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Statistical Inferences Hypothesis Tests
STATISTICAL INFERENCES HYPOTHESIS TESTS Maªgorzata Murat BASIC IDEAS Suppose we have collected a representative sample that gives some information concerning a mean or other statistical quantity. There are two main questions for which statistical inference may provide answers. 1. Are the sample quantity and a corresponding population quantity close enough together so that it is reasonable to say that the sample might have come from the population? Or are they far enough apart so that they likely represent dierent populations? 2. For what interval of values can we have a specic level of condence that the interval contains the true value of the parameter of interest? STATISTICAL INFERENCES FOR THE MEAN We can divide statistical inferences for the mean into two main categories. In one category, we already know the variance or standard deviation of the population, usually from previous measurements, and the normal distribution can be used for calculations. In the other category, we nd an estimate of the variance or standard deviation of the population from the sample itself. The normal distribution is assumed to apply to the underlying population, but another distribution related to it will usually be required for calculations. TEST OF HYPOTHESIS We are testing the hypothesis that a sample is similar enough to a particular population so that it might have come from that population. Hence we make the null hypothesis that the sample came from a population having the stated value of the population characteristic (the mean or the variation). Then we do calculations to see how reasonable such a hypothesis is. We have to keep in mind the alternative if the null hypothesis is not true, as the alternative will aect the calculations. -
A Field Experiment with Job Seekers in Germany Search:Learning Job About IZA DP No
IZA DP No. 9040 Learning about Job Search: A Field Experiment with Job Seekers in Germany Steffen Altmann Armin Falk Simon Jäger Florian Zimmermann May 2015 DISCUSSION PAPER SERIES Forschungsinstitut zur Zukunft der Arbeit Institute for the Study of Labor Learning about Job Search: A Field Experiment with Job Seekers in Germany Steffen Altmann University of Copenhagen and IZA Armin Falk University of Bonn, CEPR, CESifo, DIW, IZA and MPI Simon Jäger Harvard University and IZA Florian Zimmermann University of Zurich, CESifo and IZA Discussion Paper No. 9040 May 2015 IZA P.O. Box 7240 53072 Bonn Germany Phone: +49-228-3894-0 Fax: +49-228-3894-180 E-mail: [email protected] Any opinions expressed here are those of the author(s) and not those of IZA. Research published in this series may include views on policy, but the institute itself takes no institutional policy positions. The IZA research network is committed to the IZA Guiding Principles of Research Integrity. The Institute for the Study of Labor (IZA) in Bonn is a local and virtual international research center and a place of communication between science, politics and business. IZA is an independent nonprofit organization supported by Deutsche Post Foundation. The center is associated with the University of Bonn and offers a stimulating research environment through its international network, workshops and conferences, data service, project support, research visits and doctoral program. IZA engages in (i) original and internationally competitive research in all fields of labor economics, (ii) development of policy concepts, and (iii) dissemination of research results and concepts to the interested public. -
The Focused Information Criterion in Logistic Regression to Predict Repair of Dental Restorations
THE FOCUSED INFORMATION CRITERION IN LOGISTIC REGRESSION TO PREDICT REPAIR OF DENTAL RESTORATIONS Cecilia CANDOLO1 ABSTRACT: Statistical data analysis typically has several stages: exploration of the data set; deciding on a class or classes of models to be considered; selecting the best of them according to some criterion and making inferences based on the selected model. The cycle is usually iterative and will involve subject-matter considerations as well as statistical insights. The conclusion reached after such a process depends on the model(s) selected, but the consequent uncertainty is not usually incorporated into the inference. This may lead to underestimation of the uncertainty about quantities of interest and overoptimistic and biased inferences. This framework has been the aim of research under the terminology of model uncertainty and model averanging in both, frequentist and Bayesian approaches. The former usually uses the Akaike´s information criterion (AIC), the Bayesian information criterion (BIC) and the bootstrap method. The last weigths the models using the posterior model probabilities. This work consider model selection uncertainty in logistic regression under frequentist and Bayesian approaches, incorporating the use of the focused information criterion (FIC) (CLAESKENS and HJORT, 2003) to predict repair of dental restorations. The FIC takes the view that a best model should depend on the parameter under focus, such as the mean, or the variance, or the particular covariate values. In this study, the repair or not of dental restorations in a period of eighteen months depends on several covariates measured in teenagers. The data were kindly provided by Juliana Feltrin de Souza, a doctorate student at the Faculty of Dentistry of Araraquara - UNESP. -
Field Experiments in Development Economics1 Esther Duflo Massachusetts Institute of Technology
Field Experiments in Development Economics1 Esther Duflo Massachusetts Institute of Technology (Department of Economics and Abdul Latif Jameel Poverty Action Lab) BREAD, CEPR, NBER January 2006 Prepared for the World Congress of the Econometric Society Abstract There is a long tradition in development economics of collecting original data to test specific hypotheses. Over the last 10 years, this tradition has merged with an expertise in setting up randomized field experiments, resulting in an increasingly large number of studies where an original experiment has been set up to test economic theories and hypotheses. This paper extracts some substantive and methodological lessons from such studies in three domains: incentives, social learning, and time-inconsistent preferences. The paper argues that we need both to continue testing existing theories and to start thinking of how the theories may be adapted to make sense of the field experiment results, many of which are starting to challenge them. This new framework could then guide a new round of experiments. 1 I would like to thank Richard Blundell, Joshua Angrist, Orazio Attanasio, Abhijit Banerjee, Tim Besley, Michael Kremer, Sendhil Mullainathan and Rohini Pande for comments on this paper and/or having been instrumental in shaping my views on these issues. I thank Neel Mukherjee and Kudzai Takavarasha for carefully reading and editing a previous draft. 1 There is a long tradition in development economics of collecting original data in order to test a specific economic hypothesis or to study a particular setting or institution. This is perhaps due to a conjunction of the lack of readily available high-quality, large-scale data sets commonly available in industrialized countries and the low cost of data collection in developing countries, though development economists also like to think that it has something to do with the mindset of many of them. -
On Boundaries Between Field Experiment, Action Research and Design Research
Pertti Järvinen On boundaries between field experiment, action research and design research UNIVERSITY OF TAMPERE SCHOOL OF INFORMATION SCIENCES REPORTS IN INFORMATION SCIENCES 14 TAMPERE 2012 UNIVERSITY OF TAMPERE SCHOOL OF INFORMATION SCIENCES REPORTS IN INFORMATION SCIENCES 14 JUNE 2012 Pertti Järvinen On boundaries between field experiment, action research and design research SCHOOL OF INFORMATION SCIENCES FIN‐33014 UNIVERSITY OF TAMPERE ISBN 978‐951‐44‐8883‐2 ISSN‐L 1799‐8158 ISSN 1799‐8158 On boundaries between field experiment, action research and design research Pertti Järvinen School of Information Sciences University of Tampere Abstract The practice-science gap is often emphasized during the last years. It has also had such a form as competition between relevance and rigor, although both must be taken care. The three research methods (field experiment, action research and design research) are sometimes recommended to be used interchangeable. But we shall show they are quite different. We try to analyze and describe their boundaries and division of labor between practitioners and researchers. We shall also correct some long-lasting misconceptions and propose some further research topic. Introduction Mathiassen and Nielsen (2008) studied the articles published in the Scandinavian Journal of Information Systems during 20 years and found that empirical articles have a great share of the all the published articles. Majority of the authors are from the Scandinavian countries. This seems to show that practice is much appreciated among the Scandinavian researchers and practical emphasis is characteristic in the Scandinavian research culture. We shall in this paper consider three empirical research methods (field experiment, action research and design research). -
Field Experiments: a Bridge Between Lab and Naturally-Occurring Data
NBER WORKING PAPER SERIES FIELD EXPERIMENTS: A BRIDGE BETWEEN LAB AND NATURALLY-OCCURRING DATA John A. List Working Paper 12992 http://www.nber.org/papers/w12992 NATIONAL BUREAU OF ECONOMIC RESEARCH 1050 Massachusetts Avenue Cambridge, MA 02138 March 2007 *This study is based on plenary talks at the 2005 International Meetings of the Economic Science Association, the 2006 Canadian Economic Association, and the 2006 Australian Econometric Association meetings. The paper is written as an introduction to the BE-JEAP special issue on Field Experiments that I have edited; thus my focus is on the areas to which these studies contribute. Some of the arguments parallel those contained in my previous work, most notably the working paper version of Levitt and List (2006) and Harrison and List (2004). Don Fullerton, Dean Karlan, Charles Manski, and an anonymous reporter provided remarks that improved the study. The views expressed herein are those of the author(s) and do not necessarily reflect the views of the National Bureau of Economic Research. © 2007 by John A. List. All rights reserved. Short sections of text, not to exceed two paragraphs, may be quoted without explicit permission provided that full credit, including © notice, is given to the source. Field Experiments: A Bridge Between Lab and Naturally-Occurring Data John A. List NBER Working Paper No. 12992 March 2007 JEL No. C9,C90,C91,C92,C93,D01,H41,Q5,Q51 ABSTRACT Laboratory experiments have been used extensively in economics in the past several decades to lend both positive and normative insights into a myriad of important economic issues. -
What Is Statistic?
What is Statistic? OPRE 6301 In today’s world. ...we are constantly being bombarded with statistics and statistical information. For example: Customer Surveys Medical News Demographics Political Polls Economic Predictions Marketing Information Sales Forecasts Stock Market Projections Consumer Price Index Sports Statistics How can we make sense out of all this data? How do we differentiate valid from flawed claims? 1 What is Statistics?! “Statistics is a way to get information from data.” Statistics Data Information Data: Facts, especially Information: Knowledge numerical facts, collected communicated concerning together for reference or some particular fact. information. Statistics is a tool for creating an understanding from a set of numbers. Humorous Definitions: The Science of drawing a precise line between an unwar- ranted assumption and a forgone conclusion. The Science of stating precisely what you don’t know. 2 An Example: Stats Anxiety. A business school student is anxious about their statistics course, since they’ve heard the course is difficult. The professor provides last term’s final exam marks to the student. What can be discerned from this list of numbers? Statistics Data Information List of last term’s marks. New information about the statistics class. 95 89 70 E.g. Class average, 65 Proportion of class receiving A’s 78 Most frequent mark, 57 Marks distribution, etc. : 3 Key Statistical Concepts. Population — a population is the group of all items of interest to a statistics practitioner. — frequently very large; sometimes infinite. E.g. All 5 million Florida voters (per Example 12.5). Sample — A sample is a set of data drawn from the population. -
Structured Statistical Models of Inductive Reasoning
CORRECTED FEBRUARY 25, 2009; SEE LAST PAGE Psychological Review © 2009 American Psychological Association 2009, Vol. 116, No. 1, 20–58 0033-295X/09/$12.00 DOI: 10.1037/a0014282 Structured Statistical Models of Inductive Reasoning Charles Kemp Joshua B. Tenenbaum Carnegie Mellon University Massachusetts Institute of Technology Everyday inductive inferences are often guided by rich background knowledge. Formal models of induction should aim to incorporate this knowledge and should explain how different kinds of knowledge lead to the distinctive patterns of reasoning found in different inductive contexts. This article presents a Bayesian framework that attempts to meet both goals and describe 4 applications of the framework: a taxonomic model, a spatial model, a threshold model, and a causal model. Each model makes probabi- listic inferences about the extensions of novel properties, but the priors for the 4 models are defined over different kinds of structures that capture different relationships between the categories in a domain. The framework therefore shows how statistical inference can operate over structured background knowledge, and the authors argue that this interaction between structure and statistics is critical for explaining the power and flexibility of human reasoning. Keywords: inductive reasoning, property induction, knowledge representation, Bayesian inference Humans are adept at making inferences that take them beyond This article describes a formal approach to inductive inference the limits of their direct experience. -
Statistical Inference: Paradigms and Controversies in Historic Perspective
Jostein Lillestøl, NHH 2014 Statistical inference: Paradigms and controversies in historic perspective 1. Five paradigms We will cover the following five lines of thought: 1. Early Bayesian inference and its revival Inverse probability – Non-informative priors – “Objective” Bayes (1763), Laplace (1774), Jeffreys (1931), Bernardo (1975) 2. Fisherian inference Evidence oriented – Likelihood – Fisher information - Necessity Fisher (1921 and later) 3. Neyman- Pearson inference Action oriented – Frequentist/Sample space – Objective Neyman (1933, 1937), Pearson (1933), Wald (1939), Lehmann (1950 and later) 4. Neo - Bayesian inference Coherent decisions - Subjective/personal De Finetti (1937), Savage (1951), Lindley (1953) 5. Likelihood inference Evidence based – likelihood profiles – likelihood ratios Barnard (1949), Birnbaum (1962), Edwards (1972) Classical inference as it has been practiced since the 1950’s is really none of these in its pure form. It is more like a pragmatic mix of 2 and 3, in particular with respect to testing of significance, pretending to be both action and evidence oriented, which is hard to fulfill in a consistent manner. To keep our minds on track we do not single out this as a separate paradigm, but will discuss this at the end. A main concern through the history of statistical inference has been to establish a sound scientific framework for the analysis of sampled data. Concepts were initially often vague and disputed, but even after their clarification, various schools of thought have at times been in strong opposition to each other. When we try to describe the approaches here, we will use the notions of today. All five paradigms of statistical inference are based on modeling the observed data x given some parameter or “state of the world” , which essentially corresponds to stating the conditional distribution f(x|(or making some assumptions about it). -
Understanding Statistical Hypothesis Testing: the Logic of Statistical Inference
Review Understanding Statistical Hypothesis Testing: The Logic of Statistical Inference Frank Emmert-Streib 1,2,* and Matthias Dehmer 3,4,5 1 Predictive Society and Data Analytics Lab, Faculty of Information Technology and Communication Sciences, Tampere University, 33100 Tampere, Finland 2 Institute of Biosciences and Medical Technology, Tampere University, 33520 Tampere, Finland 3 Institute for Intelligent Production, Faculty for Management, University of Applied Sciences Upper Austria, Steyr Campus, 4040 Steyr, Austria 4 Department of Mechatronics and Biomedical Computer Science, University for Health Sciences, Medical Informatics and Technology (UMIT), 6060 Hall, Tyrol, Austria 5 College of Computer and Control Engineering, Nankai University, Tianjin 300000, China * Correspondence: [email protected]; Tel.: +358-50-301-5353 Received: 27 July 2019; Accepted: 9 August 2019; Published: 12 August 2019 Abstract: Statistical hypothesis testing is among the most misunderstood quantitative analysis methods from data science. Despite its seeming simplicity, it has complex interdependencies between its procedural components. In this paper, we discuss the underlying logic behind statistical hypothesis testing, the formal meaning of its components and their connections. Our presentation is applicable to all statistical hypothesis tests as generic backbone and, hence, useful across all application domains in data science and artificial intelligence. Keywords: hypothesis testing; machine learning; statistics; data science; statistical inference 1. Introduction We are living in an era that is characterized by the availability of big data. In order to emphasize the importance of this, data have been called the ‘oil of the 21st Century’ [1]. However, for dealing with the challenges posed by such data, advanced analysis methods are needed. -
Introduction to Statistical Methods Lecture 1: Basic Concepts & Descriptive Statistics
Introduction to Statistical Methods Lecture 1: Basic Concepts & Descriptive Statistics Theophanis Tsandilas [email protected] !1 Course information Web site: https://www.lri.fr/~fanis/courses/Stats2019 My email: [email protected] Slack workspace: stats-2019.slack.com !2 Course calendar !3 Lecture overview Part I 1. Basic concepts: data, populations & samples 2. Why learning statistics? 3. Course overview & teaching approach Part II 4. Types of data 5. Basic descriptive statistics Part III 6. Introduction to R !4 Part I. Basic concepts !5 Data vs. numbers Numbers are abstract tokens or symbols used for counting or measuring1 Data can be numbers but represent « real world » entities 1Several definitions in these slides are borrowed from Baguley’s book on Serious Stats Example Take a look at this set of numbers: 8 10 8 12 14 13 12 13 Context is important in understanding what they represent ! The age in years of 8 children ! The grades (out of 20) of 8 students ! The number of errors made by 8 participants in an experiment from a series of 100 experimental trials ! A memorization score of the same individual over repeated tests !7 Sampling The context depends on the process that generated the data ! collecting a subset (sample) of observations from a larger set (population) of observations of interest The idea of taking a sample from a population is central to understanding statistics and the heart of most statistical procedures. !8 Statistics A sample, being a subset of the whole population, won’t necessarily resemble it. Thus, the information the sample provides about the population is uncertain. -
Power(Ful) Guidelines for Experimental Economists
Power(ful) Guidelines for Experimental Economists Kathryn N. Vasilaky and J. Michelle Brock Abstract Statistical power is an important detail to consider in the design phase of any experi- ment. This note serves as a reference for experimental economists on power calculations. We synthesize many of the questions and issues frequently brought up regarding power calculations and the literature that surrounds that. We provide practical coded exam- ples and tools available for calculating power, and suggest when and how to report power calculations in published studies. Keywords: statistical power, experiments, design, significance. JEL Classification: C9. Contact details: J. Michelle Brock, Principal Economist, One Exchange Square, London, EC2A 2JN, UK Phone: +44 20 7338 7193; email: [email protected]. Kathryn N. Vasilaky is an Assistant Professor at California Polytechnic University and Research Affiliate at the Columbia University International Research Institute for Climate and Society. J. Michelle Brock is a Principal Economist at the EBRD and a Research Affiliate at the Centre for Economic Policy Research (CEPR). Thanks to contributions from the ESA discussion forum. The working paper series has been produced to stimulate debate on the economic transition and develop- ment. Views presented are those of the authors and not necessarily of the EBRD. Working Paper No. 239 Prepared in December 2019 Power(ful) Guidelines for Experimental Economists ∗ Kathryn N Vasilaky y J Michelle Brock z December 19, 2019 Abstract Statistical power is an important detail to consider in the design phase of any experiment. This note serves as a reference on power calculations for experimental economists. We syn- thesize many of the questions and issues frequently brought up regarding power calculations and the literature that surrounds that.