Statistical Inference Bibliography 1920-Present . 1. Misc. 2 on Bias and Randomness. 2. Misc. 3 Lopsided Reasoning. 3. Pearson
Total Page：16
File Type：pdf, Size：1020Kb
Load more
Recommended publications
-
Sequential Analysis Tests and Confidence Intervals
D. Siegmund Sequential Analysis Tests and Confidence Intervals Series: Springer Series in Statistics The modern theory of Sequential Analysis came into existence simultaneously in the United States and Great Britain in response to demands for more efficient sampling inspection procedures during World War II. The develop ments were admirably summarized by their principal architect, A. Wald, in his book Sequential Analysis (1947). In spite of the extraordinary accomplishments of this period, there remained some dissatisfaction with the sequential probability ratio test and Wald's analysis of it. (i) The open-ended continuation region with the concomitant possibility of taking an arbitrarily large number of observations seems intol erable in practice. (ii) Wald's elegant approximations based on "neglecting the excess" of the log likelihood ratio over the stopping boundaries are not especially accurate and do not allow one to study the effect oftaking observa tions in groups rather than one at a time. (iii) The beautiful optimality property of the sequential probability ratio test applies only to the artificial problem of 1985, XI, 274 p. testing a simple hypothesis against a simple alternative. In response to these issues and to new motivation from the direction of controlled clinical trials numerous modifications of the sequential probability ratio test were proposed and their properties studied-often Printed book by simulation or lengthy numerical computation. (A notable exception is Anderson, 1960; see III.7.) In the past decade it has become possible to give a more complete theoretical Hardcover analysis of many of the proposals and hence to understand them better. ▶ 119,99 € | £109.99 | $149.99 ▶ *128,39 € (D) | 131,99 € (A) | CHF 141.50 eBook Available from your bookstore or ▶ springer.com/shop MyCopy Printed eBook for just ▶ € | $ 24.99 ▶ springer.com/mycopy Order online at springer.com ▶ or for the Americas call (toll free) 1-800-SPRINGER ▶ or email us at: [email protected]. -
Trial Sequential Analysis: Novel Approach for Meta-Analysis
Anesth Pain Med 2021;16:138-150 https://doi.org/10.17085/apm.21038 Review pISSN 1975-5171 • eISSN 2383-7977 Trial sequential analysis: novel approach for meta-analysis Hyun Kang Received April 19, 2021 Department of Anesthesiology and Pain Medicine, Chung-Ang University College of Accepted April 25, 2021 Medicine, Seoul, Korea Systematic reviews and meta-analyses rank the highest in the evidence hierarchy. However, they still have the risk of spurious results because they include too few studies and partici- pants. The use of trial sequential analysis (TSA) has increased recently, providing more infor- mation on the precision and uncertainty of meta-analysis results. This makes it a powerful tool for clinicians to assess the conclusiveness of meta-analysis. TSA provides monitoring boundaries or futility boundaries, helping clinicians prevent unnecessary trials. The use and Corresponding author Hyun Kang, M.D., Ph.D. interpretation of TSA should be based on an understanding of the principles and assump- Department of Anesthesiology and tions behind TSA, which may provide more accurate, precise, and unbiased information to Pain Medicine, Chung-Ang University clinicians, patients, and policymakers. In this article, the history, background, principles, and College of Medicine, 84 Heukseok-ro, assumptions behind TSA are described, which would lead to its better understanding, imple- Dongjak-gu, Seoul 06974, Korea mentation, and interpretation. Tel: 82-2-6299-2586 Fax: 82-2-6299-2585 E-mail: [email protected] Keywords: Interim analysis; Meta-analysis; Statistics; Trial sequential analysis. INTRODUCTION termined number of patients was reached [2]. A systematic review is a research method that attempts Sequential analysis is a statistical method in which the fi- to collect all empirical evidence according to predefined nal number of patients analyzed is not predetermined, but inclusion and exclusion criteria to answer specific and fo- sampling or enrollment of patients is decided by a prede- cused questions [3]. -
Detecting Reinforcement Patterns in the Stream of Naturalistic Observations of Social Interactions
Portland State University PDXScholar Dissertations and Theses Dissertations and Theses 7-14-2020 Detecting Reinforcement Patterns in the Stream of Naturalistic Observations of Social Interactions James Lamar DeLaney 3rd Portland State University Follow this and additional works at: https://pdxscholar.library.pdx.edu/open_access_etds Part of the Developmental Psychology Commons Let us know how access to this document benefits ou.y Recommended Citation DeLaney 3rd, James Lamar, "Detecting Reinforcement Patterns in the Stream of Naturalistic Observations of Social Interactions" (2020). Dissertations and Theses. Paper 5553. https://doi.org/10.15760/etd.7427 This Thesis is brought to you for free and open access. It has been accepted for inclusion in Dissertations and Theses by an authorized administrator of PDXScholar. Please contact us if we can make this document more accessible: [email protected]. Detecting Reinforcement Patterns in the Stream of Naturalistic Observations of Social Interactions by James Lamar DeLaney 3rd A thesis submitted in partial fulfillment of the requirements for the degree of Master of Science in Psychology Thesis Committee: Thomas Kindermann, Chair Jason Newsom Ellen A. Skinner Portland State University i Abstract How do consequences affect future behaviors in real-world social interactions? The term positive reinforcer refers to those consequences that are associated with an increase in probability of an antecedent behavior (Skinner, 1938). To explore whether reinforcement occurs under naturally occuring conditions, many studies use sequential analysis methods to detect contingency patterns (see Quera & Bakeman, 1998). This study argues that these methods do not look at behavior change following putative reinforcers, and thus, are not sufficient for declaring reinforcement effects arising in naturally occuring interactions, according to the Skinner’s (1938) operational definition of reinforcers. -
Rothamsted in the Making of Sir Ronald Fisher Scd FRS
Rothamsted in the Making of Sir Ronald Fisher ScD FRS John Aldrich University of Southampton RSS September 2019 1 Finish 1962 “the most famous statistician and mathematical biologist in the world” dies Start 1919 29 year-old Cambridge BA in maths with no prospects takes temporary job at Rothamsted Experimental Station In between 1919-33 at Rothamsted he makes a career for himself by creating a career 2 Rothamsted helped make Fisher by establishing and elevating the office of agricultural statistician—a position in which Fisher was unsurpassed by letting him do other things—including mathematical statistics, genetics and eugenics 3 Before Fisher … (9 slides) The problems were already there viz. o the relationship between harvest and weather o design of experimental trials and the analysis of their results Leading figures in agricultural science believed the problems could be treated statistically 4 Established in 1843 by Lawes and Gilbert to investigate the effective- ness of fertilisers Sir John Bennet Lawes Sir Joseph Henry Gilbert (1814-1900) land-owner, fertiliser (1817-1901) professional magnate and amateur scientist scientist (chemist) In 1902 tired Rothamsted gets make-over when Daniel Hall becomes Director— public money feeds growth 5 Crops and weather and experimental trials Crops & the weather o examined by agriculturalists—e.g. Lawes & Gilbert 1880 o subsequently treated more by meteorologists Experimental trials a hotter topic o treated in Journal of Agricultural Science o by leading figures Wood of Cambridge and Hall -
Statistical Significance Testing in Information Retrieval:An Empirical
Statistical Significance Testing in Information Retrieval: An Empirical Analysis of Type I, Type II and Type III Errors Julián Urbano Harlley Lima Alan Hanjalic Delft University of Technology Delft University of Technology Delft University of Technology The Netherlands The Netherlands The Netherlands [email protected] [email protected] [email protected] ABSTRACT 1 INTRODUCTION Statistical significance testing is widely accepted as a means to In the traditional test collection based evaluation of Information assess how well a difference in effectiveness reflects an actual differ- Retrieval (IR) systems, statistical significance tests are the most ence between systems, as opposed to random noise because of the popular tool to assess how much noise there is in a set of evaluation selection of topics. According to recent surveys on SIGIR, CIKM, results. Random noise in our experiments comes from sampling ECIR and TOIS papers, the t-test is the most popular choice among various sources like document sets [18, 24, 30] or assessors [1, 2, 41], IR researchers. However, previous work has suggested computer but mainly because of topics [6, 28, 36, 38, 43]. Given two systems intensive tests like the bootstrap or the permutation test, based evaluated on the same collection, the question that naturally arises mainly on theoretical arguments. On empirical grounds, others is “how well does the observed difference reflect the real difference have suggested non-parametric alternatives such as the Wilcoxon between the systems and not just noise due to sampling of topics”? test. Indeed, the question of which tests we should use has accom- Our field can only advance if the published retrieval methods truly panied IR and related fields for decades now. -
Basic Statistics
Statistics Kristof Reid Assistant Professor Medical University of South Carolina Core Curriculum V5 Financial Disclosures • None Core Curriculum V5 Further Disclosures • I am not a statistician • I do like making clinical decisions based on appropriately interpreted data Core Curriculum V5 Learning Objectives • Understand why knowing statistics is important • Understand the basic principles and statistical test • Understand common statistical errors in the medical literature Core Curriculum V5 Why should I care? Indications for statistics Core Curriculum V5 47% unable to determine study design 31% did not understand p values 38% did not understand sensitivity and specificity 83% could not use odds ratios Araoye et al, JBJS 2020;102(5):e19 Core Curriculum V5 50% (or more!) of clinical research publications have at least one statistical error Thiese et al, Journal of thoracic disease, 2016-08, Vol.8 (8), p.E726-E730 Core Curriculum V5 17% of conclusions not justified by results 39% of studies used the wrong analysis Parsons et al, J Bone Joint Surg Br. 2011;93-B(9):1154-1159. Core Curriculum V5 Are these two columns different? Column A Column B You have been asked by your insurance carrier 19 10 12 11 to prove that your total hip patient outcomes 10 9 20 19 are not statistically different than your competitor 10 17 14 10 next door. 21 19 24 13 Column A is the patient reported score for you 12 18 and column B for your competitor 17 8 12 17 17 10 9 9 How would you prove you are 24 10 21 9 18 18 different or better? 13 4 18 8 12 14 15 15 14 17 Core Curriculum V5 Are they still the same? Column A: Mean=15 Column B: Mean=12 SD=4 Core Curriculum V5 We want to know if we're making a difference Core Curriculum V5 What is statistics? a. -
Principles of the Design and Analysis of Experiments
A FRESH LOOK AT THE BASIC PRINCIPLES OF THE DESIGN AND ANALYSIS OF EXPERIMENTS F. YATES ROTHAMSTED EXPERIMENTAL STATION, HARPENDEN 1. Introduction When Professor Neyman invited me to attend the Fifth Berkeley Symposium, and give a paper on the basic principles of the design and analysis of experiments, I was a little hesitant. I felt certain that all those here must be thoroughly conversant with these basic principles, and that to mull over them again would be of little interest. This, however, is the first symposium to be held since Sir Ronald Fisher's death, and it does therefore seem apposite that a paper discussing some aspect of his work should be given. If so, what could be better than the design and analysis of experiments, which in its modern form he created? I do not propose today to give a history of the development of the subject. This I did in a paper presented in 1963 to the Seventh International Biometrics Congress [14]. Instead I want to take a fresh look at the logical principles Fisher laid down, and the action that flows from them; also briefly to consider certain modern trends, and see how far they are really of value. 2. General principles Fisher, in his first formal exposition of experimental design [4] laid down three basic principles: replication; randomization; local control. Replication and local control (for example, arrangement in blocks or rows and columns of a square) were not new, but the idea of assigning the treatments at random (subject to the restrictions imposed by the local control) was novel, and proved to be a most fruitful contribution. -
Sequential Analysis Exercises
Sequential analysis Exercises : 1. What is the practical idea at origin of sequential analysis ? 2. In which cases sequential analysis is appropriate ? 3. What are the supposed advantages of sequential analysis ? 4. What does the values from a three steps sequential analysis in the following table are for ? nb accept refuse grains e xamined 20 0 5 40 2 7 60 6 7 5. Do I have alpha and beta risks when I use sequential analysis ? ______________________________________________ 1 5th ISTA seminar on statistics S Grégoire August 1999 SEQUENTIAL ANALYSIS.DOC PRINCIPLE OF THE SEQUENTIAL ANALYSIS METHOD The method originates from a practical observation. Some objects are so good or so bad that with a quick look we are able to accept or reject them. For other objects we need more information to know if they are good enough or not. In other words, we do not need to put the same effort on all the objects we control. As a result of this we may save time or money if we decide for some objects at an early stage. The general basis of sequential analysis is to define, -before the studies-, sampling schemes which permit to take consistent decisions at different stages of examination. The aim is to compare the results of examinations made on an object to control <-- to --> decisional limits in order to take a decision. At each stage of examination the decision is to accept the object if it is good enough with a chosen probability or to reject the object if it is too bad (at a chosen probability) or to continue the study if we need more information before to fall in one of the two above categories. -
Tests of Hypotheses Using Statistics
Tests of Hypotheses Using Statistics Adam Massey¤and Steven J. Millery Mathematics Department Brown University Providence, RI 02912 Abstract We present the various methods of hypothesis testing that one typically encounters in a mathematical statistics course. The focus will be on conditions for using each test, the hypothesis tested by each test, and the appropriate (and inappropriate) ways of using each test. We conclude by summarizing the di®erent tests (what conditions must be met to use them, what the test statistic is, and what the critical region is). Contents 1 Types of Hypotheses and Test Statistics 2 1.1 Introduction . 2 1.2 Types of Hypotheses . 3 1.3 Types of Statistics . 3 2 z-Tests and t-Tests 5 2.1 Testing Means I: Large Sample Size or Known Variance . 5 2.2 Testing Means II: Small Sample Size and Unknown Variance . 9 3 Testing the Variance 12 4 Testing Proportions 13 4.1 Testing Proportions I: One Proportion . 13 4.2 Testing Proportions II: K Proportions . 15 4.3 Testing r £ c Contingency Tables . 17 4.4 Incomplete r £ c Contingency Tables Tables . 18 5 Normal Regression Analysis 19 6 Non-parametric Tests 21 6.1 Tests of Signs . 21 6.2 Tests of Ranked Signs . 22 6.3 Tests Based on Runs . 23 ¤E-mail: [email protected] yE-mail: [email protected] 1 7 Summary 26 7.1 z-tests . 26 7.2 t-tests . 27 7.3 Tests comparing means . 27 7.4 Variance Test . 28 7.5 Proportions . 28 7.6 Contingency Tables . -
Statistical Significance
Statistical significance In statistical hypothesis testing,[1][2] statistical signif- 1.1 Related concepts icance (or a statistically significant result) is at- tained whenever the observed p-value of a test statis- The significance level α is the threshhold for p below tic is less than the significance level defined for the which the experimenter assumes the null hypothesis is study.[3][4][5][6][7][8][9] The p-value is the probability of false, and something else is going on. This means α is obtaining results at least as extreme as those observed, also the probability of mistakenly rejecting the null hy- given that the null hypothesis is true. The significance pothesis, if the null hypothesis is true.[22] level, α, is the probability of rejecting the null hypothe- Sometimes researchers talk about the confidence level γ sis, given that it is true.[10] This statistical technique for = (1 − α) instead. This is the probability of not rejecting testing the significance of results was developed in the the null hypothesis given that it is true. [23][24] Confidence early 20th century. levels and confidence intervals were introduced by Ney- In any experiment or observation that involves drawing man in 1937.[25] a sample from a population, there is always the possibil- ity that an observed effect would have occurred due to sampling error alone.[11][12] But if the p-value of an ob- 2 Role in statistical hypothesis test- served effect is less than the significance level, an inves- tigator may conclude that that effect reflects the charac- ing teristics of the -
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. -
Notes: Hypothesis Testing, Fisher's Exact Test
Notes: Hypothesis Testing, Fisher’s Exact Test CS 3130 / ECE 3530: Probability and Statistics for Engineers Novermber 25, 2014 The Lady Tasting Tea Many of the modern principles used today for designing experiments and testing hypotheses were intro- duced by Ronald A. Fisher in his 1935 book The Design of Experiments. As the story goes, he came up with these ideas at a party where a woman claimed to be able to tell if a tea was prepared with milk added to the cup first or with milk added after the tea was poured. Fisher designed an experiment where the lady was presented with 8 cups of tea, 4 with milk first, 4 with tea first, in random order. She then tasted each cup and reported which four she thought had milk added first. Now the question Fisher asked is, “how do we test whether she really is skilled at this or if she’s just guessing?” To do this, Fisher introduced the idea of a null hypothesis, which can be thought of as a “default position” or “the status quo” where nothing very interesting is happening. In the lady tasting tea experiment, the null hypothesis was that the lady could not really tell the difference between teas, and she is just guessing. Now, the idea of hypothesis testing is to attempt to disprove or reject the null hypothesis, or more accurately, to see how much the data collected in the experiment provides evidence that the null hypothesis is false. The idea is to assume the null hypothesis is true, i.e., that the lady is just guessing.