer, Web of Science, EBSCOhost entre otras. Dicha herramienta fue validada por criterio de expertos. Resultados: se diseñó un esquema, el que puede utilizarse de dos maneras: la primera consiste seguir el esquema hasta descubrir cuál es la técnica estadística apropiada para sus datos y la segunda: siguiendo el esquema hacia atrás, determinar si la prueba fue una elección lógica para los datos analizados. Para usarla, debe identificar variables dependientes e independientes, después llegará a una medida de síntesis o a una estimación puntual útil para sus datos, que irá seguida de una clasificación general de las pruebas estadísticas. Conclusiones: la guía propuesta es un intento de aportar una guía útil para seleccionar una técnica estadística para el análisis de datos en las investigaciones biomédicas.

Introduction: statistical analysis is divided into two components: descriptive analysis and inferential analysis, statistical tests, are divided into parametric and nonparametric. Choosing an appropriate statistical test, however, is challenging. Objective: to propose a tool, which serves to select a statistical test to those not experts in biostatistics, for biomedical research. Methods: a narrative literature review study was conducted. It was based on a review of the literature on the main statistical tests currently used, available in the literature of bibliographic databases such as Pubmed/Medline, SciELO, SCOPUS, Springer, Web of Science, EBSCOhost among others. This tool was validated by expert criteria. Results: a scheme was designed, which can be used in two ways: the first is to follow the scheme until discovering which is the appropriate statistical technique for your data and the second: following the scheme backwards, determine if the test was a logical choice for the analyzed data. To use it, you must identify dependent and independent variables, then you will arrive at a synthesis measure or a useful point estimate for your data, which will be followed by a general classification of statistical tests. Conclusions: the proposed guideline is an attempt to provide a useful guide to select a statistical technique for data analysis in biomedical research.

Introdução: a análise estatística é dividida em dois componentes: análise descritiva e análise inferencial, testes estatísticos, são divididos em paramétricos e não paramétricos. Escolher um teste estatístico apropriado, no entanto, é um desafio. Objetivo: propor uma ferramenta, que sirva para selecionar um teste estatístico para aqueles que nãosão especialistas em bioestatística, para pesquisa biomédica. Métodos: realizou-se um estudo de revisão narrativa da literatura. Baseou-se em uma revisão da literatura sobre os principais testes estatísticos atualmente utilizados, disponíveis na literatura de bases de dados bibliográficas como Pubmed/Medline, SciELO, SCOPUS, Springer, Web of Science, EBSCOhost entre outras. Esse instrumento foi validado por critérios de especialistas. Resultados: foi elaborado um esquema, que pode ser utilizado de duas formas: a primeira é seguir o esquema até descobrir qual é a técnica estatística apropriada para seus dados e a segunda: seguindo o esquema de trás para frente, determinar se o teste foi uma escolha lógica para os dados analisados. Para usá-lo, você deve identificar variáveis dependentes e independentes, então você chegará a uma medida de síntese ou uma estimativa pontual útil para seus dados, que será seguida por uma classificação geral de testes estatísticos. Conclusões: a diretriz proposta é uma tentativa de fornecer um guia útil para selecionar uma técnica estatística para análise de dados em pesquisa biomédica.

Fundamentals and Applications of the Receiver Operating Characteristic Curve Analysis in the Research of Endothelial Dysfunction in Chronic Kidney Disease.

Endothelial dysfunction (ED) starts early in chronic kidney disease (CKD) and is the hallmark of atherosclerosis in these patients. During recent years, numerous markers have emerged, aiming to predict the onset of ED in CKD patients. Therefore, there is a need to evaluate and assess the discriminatory ability (or diagnostic accuracy) of such a marker (i.e., the ability to correctly classify individuals as having a given disease or not) and identify the optimal cut-off value. A receiver operating characteristic (ROC) curve analysis has been used in the majority of the research papers evaluating the predictive ability of a marker of ED. It is a graphical plot combining pairs of sensitivity (true positive rate) on the y axis and the complement of specificity (1-specificity, false positive rate) in the x axis, corresponding to several of the cut-off values covering the complete range of possible values that this test/marker might take. Herein, using a series of practical examples derived from clinical studies on ED in the special population of CKD, we address the principles, fundamentals, advantages and limitations regarding the interpretation of the ROC analysis.

A Fast and Efficient Ensemble Transfer Entropy and Applications in Neural Signals.

The ensemble transfer entropy (TEensemble) refers to the transfer entropy estimated from an ensemble of realizations. Due to its time-resolved analysis, it is adapted to analyze the dynamic interaction between brain regions. However, in the traditional TEensemble, multiple sets of surrogate data should be used to construct the null hypothesis distribution, which dramatically increases the computational complexity. To reduce the computational cost, a fast, efficient TEensemble with a simple statistical test method is proposed here, in which just one set of surrogate data is involved. To validate the improved efficiency, the simulated neural signals are used to compare the characteristics of the novel TEensemble with those of the traditional TEensemble. The results show that the time consumption is reduced by two or three magnitudes in the novel TEensemble. Importantly, the proposed TEensemble could accurately track the dynamic interaction process and detect the strength and the direction of interaction robustly even in the presence of moderate noises. The novel TEensemble reaches its steady state with the increased samples, which is slower than the traditional method. Furthermore, the effectiveness of the novel TEensemble was verified in the actual neural signals. Accordingly, the TEensemble proposed in this work may provide a suitable way to investigate the dynamic interactions between brain regions.

Euarchontoglires Challenged by Incomplete Lineage Sorting.

Euarchontoglires, once described as Supraprimates, comprise primates, colugos, tree shrews, rodents, and lagomorphs in a clade that evolved about 90 million years ago (mya) from a shared ancestor with Laurasiatheria. The rapid speciation of groups within Euarchontoglires, and the subsequent inherent incomplete marker fixation in ancestral lineages, led to challenged attempts at phylogenetic reconstructions, particularly for the phylogenetic position of tree shrews. To resolve this conundrum, we sampled genome-wide presence/absence patterns of transposed elements (TEs) from all representatives of Euarchontoglires. This specific marker system has the advantage that phylogenetic diagnostic characters can be extracted in a nearly unbiased fashion genome-wide from reference genomes. Their insertions are virtually free of homoplasy. We simultaneously employed two computational tools, the genome presence/absence compiler (GPAC) and 2-n-way, to find a maximum of diagnostic insertions from more than 3 million TE positions. From 361 extracted diagnostic TEs, 132 provide significant support for the current resolution of Primatomorpha (Primates plus Dermoptera), 94 support the union of Euarchonta (Primates, Dermoptera, plus Scandentia), and 135 marker insertion patterns support a variety of alternative phylogenetic scenarios. Thus, whole genome-level analysis and a virtually homoplasy-free marker system offer an opportunity to finally resolve the notorious phylogenetic challenges that nature produces in rapidly diversifying groups.

Comparison of Electrodermal Activity from Multiple Body Locations Based on Standard EDA Indices' Quality and Robustness against Motion Artifact.

The most traditional sites for electrodermal activity (EDA) data collection, palmar locations such as fingers or palms, are not usually recommended for ambulatory monitoring given that subjects have to use their hands regularly during their daily activities, and therefore, alternative sites are often sought for EDA data collection. In this study, we collected EDA signals (n = 23 subjects, 19 male) from four measurement sites (forehead, back of neck, finger, and inner edge of foot) during cognitive stress and induction of mild motion artifacts by walking and one-handed weightlifting. Furthermore, we computed several EDA indices from the EDA signals obtained from different sites and evaluated their efficiency to classify cognitive stress from the baseline state. We found a high within-subject correlation between the EDA signals obtained from the finger and the feet. Consistently high correlation was also found between the finger and the foot EDA in both the phasic and tonic components. Statistically significant differences were obtained between the baseline and cognitive stress stage only for the EDA indices computed from the finger and the foot EDA. Moreover, the receiver operating characteristic curve for cognitive stress detection showed a higher area-under-the-curve for the EDA indices computed from the finger and foot EDA. We also evaluated the robustness of the different body sites against motion artifacts and found that the foot EDA location was the best alternative to other sites.

Is the New EN689 a Better Standard to Test Compliance With Occupational Exposure Limits in the Workplace?

OBJECTIVE: To evaluate the performance of three measurement strategies to test compliance with occupational exposure limits of similarly exposed groups (SEGs): the old and new versions of EN689, and the BOHS-NVvA guidance on measuring compliance. METHODS: Respirable dust exposures concentrations (n = 1383) measured within the member companies of IMA-Europe were used to compare compliance decisions between the three measurement strategies. A total of 210 SEGs of which 158 with repeated measurements were analysed. An R studio OHcomplianceStrategies package was created for the purpose. RESULTS: The old EN689 strategy resulted in the highest number of compliant SEGs in the preliminary tests and statistical test (49-52% and 83%) with lower percentages of compliance with the new EN689 standard (32-44% and 71%). The percentage of non-compliant SEGs was relatively similar between the old and new EN689 for the preliminary tests (1-12% versus 6-11%). However, the new EN689 declared almost twofold more SEGs non-compliant when applying the statistical test (29% versus 17%). The BOHS-NVvA individual test showed results in between the 26% non-compliant SEGs. CONCLUSION: This study showed differences in compliance decisions between the old and new EN689, with the new EN689 being considerably more stringent and resulting in more non-compliant SEGs.

Statistics decrypted-a comprehensive review and smartphone-assisted five-step approach for good statistical practice.

BACKGROUND: Statistic scripts are often made by mathematicians and cryptic for clinicians or non-mathematician scientists. Nevertheless, almost all research projects necessitate the application of some statistical tests or at least an understanding thereof. The present review aims on giving an overview of the most common statistical terms and concepts. It further ensures good statistical practice by providing a five-step approach guiding the reader to the correct statistical test. METHODS AND RESULTS: First, different types of variables and measurements to describe a data set with means of descriptive statistics are introduced. The basic thoughts and tools of interferential statistics are presented, and different types of bias are discussed. Then in the final paragraph, the most commonly used statistical tests are described. A smartphone app accessible via QR code finally guides the reader in five steps to the correct statistical test, depending on the data used in order to avoid commonly performed mistakes. CONCLUSIONS: The five-step approach sets a new minimal standard for good statistical practice.

SpatialCorr identifies gene sets with spatially varying correlation structure.

Recent advances in spatially resolved transcriptomics technologies enable both the measurement of genome-wide gene expression profiles and their mapping to spatial locations within a tissue. A first step in spatial transcriptomics data analysis is identifying genes with expression that varies spatially, and robust statistical methods exist to address this challenge. While useful, these methods do not detect spatial changes in the coordinated expression within a group of genes. To this end, we present SpatialCorr, a method for identifying sets of genes with spatially varying correlation structure. Given a collection of gene sets pre-defined by a user, SpatialCorr tests for spatially induced differences in the correlation of each gene set within tissue regions, as well as between and among regions. An application to cutaneous squamous cell carcinoma demonstrates the power of the approach for revealing biological insights not identified using existing methods.

Lepidium meyenii (maca) and soy isoflavones reduce cardiac stunning of ischemia-reperfusion in rats by mitochondrial mechanisms.

BACKGROUND AND AIM: Phytoestrogens are traditionally used for cardiovascular risks but direct effects on the ischemic heart remain unclear. Plants with phytoestrogens are used for reducing menopausic symptoms and they could also be cardioprotectives. Here we investigated whether maca (Lepidium meyenii) contains isoflavones and prevents cardiac stunning, in comparison to soy isoflavones. EXPERIMENTAL PROCEDURE: Both products were orally and daily administered to rats during 1 week before exposing isolated hearts to ischemia/reperfusion (I/R). Young male (YM), female (YF) and aged female (AgF) rats treated with maca (MACA, 1 g/kg/day) or soy isoflavones (ISOF, 100 mg/kg/day) were compared to acute daidzein (DAZ, 5 mg/kg i.p.) and non-treated rat groups. Isolated ventricles were perfused inside a calorimeter to simultaneously measure contractile and calorimetrical signals before and during I/R. RESULTS AND CONCLUSIONS: Maca has genistein and daidzein. MACA and ISOF improved the post-ischemic contractile recovery (PICR) and muscle economy (P/Ht) in YM and YF hearts, but not in AgF hearts. DAZ improved PICR and P/Ht more in YM than in YF. The mKATP channels blockade reduced both PICR and P/Ht in DAZ-treated YM hearts, without affecting them in ISOF or MACA-treated YM hearts. In MACA treated YF hearts, the simultaneous blockade of NOS and mKATP channels, or the mNCX blockade reduced cardioprotection. Results show that subacute oral treatment with maca or with soy isoflavones was strongly preventive of cardiac ischemic dysfunction, more than the acute administration of a pure isoflavone (daidzein, genistein). Maca induced synergistic and complex mechanisms which prevented mitochondrial calcium overload.

Design and Analysis Methods for Trials with AI-Based Diagnostic Devices for Breast Cancer.

Imaging is important in cancer diagnostics. It takes a long period of medical training and clinical experience for radiologists to be able to accurately interpret diagnostic images. With the advance of big data analysis, machine learning and AI-based devices are currently under development and taking a role in imaging diagnostics. If an AI-based imaging device can read the image as accurately as experienced radiologists, it may be able to help radiologists increase the accuracy of their reading and manage their workloads. In this paper, we consider two potential study objectives of a clinical trial to evaluate an AI-based device for breast cancer diagnosis by comparing its concordance with human radiologists. We propose statistical design and analysis methods for each study objective. Extensive numerical studies are conducted to show that the proposed statistical testing methods control the type I error rate accurately and the design methods provide required sample sizes with statistical powers close to pre-specified nominal levels. The proposed methods were successfully used to design and analyze a real device trial.

How to choose and interpret a statistical test? An update for budding researchers.

Postgraduate medical students are often not able to select and interpret the findings of statistical tests during their thesis or research projects. To go ahead with selection of tests to be performed, researchers need to determine the objectives of study, types of variables, analysis and the study design, number of groups and data sets, and the types of distribution. In this review, we summarize and explain various statistical tests to help postgraduate medical students to select the most appropriate techniques for their thesis and dissertation.

A Comparative Study of Common Nature-Inspired Algorithms for Continuous Function Optimization.

Over previous decades, many nature-inspired optimization algorithms (NIOAs) have been proposed and applied due to their importance and significance. Some survey studies have also been made to investigate NIOAs and their variants and applications. However, these comparative studies mainly focus on one single NIOA, and there lacks a comprehensive comparative and contrastive study of the existing NIOAs. To fill this gap, we spent a great effort to conduct this comprehensive survey. In this survey, more than 120 meta-heuristic algorithms have been collected and, among them, the most popular and common 11 NIOAs are selected. Their accuracy, stability, efficiency and parameter sensitivity are evaluated based on the 30 black-box optimization benchmarking (BBOB) functions. Furthermore, we apply the Friedman test and Nemenyi test to analyze the performance of the compared NIOAs. In this survey, we provide a unified formal description of the 11 NIOAs in order to compare their similarities and differences in depth and a systematic summarization of the challenging problems and research directions for the whole NIOAs field. This comparative study attempts to provide a broader perspective and meaningful enlightenment to understand NIOAs.

Valid and powerful second-level group statistics for decoding accuracy: Information prevalence inference using the i-th order statistic (i-test).

In functional magnetic resonance imaging (fMRI) decoding studies using pattern classification, a second-level group statistical test is typically performed after first-level decoding analyses for individual participants. In the second-level test, the mean decoding accuracy across participants is often tested against the chance-level accuracy (for example, one-sample Student t-test) to check whether information about the label, such as, experimental condition or cognitive content, is included in brain activation. Meanwhile, Allefeld et al., (2016) highlighted that significant results for such tests only indicate that "there are some people in the population whose fMRI data carry information about the experimental condition." Therefore, such tests failed to conclude whether the effect is typical in the population. Based on this argument, they proposed an alternative method implementing the prevalence inference. In the present study, that method is extended to propose a novel statistical test called as the "information prevalence inference using the i-th order statistic" (i-test). The i-test has a high statistical power compared with the method proposed in Allefeld et al., (2016) and provides an inference regarding the typical effect in the population. In the i-test, the i-th lowest sample decoding accuracy (the i-th order statistic) is compared to the null distribution to verify whether the proportion of higher-than-chance decoding accuracy in the population (information prevalence) is higher than the threshold. Hence, a significant result in the i-test is interpreted as a majority of the population has information about the label in the brain. Theoretical details of the i-test are provided, its high statistical power is identified by numerical calculation, and the application of this method in an fMRI decoding is demonstrated.