Teaching Statistics for Use in Epidemiology
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Projections of Education Statistics to 2022 Forty-First Edition
Projections of Education Statistics to 2022 Forty-first Edition 20192019 20212021 20182018 20202020 20222022 NCES 2014-051 U.S. DEPARTMENT OF EDUCATION Projections of Education Statistics to 2022 Forty-first Edition FEBRUARY 2014 William J. Hussar National Center for Education Statistics Tabitha M. Bailey IHS Global Insight NCES 2014-051 U.S. DEPARTMENT OF EDUCATION U.S. Department of Education Arne Duncan Secretary Institute of Education Sciences John Q. Easton Director National Center for Education Statistics John Q. Easton Acting Commissioner The National Center for Education Statistics (NCES) is the primary federal entity for collecting, analyzing, and reporting data related to education in the United States and other nations. It fulfills a congressional mandate to collect, collate, analyze, and report full and complete statistics on the condition of education in the United States; conduct and publish reports and specialized analyses of the meaning and significance of such statistics; assist state and local education agencies in improving their statistical systems; and review and report on education activities in foreign countries. NCES activities are designed to address high-priority education data needs; provide consistent, reliable, complete, and accurate indicators of education status and trends; and report timely, useful, and high-quality data to the U.S. Department of Education, the Congress, the states, other education policymakers, practitioners, data users, and the general public. Unless specifically noted, all information contained herein is in the public domain. We strive to make our products available in a variety of formats and in language that is appropriate to a variety of audiences. You, as our customer, are the best judge of our success in communicating information effectively. -
Use of Statistical Tables
TUTORIAL | SCOPE USE OF STATISTICAL TABLES Lucy Radford, Jenny V Freeman and Stephen J Walters introduce three important statistical distributions: the standard Normal, t and Chi-squared distributions PREVIOUS TUTORIALS HAVE LOOKED at hypothesis testing1 and basic statistical tests.2–4 As part of the process of statistical hypothesis testing, a test statistic is calculated and compared to a hypothesised critical value and this is used to obtain a P- value. This P-value is then used to decide whether the study results are statistically significant or not. It will explain how statistical tables are used to link test statistics to P-values. This tutorial introduces tables for three important statistical distributions (the TABLE 1. Extract from two-tailed standard Normal, t and Chi-squared standard Normal table. Values distributions) and explains how to use tabulated are P-values corresponding them with the help of some simple to particular cut-offs and are for z examples. values calculated to two decimal places. STANDARD NORMAL DISTRIBUTION TABLE 1 The Normal distribution is widely used in statistics and has been discussed in z 0.00 0.01 0.02 0.03 0.050.04 0.05 0.06 0.07 0.08 0.09 detail previously.5 As the mean of a Normally distributed variable can take 0.00 1.0000 0.9920 0.9840 0.9761 0.9681 0.9601 0.9522 0.9442 0.9362 0.9283 any value (−∞ to ∞) and the standard 0.10 0.9203 0.9124 0.9045 0.8966 0.8887 0.8808 0.8729 0.8650 0.8572 0.8493 deviation any positive value (0 to ∞), 0.20 0.8415 0.8337 0.8259 0.8181 0.8103 0.8206 0.7949 0.7872 0.7795 0.7718 there are an infinite number of possible 0.30 0.7642 0.7566 0.7490 0.7414 0.7339 0.7263 0.7188 0.7114 0.7039 0.6965 Normal distributions. -
The Statistical Significance of Randomized Controlled Trial Results Is Frequently Fragile: a Case for a Fragility Index
The statistical significance of randomized controlled trial results is frequently fragile: A case for a Fragility Index Walsh, M., Srinathan, S. K., McAuley, D. F., Mrkobrada, M., Levine, O., Ribic, C., Molnar, A. O., Dattani, N. D., Burke, A., Guyatt, G., Thabane, L., Walter, S. D., Pogue, J., & Devereaux, P. J. (2014). The statistical significance of randomized controlled trial results is frequently fragile: A case for a Fragility Index. Journal of Clinical Epidemiology, 67(6), 622-628. https://doi.org/10.1016/j.jclinepi.2013.10.019 Published in: Journal of Clinical Epidemiology Document Version: Publisher's PDF, also known as Version of record Queen's University Belfast - Research Portal: Link to publication record in Queen's University Belfast Research Portal Publisher rights 2014 The Authors. Published by Elsevier Inc. This is an open access article published under a Creative Commons Attribution-NonCommercial-NoDerivs License (https://creativecommons.org/licenses/by-nc-nd/3.0/), which permits distribution and reproduction for non-commercial purposes, provided the author and source are cited. General rights Copyright for the publications made accessible via the Queen's University Belfast Research Portal is retained by the author(s) and / or other copyright owners and it is a condition of accessing these publications that users recognise and abide by the legal requirements associated with these rights. Take down policy The Research Portal is Queen's institutional repository that provides access to Queen's research output. Every effort has been made to ensure that content in the Research Portal does not infringe any person's rights, or applicable UK laws. -
Why Do You Need a Biostatistician? Antonia Zapf1* , Geraldine Rauch2 and Meinhard Kieser3
Zapf et al. BMC Medical Research Methodology (2020) 20:23 https://doi.org/10.1186/s12874-020-0916-4 DEBATE Open Access Why do you need a biostatistician? Antonia Zapf1* , Geraldine Rauch2 and Meinhard Kieser3 Abstract The quality of medical research importantly depends, among other aspects, on a valid statistical planning of the study, analysis of the data, and reporting of the results, which is usually guaranteed by a biostatistician. However, there are several related professions next to the biostatistician, for example epidemiologists, medical informaticians and bioinformaticians. For medical experts, it is often not clear what the differences between these professions are and how the specific role of a biostatistician can be described. For physicians involved in medical research, this is problematic because false expectations often lead to frustration on both sides. Therefore, the aim of this article is to outline the tasks and responsibilities of biostatisticians in clinical trials as well as in other fields of application in medical research. Keywords: Medical research, Biostatistician, Tasks, Responsibilities Background Biometric Society (IBS) provides a definition of biomet- What is a biostatistician, what does he or she actually do rics as a ‘field of development of statistical and mathem- and what distinguishes him or her from, for example, an atical methods applicable in the biological sciences’ [2]. epidemiologist? If we would ask this our main cooper- In here, we will focus on (human) medicine as area of ation partners like physicians or biologists, they probably application, but the results can be easily transferred to could not give a satisfying answer. This is problematic the other biological sciences like, for example, agricul- because false expectations often lead to frustration on ture or ecology. -
On the Meaning and Use of Kurtosis
Psychological Methods Copyright 1997 by the American Psychological Association, Inc. 1997, Vol. 2, No. 3,292-307 1082-989X/97/$3.00 On the Meaning and Use of Kurtosis Lawrence T. DeCarlo Fordham University For symmetric unimodal distributions, positive kurtosis indicates heavy tails and peakedness relative to the normal distribution, whereas negative kurtosis indicates light tails and flatness. Many textbooks, however, describe or illustrate kurtosis incompletely or incorrectly. In this article, kurtosis is illustrated with well-known distributions, and aspects of its interpretation and misinterpretation are discussed. The role of kurtosis in testing univariate and multivariate normality; as a measure of departures from normality; in issues of robustness, outliers, and bimodality; in generalized tests and estimators, as well as limitations of and alternatives to the kurtosis measure [32, are discussed. It is typically noted in introductory statistics standard deviation. The normal distribution has a kur- courses that distributions can be characterized in tosis of 3, and 132 - 3 is often used so that the refer- terms of central tendency, variability, and shape. With ence normal distribution has a kurtosis of zero (132 - respect to shape, virtually every textbook defines and 3 is sometimes denoted as Y2)- A sample counterpart illustrates skewness. On the other hand, another as- to 132 can be obtained by replacing the population pect of shape, which is kurtosis, is either not discussed moments with the sample moments, which gives or, worse yet, is often described or illustrated incor- rectly. Kurtosis is also frequently not reported in re- ~(X i -- S)4/n search articles, in spite of the fact that virtually every b2 (•(X i - ~')2/n)2' statistical package provides a measure of kurtosis. -
The Probability Lifesaver: Order Statistics and the Median Theorem
The Probability Lifesaver: Order Statistics and the Median Theorem Steven J. Miller December 30, 2015 Contents 1 Order Statistics and the Median Theorem 3 1.1 Definition of the Median 5 1.2 Order Statistics 10 1.3 Examples of Order Statistics 15 1.4 TheSampleDistributionoftheMedian 17 1.5 TechnicalboundsforproofofMedianTheorem 20 1.6 TheMedianofNormalRandomVariables 22 2 • Greetings again! In this supplemental chapter we develop the theory of order statistics in order to prove The Median Theorem. This is a beautiful result in its own, but also extremely important as a substitute for the Central Limit Theorem, and allows us to say non- trivial things when the CLT is unavailable. Chapter 1 Order Statistics and the Median Theorem The Central Limit Theorem is one of the gems of probability. It’s easy to use and its hypotheses are satisfied in a wealth of problems. Many courses build towards a proof of this beautiful and powerful result, as it truly is ‘central’ to the entire subject. Not to detract from the majesty of this wonderful result, however, what happens in those instances where it’s unavailable? For example, one of the key assumptions that must be met is that our random variables need to have finite higher moments, or at the very least a finite variance. What if we were to consider sums of Cauchy random variables? Is there anything we can say? This is not just a question of theoretical interest, of mathematicians generalizing for the sake of generalization. The following example from economics highlights why this chapter is more than just of theoretical interest. -
Medical Statistics PDF File 9
M249 Practical modern statistics Medical statistics About this module M249 Practical modern statistics uses the software packages IBM SPSS Statistics (SPSS Inc.) and WinBUGS, and other software. This software is provided as part of the module, and its use is covered in the Introduction to statistical modelling and in the four computer books associated with Books 1 to 4. This publication forms part of an Open University module. Details of this and other Open University modules can be obtained from the Student Registration and Enquiry Service, The Open University, PO Box 197, Milton Keynes MK7 6BJ, United Kingdom (tel. +44 (0)845 300 60 90; email [email protected]). Alternatively, you may visit the Open University website at www.open.ac.uk where you can learn more about the wide range of modules and packs offered at all levels by The Open University. To purchase a selection of Open University materials visit www.ouw.co.uk, or contact Open University Worldwide, Walton Hall, Milton Keynes MK7 6AA, United Kingdom for a brochure (tel. +44 (0)1908 858779; fax +44 (0)1908 858787; email [email protected]). Note to reader Mathematical/statistical content at the Open University is usually provided to students in printed books, with PDFs of the same online. This format ensures that mathematical notation is presented accurately and clearly. The PDF of this extract thus shows the content exactly as it would be seen by an Open University student. Please note that the PDF may contain references to other parts of the module and/or to software or audio-visual components of the module. -
Testing Hypotheses
Chapter 7 Testing Hypotheses Chapter Learning Objectives Understanding the assumptions of statistical hypothesis testing Defining and applying the components in hypothesis testing: the research and null hypotheses, sampling distribution, and test statistic Understanding what it means to reject or fail to reject a null hypothesis Applying hypothesis testing to two sample cases, with means or proportions n the past, the increase in the price of gasoline could be attributed to major national or global event, such as the Lebanon and Israeli war or Hurricane Katrina. However, in 2005, the price for a Igallon of regular gasoline reached $3.00 and remained high for a long time afterward. The impact of unpredictable fuel prices is still felt across the nation, but the burden is greater among distinct social economic groups and geographic areas. Lower-income Americans spend eight times more of their disposable income on gasoline than wealthier Americans do.1 For example, in Wilcox, Alabama, individuals spend 12.72% of their income to fuel one vehicle, while in Hunterdon Co., New Jersey, people spend 1.52%. Nationally, Americans spend 3.8% of their income fueling one vehicle. The first state to reach the $3.00-per-gallon milestone was California in 2005. California’s drivers were especially hit hard by the rising price of gas, due in part to their reliance on automobiles, especially for work commuters. Analysts predicted that gas prices would continue to rise nationally. Declines in consumer spending and confidence in the economy have been attributed in part to the high (and rising) cost of gasoline. In 2010, gasoline prices have remained higher for states along the West Coast, particularly in Alaska and California. -
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 . -
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. -
The Use of Stata in Medical Statistics and Epidemiology: a Long Journey
A retrospective view Stata Progress Epidemiology and Biostatistics with Stata My Journey with Stata The use of Stata in Medical Statistics and Epidemiology: a long journey Rino Bellocco, Sc.D. Department of Statistics and Quantitative Methods University of Milano-Bicocca & Department of Medical Epidemiology and Biostatistics Karolinska Institutet Nordic and Baltic Stata Users Group meeting, Stockholm, September 1, 2017 1 / 44 A retrospective view Stata Progress Epidemiology and Biostatistics with Stata My Journey with Stata Outline A retrospective view Stata Progress Epidemiology and Biostatistics with Stata My Journey with Stata 2 / 44 A retrospective view Stata Progress Epidemiology and Biostatistics with Stata My Journey with Stata Outline A retrospective view Stata Progress Epidemiology and Biostatistics with Stata My Journey with Stata 3 / 44 A retrospective view Stata Progress Epidemiology and Biostatistics with Stata My Journey with Stata Some History 1985-1995 • Version 1.0 - 1.5, January 1985 - February 1987 (around 48 commands, regress logit ) 4 / 44 N. J. Cox 15 Table 2: Releases of Stata 1.0 January 1985 3.1 August 1993 1.1 February 1985 4.0 January 1995 1.2 March 1985 5.0 October 1996 1.4 August 1986 6.0 January 1999 1.5 February 1987 7.0 December 2000 2.0 June 1988 8.0 January 2003 A retrospective view Stata2.05 Progress June 1989Epidemiology and Biostatistics8.1 July with 2003 Stata My Journey with Stata 2.1 September 1990 8.2 October 2003 3.0 MarchBasic 1992 Commands Table 3: Stata 1.0 and Stata 1.1 append dir infile plot spool beep do input query summarize by drop label regress tabulate capture erase list rename test confirm exit macro replace type convert expand merge run use correlate format modify save count generate more set describe help outfile sort Stata 1.0 had int, long, float,anddouble variables; it did not have byte or str#. -
Medical Statistics Made Easy Medical Statistics Made Easy M
MEDICAL STATISTICS MADE EASY STATISTICS MEDICAL MEDICAL STATISTICS MADE EASY M. HARRIS and G. TAYLOR 4th EDITION HARRIS and TAYLOR 4 MEDICAL STATISTICS MADE EASY 4 MSME_Book.indb 1 17/08/2020 12:10 MSME_4e_234x156_Prelims.indd 1 06/05/2020 16:02 MEDICAL STATISTICS MADE EASY 4 Michael Harris Professor of Primary Care and former General Practitioner, Bath, UK and Gordon Taylor Professor of Medical Statistics, College of Medicine and Health, University of Exeter, UK MSME_Book.indb 3 17/08/2020 12:10 MSME_4e_234x156_Prelims.indd 3 06/05/2020 16:02 Fourth edition © Scion Publishing Ltd, 2021 ISBN 978 1 911510 63 5 Third edition published in 2014 by Scion Publishing Ltd (978 1 907904 03 5) Second edition published in 2008 by Scion Publishing Ltd (978 1 904842 55 2) First edition published in 2003 by Martin Dunitz (1 85996 219 X) Scion Publishing Limited The Old Hayloft, Vantage Business Park, Bloxham Road, Banbury OX16 9UX, UK www.scionpublishing.com Important Note from the Publisher The information contained within this book was obtained by Scion Publishing Ltd from sources believed by us to be reliable. However, while every effort has been made to ensure its accuracy, no responsibility for loss or injury whatsoever occasioned to any person acting or refraining from action as a result of information contained herein can be accepted by the authors or publishers. Readers are reminded that medicine is a constantly evolving science and while the authors and publishers have ensured that all dosages, applications and practices are based on current indications, there may be specific practices which differ between communities.