scholarly journals Inferring exemplar discriminability in brain representations

2016 ◽  
Author(s):  
Hamed Nili ◽  
Alexander Walther ◽  
Arjen Alink ◽  
Nikolaus Kriegeskorte
Keyword(s):  
Fixed Effects ◽  
Statistical Tests ◽  
Random Effect ◽  
Nonparametric Tests ◽  
Test Statistics ◽  
Brain Response ◽  
Test Statistic ◽  
Mahalanobis Distances ◽  
Linear Discriminant ◽  
Wide Range

AbstractRepresentational distinctions within categories are important in all perceptual modalities and also in cognitive and motor representations. Recent pattern-information studies of brain activity have used condition-rich designs to sample the stimulus space more densely. To test whether brain response patterns discriminate among a set of stimuli (e.g. exemplars within a category) with good sensitivity, we can pool statistical evidence over all pairwise comparisons. A popular test statistic reflecting exemplar information is the exemplar discriminability index (EDI), which is defined as the average of the pattern dissimilarity estimates between different exemplars minus the average of the pattern dissimilarity estimates between repetitions of identical exemplars. The EDI is commonly tested with a t test (H0: population mean EDI = 0) across subjects (subject as random effect). However, it is unclear whether this approach is either valid or optimal. Here we describe a wide range of statistical tests of exemplar discriminability and assess the validity (specificity) and power (sensitivity) of each test. The tests include previously used and novel, parametric and nonparametric tests, which treat subject as a random or fixed effect, and are based on different dissimilarity measures, different test statistics, and different inference procedures. We use simulated and real data to determine which tests are valid and which are most sensitive. The popular across-subject t test of the EDI (typically using correlation distance as the pattern dissimilarity measure) requires the assumption that the EDI is 0-mean normal under H0, which is not strictly true. Reassuringly, our simulations suggest that the test controls the false-positives rate at the nominal level and is thus valid in practice. However, test statistics based on average Mahalanobis distances or average linear-discriminant t values (both accounting for the multivariate error covariance among responses) are substantially more powerful for both random- and fixed-effects inference. We suggest preferred procedures for safely and sensitively detecting subtle pattern differences between exemplars.

scholarly journals Selected Statistical Tests for Median and Their Properties

2017 ◽  
Vol 4 (330) ◽  
Author(s):  
Dorota Pekasiewicz ◽  
Agata Szczukocka
Keyword(s):  
Population Distribution ◽  
Simulation Analysis ◽  
Alternative Hypothesis ◽  
Statistical Tests ◽  
Bootstrap Method ◽  
Nonparametric Tests ◽  
Small Samples ◽  
Test Statistic ◽  
Sample Median ◽  
Critical Regions

In the paper, a selection of statistical tests for median are presented. In particular, parametric and nonparametric significance tests are considered. In the case of parametric tests the critical regions are constructed on the basis of the known population distribution and the form of the alternative hypothesis. For chosen distributions the critical values are presented. In the case of nonparametric tests we consider tests for which the sample median dispersion is estimated based on order statistics of appropriate ranks. The use of the bootstrap method for the median dispersion estimation in the test statistic construction is the author’s own proposal. The simulation analysis of the nonparametric tests’ properties allows to compare these tests with each other, showing better results for the bootstrap variant, especially for small samples.

scholarly journals Rounded Input Variables, Exact Test Statistics (RIVETS)

2019 ◽  
Author(s):  
Nicholas J. L. Brown ◽  
James Heathers
Keyword(s):  
Statistical Tests ◽  
T Test ◽  
Test Statistics ◽  
Test Statistic ◽  
Statistical Software ◽  
Exact Test ◽  
Manual Intervention ◽  
Software Packages ◽  
Rounded Form ◽  
Input Variables

Most statistical software packages report the input values to statistical tests (e.g., means and standard deviations for an unpaired t test) in a rounded form (e.g., to two decimal places), with this rounding having been performed after the test statistic has been calculated. However, in some cases, the input values are rounded before the test statistic is calculated, most likely because of some form of manual intervention by the researcher. We describe a method that enables the probabilistic identification of detecting this rounding, the conditions required for this method to be applicable, the tests where pre-calculation rounding can be detected, and the implications of its detection.

scholarly journals Measuring economic growth in OPEC countries : A panel data approach

2015 ◽  
Vol 4 (2) ◽  
pp. 345
Author(s):  
Johnson Taiwo Olajide ◽  
Jubril Oluwatoyin Fantola ◽  
Olufemi Aderemi Ayansola
Keyword(s):  
Economic Growth ◽  
Purchasing Power Parity ◽  
Fixed Effects ◽  
Random Effect ◽  
Developed Countries ◽  
Ordinary Least Squares ◽  
Positive Influence ◽  
Fixed Effects Model ◽  
Power Parity ◽  
Test Statistic

<p>Most of the developing and under-developed countries have been facing a lot of challenges on the issue of economic growth, despite the fact that they are endowed with both natural and human resources. This study examines the determinants of real per Capita GDP growth in Organization of the Petroleum Exporting Countries (OPEC) using a panel of twelve countries for the period of 1986 and 2010.The pooled Ordinary Least Squares (OLS), Fixed Effect (FE) and Random Effect (RE) models were employed to assess the relationship between CGDP and other economic variables used. The result showed that price level of consumptions (pc) and investment share (ci) are the important factors of CGDP that contribute to the economic growth of OPEC countries. The result also established that exchange rate (Xrat), price of GDP (p), purchasing power parity (ppp) and ci have a positive influence on CGDP. The test statistic revealed that Random Effects Model (REM) estimator is more efficient than OLS and that there is no significance difference between Fixed Effects Model (FEM) and REM estimators.</p>

A USE OF NONPARAMETRIC TESTS FOR DEA-DISCRIMINANT ANALYSIS: A METHODOLOGICAL COMPARISON

2004 ◽  
Vol 21 (02) ◽  
pp. 179-195 ◽  
Author(s):  
TOSHIYUKI SUEYOSHI ◽  
SHIUH-NAN HWANG
Keyword(s):  
Discriminant Analysis ◽  
Group Membership ◽  
Financial Analysis ◽  
Statistical Tests ◽  
Nonparametric Tests ◽  
Systems Science ◽  
Data Envelopment ◽  
Statistical Tool ◽  
Linear Discriminant ◽  
New Type

Discriminant Analysis (DA) is a statistical tool that can predict the group membership of a newly sampled observation. Sueyoshi (European Journal of Operational Research, 115 (1999) 564; 131 (2001) 324; 152 (2004) 45) and Sueyoshi and Kirihara (International Journal of Systems Science, 29 (1998) 1249) have recently proposed a new type of nonparametric DA approach that provides a set of weights of a linear discriminant function, consequently yielding an evaluation score for the determination of group membership. The nonparametric DA is referred to as "Data Envelopment Analysis-Discriminant Analysis (DEA-DA)," because it maintains its discriminant capabilities by incorporating the nonparametric feature of DEA into DA. In this study, a use of two statistical tests is proposed for DEA-DA and its discriminant capability is compared with DEA from a perspective of financial analysis.

scholarly journals An Implementation of Empirical Bayesian Inference and Non-Null Bootstrapping for Threshold Selection and Power Estimation in Multiple and Single Statistical Testing

2018 ◽  
Author(s):  
Bahman Nasseroleslami
Keyword(s):  
Bayesian Inference ◽  
Probability Density ◽  
Statistical Power ◽  
Statistical Tests ◽  
Gaussian Mixture ◽  
Statistical Testing ◽  
Test Statistics ◽  
Empirical Bayesian ◽  
Statistical Measures ◽  
Wide Range

AbstractThe majority of conclusions and interpretations in quantitative sciences such as neuroscience are based on statistical tests. However, the statistical inferences, especially in multivariate analyses, commonly rely on the p-values, but not on more expressive measures such as posterior probabilities, false discovery rates (FDR) and statistical power (1 − β). The aim of this report is to make these statistical measures further accessible in single and multiple statistical testing. For multiple testing, the Empirical Bayesian Inference (Efron et al., 2001; Efron, 2007) was implemented using non-parametric test statistics (e.g. the Area Under the Curve of the Receiving Operator Characteristics Curve or Spearman’s rank correlation) and Gaussian Mixture Model estimation of the probability density function of the original and bootstrapped data. For single statistical tests, the same test statistics were used to construct and estimate the null and non-null probability density functions using bootstrapping under null and non-null grouping assumptions. Simulations were used to test the reliability of the results under a wide range of conditions. The results show conformity to the real truth in the simulated conditions, which is held under various conditions imposed on the simulated data. The open-source MATLAB codes are provided and the utility of the approach has been exemplified and discussed for real-world electroencephalographic signals. This implementation of Empirical Bayesian Inference and informed selection of statistical thresholds are expected to facilitate more realistic scientific deductions in versatile fields, especially in neuroscience, neural signal analysis and neuro-imaging.

scholarly journals Enlarging the Scope of Randomization and Permutation Tests in Neuroimaging and Neuroscience

2019 ◽  
Author(s):  
Eric Maris
Keyword(s):  
Rate Control ◽  
Explanatory Variable ◽  
Statistical Tests ◽  
Permutation Tests ◽  
Informed Choice ◽  
Companion Paper ◽  
Nonparametric Tests ◽  
Test Statistic ◽  
Drastic Increase ◽  
Nonparametric Statistical

AbstractEspecially for the high-dimensional data collected in neuroscience, nonparametric statistical tests are an excellent alternative for parametric statistical tests. Because of the freedom to use any function of the data as a test statistic, nonparametric tests have the potential for a drastic increase in sensitivity by making a biologically-informed choice for a test statistic. In a companion paper (Geerligs & Maris, 2020), we demonstrate that such a drastic increase is actually possible. This increase in sensitivity is only useful if, at the same time, the false alarm (FA) rate can be controlled. However, for some study types (e.g., within-participant studies), nonparametric tests do not control the FA rate (see Eklund, Nichols, & Knutsson, 2016). In the present paper, we present a family of nonparametric randomization and permutation tests of which we prove exact FA rate control. Crucially, these proofs hold for a much larger family of study types than before, and they include both within-participant studies and studies in which the explanatory variable is not under experimental control. The crucial element of this statistical innovation is the adoption of a novel but highly relevant null hypothesis: statistical independence between the biological and the explanatory variable.

An evaluation of diagnostic tests and their roles in validating forest biometric models

2004 ◽  
Vol 34 (3) ◽  
pp. 619-629 ◽  
Author(s):  
Yuqing Yang ◽  
Robert A Monserud ◽  
Shongming Huang
Keyword(s):  
Model Validation ◽  
Statistical Tests ◽  
Model Development ◽  
Nonparametric Tests ◽  
T Test ◽  
Sign Test ◽  
Rank Test ◽  
Wide Range ◽  
Kolmogorov Smirnov ◽  
Smirnov Test

Model validation is an important part of model development. It is performed to increase the credibility and gain sufficient confidence about a model. This paper evaluated the usefulness of 10 statistical tests, five parametric and five nonparametric, in validating forest biometric models. The five parametric tests are the paired t test, the Χ2 test, the separate t test, the simultaneous F test, and the novel test. The five nonparametric tests are the Brown-Mood test, the Kolmogorov–Smirnov test, the modified Kolmogorov–Smirnov test, the sign test, and the Wilcoxon signed-rank test. Nine benchmark data sets were selected to evaluate the behavior of these tests in model validation; three were collected from Alberta and six were published elsewhere. It was shown that the usefulness of statistical tests in model validation is very limited. None of the tests seems to be generic enough to work well across a wide range of models and data. Each model passed one or more tests, but not all of them. Because of this, caution should be exercised when choosing a statistical test or several tests together to try to validate a model. It is important to reduce and remove any potential personal bias in selecting a favorite test, which can influence the outcome of the results.

Validity of Randomization Tests for one-Subject Experiments

1980 ◽  
Vol 5 (3) ◽  
pp. 235-251 ◽  
Author(s):  
Eugene S. Edgington
Keyword(s):  
Statistical Tests ◽  
Test Procedure ◽  
Randomization Test ◽  
Statistical Test ◽  
Random Assignment ◽  
Randomization Tests ◽  
Test Statistic ◽  
Wide Range ◽  
Α Level

Valid Statistical tests for one-subject experiments are necessary to justify Statistical inferences and to ensure the acceptability of research reports to a wide range of journals and readers. The validity of randomization tests for one-subject experiments is examined in this paper. A randomization test is a procedure for determining significance in the following manner. A test statistic (e.g., t or F) is computed for a set of research data. The value of the test statistic is called the “obtained test statistic value.” The data are then divided repeatedly, and the test statistic is computed for each data division. If the proportion of the data divisions giving a test statistic value as large as the obtained test statistic value is no greater than α, the test statistic is significant at the α level. Any Statistical test is said to be a randomization test when the significance of its test statistic is determined by the randomization test procedure. Determination of significance by the randomization test procedure permits the valid application of any Statistical test, whether it be as simple as a t test or as complex as factorial multivariate analysis of variance, for one-subject as well as multiple-subject experiments. For the randomization test procedure to be valid for a one-subject experiment, there must be random assignment of treatment times to treatments (i.e., random determination of when each treatment is to be given); specification, before observing the data, of the test statistic and the criterion to be employed for discarding data; and, in the determination of significance, division of the data in a manner consistent with the random assignment procedure.

scholarly journals A random effects population dynamics model based on proportions-at-age and removal data for estimating total mortality

2012 ◽  
Vol 69 (11) ◽  
pp. 1881-1893 ◽  
Author(s):  
Verena M. Trenkel ◽  
Mark V. Bravington ◽  
Pascal Lorance
Keyword(s):  
Population Dynamics ◽  
Random Effects ◽  
Fixed Effects ◽  
Random Effect ◽  
Total Mortality ◽  
Estimation Bias ◽  
Effective Sample Size ◽  
Dynamics Model ◽  
Population Dynamics Model ◽  
Study Parameter

Catch curves are widely used to estimate total mortality for exploited marine populations. The usual population dynamics model assumes constant recruitment across years and constant total mortality. We extend this to include annual recruitment and annual total mortality. Recruitment is treated as an uncorrelated random effect, while total mortality is modelled by a random walk. Data requirements are minimal as only proportions-at-age and total catches are needed. We obtain the effective sample size for aggregated proportion-at-age data based on fitting Dirichlet-multinomial distributions to the raw sampling data. Parameter estimation is carried out by approximate likelihood. We use simulations to study parameter estimability and estimation bias of four model versions, including models treating mortality as fixed effects and misspecified models. All model versions were, in general, estimable, though for certain parameter values or replicate runs they were not. Relative estimation bias of final year total mortalities and depletion rates were lower for the proposed random effects model compared with the fixed effects version for total mortality. The model is demonstrated for the case of blue ling (Molva dypterygia) to the west of the British Isles for the period 1988 to 2011.

scholarly journals Effects of kinship correction on inflation of genetic interaction statistics in commonly used mouse populations

2021 ◽  
Author(s):  
Anna L Tyler ◽  
Baha El Kassaby ◽  
Georgi Kolishovski ◽  
Jake Emerson ◽  
Ann E Wells ◽  
...  
Keyword(s):  
Mixed Model ◽  
Linear Mixed Model ◽  
Genetic Interaction ◽  
Recombinant Inbred Lines ◽  
Test Statistics ◽  
Test Statistic ◽  
Kinship Matrix ◽  
Main Effect ◽  
Main Effects ◽  
Interaction Test

Abstract It is well understood that variation in relatedness among individuals, or kinship, can lead to false genetic associations. Multiple methods have been developed to adjust for kinship while maintaining power to detect true associations. However, relatively unstudied, are the effects of kinship on genetic interaction test statistics. Here we performed a survey of kinship effects on studies of six commonly used mouse populations. We measured inflation of main effect test statistics, genetic interaction test statistics, and interaction test statistics reparametrized by the Combined Analysis of Pleiotropy and Epistasis (CAPE). We also performed linear mixed model (LMM) kinship corrections using two types of kinship matrix: an overall kinship matrix calculated from the full set of genotyped markers, and a reduced kinship matrix, which left out markers on the chromosome(s) being tested. We found that test statistic inflation varied across populations and was driven largely by linkage disequilibrium. In contrast, there was no observable inflation in the genetic interaction test statistics. CAPE statistics were inflated at a level in between that of the main effects and the interaction effects. The overall kinship matrix overcorrected the inflation of main effect statistics relative to the reduced kinship matrix. The two types of kinship matrices had similar effects on the interaction statistics and CAPE statistics, although the overall kinship matrix trended toward a more severe correction. In conclusion, we recommend using a LMM kinship correction for both main effects and genetic interactions and further recommend that the kinship matrix be calculated from a reduced set of markers in which the chromosomes being tested are omitted from the calculation. This is particularly important in populations with substantial population structure, such as recombinant inbred lines in which genomic replicates are used.

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