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Parametric and Non-Parametric Statistics for Program Performance Analysis and Comparison Julien Worms, Sid Touati
Parametric and Non-Parametric Statistics for Program Performance Analysis and Comparison Julien Worms, Sid Touati To cite this version: Julien Worms, Sid Touati. Parametric and Non-Parametric Statistics for Program Performance Anal- ysis and Comparison. [Research Report] RR-8875, INRIA Sophia Antipolis - I3S; Université Nice Sophia Antipolis; Université Versailles Saint Quentin en Yvelines; Laboratoire de mathématiques de Versailles. 2017, pp.70. hal-01286112v3 HAL Id: hal-01286112 https://hal.inria.fr/hal-01286112v3 Submitted on 29 Jun 2017 HAL is a multi-disciplinary open access L’archive ouverte pluridisciplinaire HAL, est archive for the deposit and dissemination of sci- destinée au dépôt et à la diffusion de documents entific research documents, whether they are pub- scientifiques de niveau recherche, publiés ou non, lished or not. The documents may come from émanant des établissements d’enseignement et de teaching and research institutions in France or recherche français ou étrangers, des laboratoires abroad, or from public or private research centers. publics ou privés. Public Domain Parametric and Non-Parametric Statistics for Program Performance Analysis and Comparison Julien WORMS, Sid TOUATI RESEARCH REPORT N° 8875 Mar 2016 Project-Teams "Probabilités et ISSN 0249-6399 ISRN INRIA/RR--8875--FR+ENG Statistique" et AOSTE Parametric and Non-Parametric Statistics for Program Performance Analysis and Comparison Julien Worms∗, Sid Touati† Project-Teams "Probabilités et Statistique" et AOSTE Research Report n° 8875 — Mar 2016 — 70 pages Abstract: This report is a continuation of our previous research effort on statistical program performance analysis and comparison [TWB10, TWB13], in presence of program performance variability. In the previous study, we gave a formal statistical methodology to analyse program speedups based on mean or median performance metrics: execution time, energy consumption, etc. -
Non Parametric Test: Chi Square Test of Contingencies
Weblinks http://www:stat.sc.edu/_west/applets/chisqdemo1.html http://2012books.lardbucket.org/books/beginning-statistics/s15-chi-square-tests-and-f- tests.html www.psypress.com/spss-made-simple Suggested Readings Siegel, S. & Castellan, N.J. (1988). Non Parametric Statistics for the Behavioral Sciences (2nd edn.). McGraw Hill Book Company: New York. Clark- Carter, D. (2010). Quantitative psychological research: a student’s handbook (3rd edn.). Psychology Press: New York. Myers, J.L. & Well, A.D. (1991). Research Design and Statistical analysis. New York: Harper Collins. Agresti, A. 91996). An introduction to categorical data analysis. New York: Wiley. PSYCHOLOGY PAPER No.2 : Quantitative Methods MODULE No. 15: Non parametric test: chi square test of contingencies Zimmerman, D. & Zumbo, B.D. (1993). The relative power of parametric and non- parametric statistics. In G. Karen & C. Lewis (eds.), A handbook for data analysis in behavioral sciences: Methodological issues (pp. 481- 517). Hillsdale, NJ: Lawrence Earlbaum Associates, Inc. Field, A. (2005). Discovering statistics using SPSS (2nd ed.). London: Sage. Biographic Sketch Description 1894 Karl Pearson(1857-1936) was the first person to use the term “standard deviation” in one of his lectures. contributed to statistical studies by discovering Chi square. Founded statistical laboratory in 1911 in England. http://www.swlearning.com R.A. Fisher (1890- 1962) Father of modern statistics was educated at Harrow and Cambridge where he excelled in mathematics. He later became interested in theory of errors and ultimately explored statistical problems like: designing of experiments, analysis of variance. He developed methods suitable for small samples and discovered precise distributions of many sample statistics. -
Pitfalls and Options in Hypothesis Testing for Comparing Differences in Means
Annals of Nuclear Cardiology Vol. 4 No. 1 83-87 REVIEW ARTICLE Statistics in Nuclear Cardiology: So, What’s the Difference? The t-Test: Pitfalls and Options in Hypothesis Testing for Comparing Differences in Means David N. Williams, PhD1), Kathryn A. Williams, MS2) and Michael Monuteaux, ScD3) Received: June 18, 2018/Revised manuscript received: July 19, 2018/Accepted: July 30, 2018 ○C The Japanese Society of Nuclear Cardiology 2018 Abstract Decisions related to differences of the measures of central tendency of population parameters are an important part of clinical research. Choice of the appropriate statistical test is critical to avoiding errors when making those decisions. All statistical tests require that one or more assumptions be met. The t-test is one of the most widely used tools but is not appropriate when assumptions such as normality are not met, especially when small samples, <40, are used. Non-parametric tests, such as the Wilcoxon rank sum and others, offer effective alternatives when there are questions about meeting assumptions. When normality is in question, the Wilcoxon non-parametric tests offer substantially higher levels of power and an reliable alternative to the t-test. Keywords: Assumptions, Difference of means, Mann-Whitney, Non-parametric, t-test, Violations, Wilcoxon Ann Nucl Cardiol 2018; 4(1): 83 -87 ome of the most important studies in clinical research and what degree those assumptions are violated should be an S decision-making are those related to differences in important step in analysis but one that is often left un-done (2). measures of central tendency of population parameters i.e. -
Case Study Applications of Statistics in Institutional Research
/-- ; / \ \ CASE STUDY APPLICATIONS OF STATISTICS IN INSTITUTIONAL RESEARCH By MARY ANN COUGHLIN and MARIAN PAGAN( Case Study Applications of Statistics in Institutional Research by Mary Ann Coughlin and Marian Pagano Number Ten Resources in Institutional Research A JOINTPUBLICA TION OF THE ASSOCIATION FOR INSTITUTIONAL RESEARCH AND THE NORTHEASTASSO CIATION FOR INSTITUTIONAL REASEARCH © 1997 Association for Institutional Research 114 Stone Building Florida State University Ta llahassee, Florida 32306-3038 All Rights Reserved No portion of this book may be reproduced by any process, stored in a retrieval system, or transmitted in any form, or by any means, without the express written permission of the publisher. Printed in the United States To order additional copies, contact: AIR 114 Stone Building Florida State University Tallahassee FL 32306-3038 Tel: 904/644-4470 Fax: 904/644-8824 E-Mail: [email protected] Home Page: www.fsu.edul-airlhome.htm ISBN 1-882393-06-6 Table of Contents Acknowledgments •••••••••••••••••.•••••••••.....••••••••••••••••.••. Introduction .•••••••••••..•.•••••...•••••••.....••••.•••...••••••••• 1 Chapter 1: Basic Concepts ..•••••••...••••••...••••••••..••••••....... 3 Characteristics of Variables and Levels of Measurement ...................3 Descriptive Statistics ...............................................8 Probability, Sampling Theory and the Normal Distribution ................ 16 Chapter 2: Comparing Group Means: Are There Real Differences Between Av erage Faculty Salaries Across Departments? •...••••••••.••.•••••• -
Inferential Statistics Katie Rommel-Esham Education 604 Probability
Inferential Statistics Katie Rommel-Esham Education 604 Probability • Probability is the scientific way of stating the degree of confidence we have in predicting something • Tossing coins and rolling dice are examples of probability experiments • The concepts and procedures of inferential statistics provide us with the language we need to address the probabilistic nature of the research we conduct in the field of education From Samples to Populations • Probability comes into play in educational research when we try to estimate a population mean from a sample mean • Samples are used to generate the data, and inferential statistics are used to generalize that information to the population, a process in which error is inherent • Different samples are likely to generate different means. How do we determine which is “correct?” The Role of the Normal Distribution • If you were to take samples repeatedly from the same population, it is likely that, when all the means are put together, their distribution will resemble the normal curve. • The resulting normal distribution will have its own mean and standard deviation. • This distribution is called the sampling distribution and the corresponding standard deviation is known as the standard error. Remember me? Sampling Distributions • As before, with the sampling distribution, approximately 68% of the means lie within 1 standard deviation of the distribution mean and 96% would lie within 2 standard deviations • We now know the probable range of means, although individual means might vary somewhat The Probability-Inferential Statistics Connection • Armed with this information, a researcher can be fairly certain that, 68% of the time, the population mean that is generated from any given sample will be within 1 standard deviation of the mean of the sampling distribution. -
Regression Assumptions in Clinical Psychology Research Practice—A Systematic Review of Common Misconceptions
Regression assumptions in clinical psychology research practice—a systematic review of common misconceptions Anja F. Ernst and Casper J. Albers Heymans Institute for Psychological Research, University of Groningen, Groningen, The Netherlands ABSTRACT Misconceptions about the assumptions behind the standard linear regression model are widespread and dangerous. These lead to using linear regression when inappropriate, and to employing alternative procedures with less statistical power when unnecessary. Our systematic literature review investigated employment and reporting of assumption checks in twelve clinical psychology journals. Findings indicate that normality of the variables themselves, rather than of the errors, was wrongfully held for a necessary assumption in 4% of papers that use regression. Furthermore, 92% of all papers using linear regression were unclear about their assumption checks, violating APA- recommendations. This paper appeals for a heightened awareness for and increased transparency in the reporting of statistical assumption checking. Subjects Psychiatry and Psychology, Statistics Keywords Linear regression, Statistical assumptions, Literature review, Misconceptions about normality INTRODUCTION One of the most frequently employed models to express the influence of several predictors Submitted 18 November 2016 on a continuous outcome variable is the linear regression model: Accepted 17 April 2017 Published 16 May 2017 Yi D β0 Cβ1X1i Cβ2X2i C···CβpXpi C"i: Corresponding author Casper J. Albers, [email protected] This equation predicts the value of a case Yi with values Xji on the independent variables Academic editor Xj (j D 1;:::;p). The standard regression model takes Xj to be measured without error Shane Mueller (cf. Montgomery, Peck & Vining, 2012, p. 71). The various βj slopes are each a measure of Additional Information and association between the respective independent variable Xj and the dependent variable Y. -
A Causation Coefficient and Taxonomy of Correlation/Causation Relationships
A causation coefficient and taxonomy of correlation/causation relationships Joshua Brulé∗ Abstract This paper introduces a causation coefficient which is defined in terms of probabilistic causal models. This coefficient is suggested as the natural causal analogue of the Pearson correlation coefficient and permits comparing causation and correlation to each other in a simple, yet rigorous manner. Together, these coefficients provide a natural way to classify the possible correlation/causation relationships that can occur in practice and examples of each relationship are provided. In addition, the typical relationship between correlation and causation is analyzed to provide insight into why correlation and causation are often conflated. Finally, example calculations of the causation coefficient are shown on a real data set. Introduction The maxim, “Correlation is not causation”, is an important warning to analysts, but provides very little information about what causation is and how it relates to correlation. This has prompted other attempts at summarizing the relationship. For example, Tufte [1] suggests either, “Observed covariation is necessary but not sufficient for causality”, which is demonstrably false arXiv:1708.05069v1 [stat.ME] 5 Aug 2017 or, “Correlation is not causation but it is a hint”, which is correct, but still underspecified. In what sense is correlation a ‘hint’ to causation? Correlation is well understood and precisely defined. Generally speaking, correlation is any statistical relationship involving dependence, i.e. the ran- dom variables are not independent. More specifically, correlation can refer ∗Department of Computer Science, University of Maryland, College Park. [email protected] 1 to a descriptive statistic that summarizes the nature of the dependence. -
A Monte Carlo Method for Comparing Generalized Estimating Equations to Conventional Statistical Techniques Tor Discounting Data
HHS Public Access Author manuscript Author ManuscriptAuthor Manuscript Author J Exp Anal Manuscript Author Behav. Author Manuscript Author manuscript; available in PMC 2019 March 20. Published in final edited form as: J Exp Anal Behav. 2019 March ; 111(2): 207–224. doi:10.1002/jeab.497. A Monte Carlo Method for Comparing Generalized Estimating Equations to Conventional Statistical Techniques tor Discounting Data Jonathan E. Friedel1, William B. DeHart2, Anne M. Foreman1, and Michael E. Andrew1 1National Institute for Occupational Safety and Health 2Virginia Tech Carillion Research Institute Abstract Discounting is the process by which outcomes lose value. Much of discounting research has focused on differences in the degree of discounting across various groups. This research has relied heavily on conventional null hypothesis significance testing that is familiar to psychology in general such as t-tests and ANOVAs. As discounting research questions have become more complex by simultaneously focusing on within-subject and between-group differences conventional statistical testing is often not appropriate for the obtained data. Generalized estimating equations (GEE) are one type of mixed-effects model that are designed to handle autocorrelated data, such as within-subject repeated-measures data, and are therefore more appropriate for discounting data. To determine if GEE provides similar results as conventional statistical tests, were compared the techniques across 2,000 simulated data sets. The data sets were created using a Monte Carlo method based of an existing data set. Across the simulated data sets, the GEE and the conventional statistical tests generally provided similar patterns of results. As the GEE and more conventional statistical tests provide the same pattern of result, we suggest researchers use the GEE because it was designed to handle data that has the structure that is typical of discounting data. -
Nonparametric Permutation Testing
NONPARAMETRIC PERMUTATION TESTING CHAPTER 33 TONY YE WHAT IS PERMUTATION TESTING? Framework for assessing the statistical significance of EEG results. Advantages: • Does not rely on distribution assumptions • Corrections for multiple comparisons are easy to incorporate • Highly appropriate for correcting multiple comparisons in EEG data WHAT IS PARAMETRIC STATISTICAL TESTING? The test statistic is compared against a theoretical distribution of test statistics expected under the H0. • t-value • χ2-value • Correlation coefficient The probability (p-value) of obtaining a statistic under the H0 is at least as large as the observed statistic. [INSERT 33.1A] NONPARAMETRIC PERMUTATION TESTING No assumptions are made about the theoretical underlying distribution of test statistics under the H0. • Instead, the distribution is created from the data that you have! How is this done? • Shuffling condition labels over trials • Within-subject analyses • Shuffling condition labels over subjects • Group-level analyses • Recomputing the test statistic NULL-HYPOTHESIS DISTRIBUTION Evaluating your hypothesis using a t-test of alpha power between two conditions. Two types of tests: • Discrete tests • Compare conditions • Continuous tests • Correlating two continuous variables DISCRETE TESTS Compare EEG activity between Condition A & B • H0 = No difference between conditions • Random relabeling of conditions • Test Statistic (TS) = as large as the TS BEFORE the random relabeling. Steps 1. Randomly swap condition labels from many trials 2. Compute t-test across conditions 3. If TS ≠ 0, there is sampling error or outliers CONTINOUS TESTS The idea: • Testing statistical significance of a correlation coefficient What’s the difference between this and discrete tests? • TS is created by swapping data points instead of labels SIMILARITIES The data are not altered • The “mapping” of data are shuffled around. -
The Quest for Statistical Significance: Ignorance, Bias and Malpractice of Research Practitioners Joshua Abah
The Quest for Statistical Significance: Ignorance, Bias and Malpractice of Research Practitioners Joshua Abah To cite this version: Joshua Abah. The Quest for Statistical Significance: Ignorance, Bias and Malpractice of Research Practitioners. International Journal of Research & Review (www.ijrrjournal.com), 2018, 5 (3), pp.112- 129. hal-01758493 HAL Id: hal-01758493 https://hal.archives-ouvertes.fr/hal-01758493 Submitted on 4 Apr 2018 HAL is a multi-disciplinary open access L’archive ouverte pluridisciplinaire HAL, est archive for the deposit and dissemination of sci- destinée au dépôt et à la diffusion de documents entific research documents, whether they are pub- scientifiques de niveau recherche, publiés ou non, lished or not. The documents may come from émanant des établissements d’enseignement et de teaching and research institutions in France or recherche français ou étrangers, des laboratoires abroad, or from public or private research centers. publics ou privés. Distributed under a Creative Commons Attribution - NonCommercial - ShareAlike| 4.0 International License International Journal of Research and Review www.gkpublication.in E-ISSN: 2349-9788; P-ISSN: 2454-2237 Review Article The Quest for Statistical Significance: Ignorance, Bias and Malpractice of Research Practitioners Joshua Abah Abah Department of Science Education University of Agriculture, Makurdi, Nigeria ABSTRACT There is a growing body of evidence on the prevalence of ignorance, biases and malpractice among researchers which questions the authenticity, validity and integrity of the knowledge been propagated in professional circles. The push for academic relevance and career advancement have driven some research practitioners into committing gross misconduct in the form of innocent ignorance, sloppiness, malicious intent and outright fraud. -
Parametric and Nonparametric Bayesian Models for Ecological Inference in 2 × 2 Tables∗
Parametric and Nonparametric Bayesian Models for Ecological Inference in 2 × 2 Tables∗ Kosuke Imai† Department of Politics, Princeton University Ying Lu‡ Office of Population Research, Princeton University November 18, 2004 Abstract The ecological inference problem arises when making inferences about individual behavior from aggregate data. Such a situation is frequently encountered in the social sciences and epi- demiology. In this article, we propose a Bayesian approach based on data augmentation. We formulate ecological inference in 2×2 tables as a missing data problem where only the weighted average of two unknown variables is observed. This framework directly incorporates the deter- ministic bounds, which contain all information available from the data, and allow researchers to incorporate the individual-level data whenever available. Within this general framework, we first develop a parametric model. We show that through the use of an EM algorithm, the model can formally quantify the effect of missing information on parameter estimation. This is an important diagnostic for evaluating the degree of aggregation effects. Next, we introduce a nonparametric model using a Dirichlet process prior to relax the distributional assumption of the parametric model. Through simulations and an empirical application, we evaluate the rela- tive performance of our models in various situations. We demonstrate that in typical ecological inference problems, the fraction of missing information often exceeds 50 percent. We also find that the nonparametric model generally outperforms the parametric model, although the latter gives reasonable in-sample predictions when the bounds are informative. C-code, along with an R interface, is publicly available for implementing our Markov chain Monte Carlo algorithms to fit the proposed models. -
Paper Presented at the Annual Meeting of the American Educational Research Association, New York, New York, February 1971
DOCUMENT RESUME ED 048 371 TM 000 463 AUTHOR Porter, Andrew C.; 'McSweeney, Maryellen TITLE Comparison of Pank Analysis of Covariance and Nonparametric Randomized Blocks Analysis. PUB DATE Jan 71 NOTE 35p.; Paper presented at the Annual Meeting of the American Educational Research Association, New York, New York, February 1971 EDRS PRIC. EDRS Price M7-$0.65 EC-$3.29 DESCRIPTORS *Analysis cf Covariance, *Analysis of Variance, *Goodness of Fit, Hypothesis Testing, *Nonparametric Statistics, Predictor Variables, *Research Design, Sampling, Statistical Analysis ABSTRACT The relative power of three possible experimental designs under the condition that data is to be analyzed by nonparametric techniques; the comparison of the power of each nonparametric technique to its parametric analogue; and the comparison of relative powers using nonparametric and parametric techniques are discussed. The three nonparametric techniques concerned are the Kruskal-Wallis test on data where experimental units have been randomly assigned to levels of the independent variable, Friedman's rank analysis of variance (ANOVA) on data in a randomized blocks design, and a nonparametric analysis of covariance (ANCOVA). The parametric counterparts are respectively; one way analysis of variance (ANOVA) ,two-way ANOVt, and parametric ANCOVA. Sine: the nonparametric tests are based on large sample approximations, the goodness of fit for small samples is also of concern. Statements of asymptotic relative efficiency and imprecision are reviewed as suggestive of small sample powers of the designs and statistics investigated. Results of a Monte Carlo investigation are provided to further illustrate small sample power and to provide data on goodness of fit.(Author/CK) U.S. DEPARTMENT OF HEALTH.