Testing normality

2019 ◽  
Vol 86 (12) ◽  
pp. 773-783 ◽  
Author(s):  
Katy Klauenberg ◽  
Clemens Elster
Keyword(s):  
Hypothesis Testing ◽  
Normal Distribution ◽  
Multiple Testing ◽  
Hypothesis Test ◽  
Statistical Tests ◽  
Distributional Assumption ◽  
Legal Metrology ◽  
Normality Assumption ◽  
Statistical Framework ◽  
Do So

AbstractIn metrology, the normal distribution is often taken for granted, e. g. when evaluating the result of a measurement and its uncertainty, or when establishing the equivalence of measurements in key or supplementary comparisons. The correctness of this inference and subsequent conclusions is dependent on the normality assumption, such that a validation of this assumption is essential. Hypothesis testing is the formal statistical framework to do so, and this introduction will describe how statistical tests detect violations of a distributional assumption.In the metrological context we will advise on how to select such a hypothesis test, how to set it up, how to perform it and which conclusion(s) can be drawn. In addition, we calculate the number of measurements needed to decide whether a process departs from a normal distribution and quantify how sure one is about this decision then. These aspects are illustrated for the powerful Shapiro-Wilk test and by an example in legal metrology. For this application we recommend to perform 330 measurements. Briefly we also touch upon the issues of multiple testing and rounded measurements.

scholarly journals HyPhy 2.5—A Customizable Platform for Evolutionary Hypothesis Testing Using Phylogenies

2019 ◽  
Vol 37 (1) ◽  
pp. 295-299 ◽  
Author(s):  
Sergei L Kosakovsky Pond ◽  
Art F Y Poon ◽  
Ryan Velazquez ◽  
Steven Weaver ◽  
N Lance Hepler ◽  
...  
Keyword(s):  
Parameter Estimation ◽  
Natural Selection ◽  
Hypothesis Testing ◽  
Statistical Tests ◽  
Evolutionary Process ◽  
Evolutionary Models ◽  
Sequence Alignments ◽  
Multiple Sequence ◽  
Multiple Sequence Alignments ◽  
Statistical Framework

Abstract HYpothesis testing using PHYlogenies (HyPhy) is a scriptable, open-source package for fitting a broad range of evolutionary models to multiple sequence alignments, and for conducting subsequent parameter estimation and hypothesis testing, primarily in the maximum likelihood statistical framework. It has become a popular choice for characterizing various aspects of the evolutionary process: natural selection, evolutionary rates, recombination, and coevolution. The 2.5 release (available from www.hyphy.org) includes a completely re-engineered computational core and analysis library that introduces new classes of evolutionary models and statistical tests, delivers substantial performance and stability enhancements, improves usability, streamlines end-to-end analysis workflows, makes it easier to develop custom analyses, and is mostly backward compatible with previous HyPhy releases.

scholarly journals MultipleTesting.com: A tool for life science researchers for multiple hypothesis testing correction

PLoS ONE ◽  
2021 ◽  
Vol 16 (6) ◽  
pp. e0245824
Author(s):  
Otília Menyhart ◽  
Boglárka Weltz ◽  
Balázs Győrffy
Keyword(s):  
Hypothesis Testing ◽  
Multiple Testing ◽  
Life Science ◽  
Statistical Tests ◽  
Correction Method ◽  
Multiple Hypothesis Testing ◽  
Command Line ◽  
Multiple Testing Correction ◽  
Multiple Hypothesis ◽  
Correction Technique

Scientists from nearly all disciplines face the problem of simultaneously evaluating many hypotheses. Conducting multiple comparisons increases the likelihood that a non-negligible proportion of associations will be false positives, clouding real discoveries. Drawing valid conclusions require taking into account the number of performed statistical tests and adjusting the statistical confidence measures. Several strategies exist to overcome the problem of multiple hypothesis testing. We aim to summarize critical statistical concepts and widely used correction approaches while also draw attention to frequently misinterpreted notions of statistical inference. We provide a step-by-step description of each multiple-testing correction method with clear examples and present an easy-to-follow guide for selecting the most suitable correction technique. To facilitate multiple-testing corrections, we developed a fully automated solution not requiring programming skills or the use of a command line. Our registration free online tool is available at www.multipletesting.com and compiles the five most frequently used adjustment tools, including the Bonferroni, the Holm (step-down), the Hochberg (step-up) corrections, allows to calculate False Discovery Rates (FDR) and q-values. The current summary provides a much needed practical synthesis of basic statistical concepts regarding multiple hypothesis testing in a comprehensible language with well-illustrated examples. The web tool will fill the gap for life science researchers by providing a user-friendly substitute for command-line alternatives.

scholarly journals MultipleTesting.com: a tool for life science researchers for multiple hypothesis testing correction

2021 ◽  
Author(s):  
Otília Menyhárt ◽  
Boglárka Weltz ◽  
Balázs Győrffy
Keyword(s):  
Hypothesis Testing ◽  
Multiple Testing ◽  
Life Science ◽  
Statistical Tests ◽  
Correction Method ◽  
Multiple Hypothesis Testing ◽  
Command Line ◽  
Multiple Testing Correction ◽  
Multiple Hypothesis ◽  
Correction Technique

ABSTRACTScientists from nearly all disciplines face the problem of simultaneously evaluating many hypotheses. Conducting multiple comparisons increases the likelihood that a non-negligible proportion of associations will be false positives, clouding real discoveries.Drawing valid conclusions require taking into account the number of performed statistical tests and adjusting the statistical confidence measures. Several strategies exist to overcome the problem of multiple hypothesis testing. We aim to summarize critical statistical concepts and widely used correction approaches while also draw attention to frequently misinterpreted notions of statistical inference.We provide a step-by-step description of each multiple-testing correction method with clear examples and present an easy-to-follow guide for selecting the most suitable correction technique.To facilitate multiple-testing corrections, we developed a fully automated solution not requiring programming skills or the use of a command line. Our registration free online tool is available at www.multipletesting.com and compiles the five most frequently used adjustment tools, including the Bonferroni, the Holm (step-down), the Hochberg (step-up) corrections, allows to calculate False Discovery Rates (FDR) and q-values.The current summary provides a much needed practical synthesis of basic statistical concepts regarding multiple hypothesis testing in a comprehensible language with well-illustrated examples. The web tool will fill the gap for life science researchers by providing a user-friendly substitute for command-line alternatives.

scholarly journals The nuts and bolts of hypothesis testing

2015 ◽  
Vol 3 (3) ◽  
pp. 139-144 ◽  
Author(s):  
Stephanie L. Pugh ◽  
Annette Molinaro
Keyword(s):  
Hypothesis Testing ◽  
Hypothesis Test ◽  
Statistical Tests ◽  
Epidemiological Studies ◽  
Statistical Test ◽  
P Value ◽  
P Values ◽  
Multiple Tests ◽  
Alternative Hypotheses ◽  
Decision Making Tool

Abstract When reading an article published in a medical journal, statistical tests are mentioned and the results are often supported by a P value. What are these tests? What is a P value and what is its meaning? P values are used to interpret the result of a statistical test. Both are intrinsic parts of hypothesis testing, which is a decision-making tool based on probability. Most medical and epidemiological studies are designed using a hypothesis test so understanding the key principles of a hypothesis test are crucial to interpreting results of a study. From null and alternative hypotheses to the issue of multiple tests, this paper introduces concepts related to hypothesis testing that are crucial to its implementation and interpretation.

scholarly journals Consistency of the Empirical Distributions of Navigation Positioning System Errors with Theoretical Distributions—Comparative Analysis of the DGPS and EGNOS Systems in the Years 2006 and 2014

Sensors ◽  
2020 ◽  
Vol 21 (1) ◽  
pp. 31
Author(s):  
Mariusz Specht
Keyword(s):  
Normal Distribution ◽  
Root Mean Square ◽  
Statistical Tests ◽  
Position Error ◽  
Positioning System ◽  
Navigation Systems ◽  
Mean Square ◽  
Positioning Systems ◽  
Position Errors ◽  
System Errors

Positioning systems are used to determine position coordinates in navigation (air, land and marine). The accuracy of an object’s position is described by the position error and a statistical analysis can determine its measures, which usually include: Root Mean Square (RMS), twice the Distance Root Mean Square (2DRMS), Circular Error Probable (CEP) and Spherical Probable Error (SEP). It is commonly assumed in navigation that position errors are random and that their distribution are consistent with the normal distribution. This assumption is based on the popularity of the Gauss distribution in science, the simplicity of calculating RMS values for 68% and 95% probabilities, as well as the intuitive perception of randomness in the statistics which this distribution reflects. It should be noted, however, that the necessary conditions for a random variable to be normally distributed include the independence of measurements and identical conditions of their realisation, which is not the case in the iterative method of determining successive positions, the filtration of coordinates or the dependence of the position error on meteorological conditions. In the preface to this publication, examples are provided which indicate that position errors in some navigation systems may not be consistent with the normal distribution. The subsequent section describes basic statistical tests for assessing the fit between the empirical and theoretical distributions (Anderson-Darling, chi-square and Kolmogorov-Smirnov). Next, statistical tests of the position error distributions of very long Differential Global Positioning System (DGPS) and European Geostationary Navigation Overlay Service (EGNOS) campaigns from different years (2006 and 2014) were performed with the number of measurements per session being 900’000 fixes. In addition, the paper discusses selected statistical distributions that fit the empirical measurement results better than the normal distribution. Research has shown that normal distribution is not the optimal statistical distribution to describe position errors of navigation systems. The distributions that describe navigation positioning system errors more accurately include: beta, gamma, logistic and lognormal distributions.

scholarly journals Particle Size Distribution of Various Soil Materials Measured by Laser Diffraction—The Problem of Reproducibility

Minerals ◽  
2021 ◽  
Vol 11 (5) ◽  
pp. 465
Author(s):  
Cezary Polakowski ◽  
Magdalena Ryżak ◽  
Agata Sochan ◽  
Michał Beczek ◽  
Rafał Mazur ◽  
...  
Keyword(s):  
Particle Size ◽  
Particle Size Distribution ◽  
Normal Distribution ◽  
Size Distribution ◽  
Precise Measurement ◽  
Soil Analysis ◽  
Statistical Tests ◽  
Diffraction Method ◽  
Laser Diffraction ◽  
Method Analysis

Particle size distribution is an important soil parameter—therefore precise measurement of this characteristic is essential. The application of the widely used laser diffraction method for soil analysis continues to be a subject of debate. The precision of this method, proven on homogeneous samples, has been implicitly extended to soil analyses, but this has not been sufficiently well confirmed in the literature thus far. The aim of this study is to supplement the information available on the precision of the method in terms of reproducibility of soil measurement and whether the reproducibility of soil measurement is characterized by a normal distribution. To estimate the reproducibility of the laser diffraction method, thirteen various soil samples were characterized, and results were analysed statistically. The coefficient of variation acquired was lowest (3.44%) for silt and highest for sand (23.28%). Five of the thirteen tested samples were characterized by a normal distribution. The fraction content of eight samples was not characterized by normal distribution, but the extent of this phenomenon varied between soils. Although the laser diffraction method is repeatable, the measurement of soil particle size distribution can have limited reproducibility. The main cause seems to be small amounts of sand particles. The error can be amplified by the construction of the dispersion unit. Non-parametric statistical tests should be used by default for soil laser diffraction method analysis.

scholarly journals Confronting Theories of Firm Growth in Light of Degrees-of-Freedom Analysis

2015 ◽  
Vol 22 (74) ◽  
pp. 385-404
Author(s):  
Sérgio Fernando Loureiro Rezende ◽  
Ricardo Salera ◽  
José Márcio de Castro
Keyword(s):  
Degrees Of Freedom ◽  
Firm Growth ◽  
Dynamic Capabilities ◽  
Statistical Tests ◽  
Explanatory Power ◽  
Stage Theory ◽  
Chi Square ◽  
Growth Optimum ◽  
Chi Square Test ◽  
Do So

This article aims to confront four theories of firm growth – Optimum Firm Size, Stage Theory of Growth, The Theory of the Growth of the Firm and Dynamic Capabilities – with empirical data derived from a backward-looking longitudinal qualitative case of the growth trajectory of a Brazilian capital goods firm. To do so, we employed Degree of Freedom-Analysis for data analysis. This technique aims to test the empirical strengths of competing theories using statistical tests, in particular Chi-square test. Our results suggest that none of the four theories fully explained the growth of the firm we chose as empirical case. Nevertheless, Dynamic Capabilities was regarded as providing a more satisfactory explanatory power.

Uncertainty and Inference for Verification Measures

2007 ◽  
Vol 22 (3) ◽  
pp. 637-650 ◽  
Author(s):  
Ian T. Jolliffe
Keyword(s):  
Hypothesis Testing ◽  
Confidence Intervals ◽  
Multiple Testing ◽  
Prediction Intervals ◽  
Hypothesis Tests ◽  
Statistical Inferences ◽  
The Difference ◽  
Main Ideas

Abstract When a forecast is assessed, a single value for a verification measure is often quoted. This is of limited use, as it needs to be complemented by some idea of the uncertainty associated with the value. If this uncertainty can be quantified, it is then possible to make statistical inferences based on the value observed. There are two main types of inference: confidence intervals can be constructed for an underlying “population” value of the measure, or hypotheses can be tested regarding the underlying value. This paper will review the main ideas of confidence intervals and hypothesis tests, together with the less well known “prediction intervals,” concentrating on aspects that are often poorly understood. Comparisons will be made between different methods of constructing confidence intervals—exact, asymptotic, bootstrap, and Bayesian—and the difference between prediction intervals and confidence intervals will be explained. For hypothesis testing, multiple testing will be briefly discussed, together with connections between hypothesis testing, prediction intervals, and confidence intervals.

scholarly journals Tingkat Bagi Hasil, Pertumbuhan Likuiditas, dan Produk Domestik Bruto Terhadap Simpanan Mudharabah

2017 ◽  
Vol 1 (1) ◽  
pp. 15-25
Author(s):  
Ismayana Marhamah
Keyword(s):  
Gross Domestic Product ◽  
Hypothesis Testing ◽  
Hypothesis Test ◽  
Profit Sharing ◽  
T Test ◽  
Domestic Product ◽  
Gdp Growth ◽  
Islamic Banks ◽  
Independent Variable ◽  
Test Result

This study aims to determine the effect of profit sharing growth, liquidity growth, gross domestic product (GDP) growth, of mudharabah saving growth in general islamic banks. The variables studied are the influence of profit sharing rate, liquidity growth, gross domestic product (GDP) growth as independent variable and mudharabah saving growth as dependent variable. The population in this study are sharia islamic banks registered in Bank Indonesia (BI) and the amount of gross domestic productquarter-year period 2012-2016.The result of hypothesis testing (t test) shows that the profit sharing growth and gross domestic product partially has significant effect to mudharabah saving growth. Then the test result of liquidity growth partially has no effect and not significant to mudharabah saving growth. The results of simultaneous hypothesis test (test F), show that all independent variabels in this study has significant effect to mudharabah saving growth.

Sign in / Sign up

Export Citation Format

Share Document