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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 Magic of Randomization Versus the Myth of Real-World Evidence
The new england journal of medicine Sounding Board The Magic of Randomization versus the Myth of Real-World Evidence Rory Collins, F.R.S., Louise Bowman, M.D., F.R.C.P., Martin Landray, Ph.D., F.R.C.P., and Richard Peto, F.R.S. Nonrandomized observational analyses of large safety and efficacy because the potential biases electronic patient databases are being promoted with respect to both can be appreciable. For ex- as an alternative to randomized clinical trials as ample, the treatment that is being assessed may a source of “real-world evidence” about the effi- well have been provided more or less often to cacy and safety of new and existing treatments.1-3 patients who had an increased or decreased risk For drugs or procedures that are already being of various health outcomes. Indeed, that is what used widely, such observational studies may in- would be expected in medical practice, since both volve exposure of large numbers of patients. the severity of the disease being treated and the Consequently, they have the potential to detect presence of other conditions may well affect the rare adverse effects that cannot plausibly be at- choice of treatment (often in ways that cannot be tributed to bias, generally because the relative reliably quantified). Even when associations of risk is large (e.g., Reye’s syndrome associated various health outcomes with a particular treat- with the use of aspirin, or rhabdomyolysis as- ment remain statistically significant after adjust- sociated with the use of statin therapy).4 Non- ment for all the known differences between pa- randomized clinical observation may also suf- tients who received it and those who did not fice to detect large beneficial effects when good receive it, these adjusted associations may still outcomes would not otherwise be expected (e.g., reflect residual confounding because of differ- control of diabetic ketoacidosis with insulin treat- ences in factors that were assessed only incom- ment, or the rapid shrinking of tumors with pletely or not at all (and therefore could not be chemotherapy). -
(Meta-Analyses of Observational Studies in Epidemiology) Checklist
MOOSE (Meta-analyses Of Observational Studies in Epidemiology) Checklist A reporting checklist for Authors, Editors, and Reviewers of Meta-analyses of Observational Studies. You must report the page number in your manuscript where you consider each of the items listed in this checklist. If you have not included this information, either revise your manuscript accordingly before submitting or note N/A. Reporting Criteria Reported (Yes/No) Reported on Page No. Reporting of Background Problem definition Hypothesis statement Description of Study Outcome(s) Type of exposure or intervention used Type of study design used Study population Reporting of Search Strategy Qualifications of searchers (eg, librarians and investigators) Search strategy, including time period included in the synthesis and keywords Effort to include all available studies, including contact with authors Databases and registries searched Search software used, name and version, including special features used (eg, explosion) Use of hand searching (eg, reference lists of obtained articles) List of citations located and those excluded, including justification Method for addressing articles published in languages other than English Method of handling abstracts and unpublished studies Description of any contact with authors Reporting of Methods Description of relevance or appropriateness of studies assembled for assessing the hypothesis to be tested Rationale for the selection and coding of data (eg, sound clinical principles or convenience) Documentation of how data were classified -
Quasi-Experimental Studies in the Fields of Infection Control and Antibiotic Resistance, Ten Years Later: a Systematic Review
HHS Public Access Author manuscript Author ManuscriptAuthor Manuscript Author Infect Control Manuscript Author Hosp Epidemiol Manuscript Author . Author manuscript; available in PMC 2019 November 12. Published in final edited form as: Infect Control Hosp Epidemiol. 2018 February ; 39(2): 170–176. doi:10.1017/ice.2017.296. Quasi-experimental Studies in the Fields of Infection Control and Antibiotic Resistance, Ten Years Later: A Systematic Review Rotana Alsaggaf, MS, Lyndsay M. O’Hara, PhD, MPH, Kristen A. Stafford, PhD, MPH, Surbhi Leekha, MBBS, MPH, Anthony D. Harris, MD, MPH, CDC Prevention Epicenters Program Department of Epidemiology and Public Health, University of Maryland School of Medicine, Baltimore, Maryland. Abstract OBJECTIVE.—A systematic review of quasi-experimental studies in the field of infectious diseases was published in 2005. The aim of this study was to assess improvements in the design and reporting of quasi-experiments 10 years after the initial review. We also aimed to report the statistical methods used to analyze quasi-experimental data. DESIGN.—Systematic review of articles published from January 1, 2013, to December 31, 2014, in 4 major infectious disease journals. METHODS.—Quasi-experimental studies focused on infection control and antibiotic resistance were identified and classified based on 4 criteria: (1) type of quasi-experimental design used, (2) justification of the use of the design, (3) use of correct nomenclature to describe the design, and (4) statistical methods used. RESULTS.—Of 2,600 articles, 173 (7%) featured a quasi-experimental design, compared to 73 of 2,320 articles (3%) in the previous review (P<.01). Moreover, 21 articles (12%) utilized a study design with a control group; 6 (3.5%) justified the use of a quasi-experimental design; and 68 (39%) identified their design using the correct nomenclature. -
Epidemiology and Biostatistics (EPBI) 1
Epidemiology and Biostatistics (EPBI) 1 Epidemiology and Biostatistics (EPBI) Courses EPBI 2219. Biostatistics and Public Health. 3 Credit Hours. This course is designed to provide students with a solid background in applied biostatistics in the field of public health. Specifically, the course includes an introduction to the application of biostatistics and a discussion of key statistical tests. Appropriate techniques to measure the extent of disease, the development of disease, and comparisons between groups in terms of the extent and development of disease are discussed. Techniques for summarizing data collected in samples are presented along with limited discussion of probability theory. Procedures for estimation and hypothesis testing are presented for means, for proportions, and for comparisons of means and proportions in two or more groups. Multivariable statistical methods are introduced but not covered extensively in this undergraduate course. Public Health majors, minors or students studying in the Public Health concentration must complete this course with a C or better. Level Registration Restrictions: May not be enrolled in one of the following Levels: Graduate. Repeatability: This course may not be repeated for additional credits. EPBI 2301. Public Health without Borders. 3 Credit Hours. Public Health without Borders is a course that will introduce you to the world of disease detectives to solve public health challenges in glocal (i.e., global and local) communities. You will learn about conducting disease investigations to support public health actions relevant to affected populations. You will discover what it takes to become a field epidemiologist through hands-on activities focused on promoting health and preventing disease in diverse populations across the globe. -
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. -
Clinical Performance Assessment: Considerations for Computer
Contains Nonbinding Recommendations Clinical Performance Assessment: Considerations for Computer-Assisted Detection Devices Applied to Radiology Images and Radiology Device Data in - Premarket Notification (510(k)) Submissions Guidance for Industry and FDA Staff Document issued on: January 22, 2020 Document originally issued on July 3, 2012 For questions regarding this guidance document, contact Nicholas Petrick at 301-796-2563, or by e- mail at [email protected]; or Robert Ochs at 301-796-6661, or by e-mail at [email protected]. U.S. Department of Health and Human Services Food and Drug Administration Center for Devices and Radiological Health Contains Nonbinding Recommendations Preface Public Comment You may submit electronic comments and suggestions at any time for Agency consideration to https://www.regulations.gov. Submit written comments to the Dockets Management Staff, Food and Drug Administration, 5630 Fishers Lane, Room 1061, (HFA-305), Rockville, MD 20852. Identify all comments with the docket number FDA-2009-D-0503. Comments may not be acted upon by the Agency until the document is next revised or updated. Additional Copies Additional copies are available from the Internet. You may also send an e-mail request to CDRH- [email protected] to receive a copy of the guidance. Please use the document number (1698) to identify the guidance you are requesting. Table of Contents 1. INTRODUCTION .................................................................................................................... 4 2. -
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. -
FDA Guidance: “Design Considerations for Pivotal Clinical Investigations for Medical Devices”
FDA Guidance: “Design Considerations for Pivotal Clinical Investigations for Medical Devices” Greg Campbell, Ph.D. Director, Division of Biostatistics Center for Devices and Radiological Health U.S. Food and Drug Administration [email protected] FDA Stakeholder Webinar December 4, 2013 Design Considerations for Pivotal Clinical Investigations • http://www.fda.gov/medicaldevices/deviceregulation andguidance/guidancedocuments/ucm373750.htm • Draft issued Aug. 15, 2011; Final issued Nov. 7, 2013. • It is guidance for industry, clinical investigators, institutional review boards and FDA staff. 2 Design Considerations for Pivotal Clinical Investigations • Guidance should help manufacturers select appropriate trial design. • Better trial design and improve the quality of data that may better support the safety and effectiveness of a device. • Better quality data may lead to timelier FDA approval or clearance of premarket submissions and speed U.S. patient access to new devices. 3 Outline • Regulatory Considerations • Principles for the Choice of Clinical Study Design • Clinical Outcome Studies – RCTs – Controls – Non-Randomized Controls – Observational Uncontrolled One-Arm Studies • OPCs and Performance Goals – Diagnostic Clinical Outcome Studies • Diagnostic Clinical Performance Studies • Sustaining the Level of Evidence of Studies • Protocol and Statistical Analysis Plan • Closing Remarks 4 Stages of Medical Device Clinical Studies 1) Exploratory Stage – first-in-human and feasibility/pilot studies, iterative learning and product development. 2) Pivotal Stage – definitive study to support the safety and effectiveness evaluation of the medical device for its intended use. 3) Postmarket Stage – includes studies intended to better understand the long-term effectiveness and safety of the device, including rare adverse events. Not all products will go through all stages. -
Guidelines for Reporting Meta-Epidemiological Methodology Research
EBM Primer Evid Based Med: first published as 10.1136/ebmed-2017-110713 on 12 July 2017. Downloaded from Guidelines for reporting meta-epidemiological methodology research Mohammad Hassan Murad, Zhen Wang 10.1136/ebmed-2017-110713 Abstract The goal is generally broad but often focuses on exam- Published research should be reported to evidence users ining the impact of certain characteristics of clinical studies on the observed effect, describing the distribu- Evidence-Based Practice with clarity and transparency that facilitate optimal tion of research evidence in a specific setting, exam- Center, Mayo Clinic, Rochester, appraisal and use of evidence and allow replication Minnesota, USA by other researchers. Guidelines for such reporting ining heterogeneity and exploring its causes, identifying are available for several types of studies but not for and describing plausible biases and providing empirical meta-epidemiological methodology studies. Meta- evidence for hypothesised associations. Unlike classic Correspondence to: epidemiological studies adopt a systematic review epidemiology, the unit of analysis for meta-epidemio- Dr Mohammad Hassan Murad, or meta-analysis approach to examine the impact logical studies is a study, not a patient. The outcomes Evidence-based Practice Center, of certain characteristics of clinical studies on the of meta-epidemiological studies are usually not clinical Mayo Clinic, 200 First Street 6–8 observed effect and provide empirical evidence for outcomes. SW, Rochester, MN 55905, USA; hypothesised associations. The unit of analysis in meta- In this guide, we adapt the items used in the PRISMA murad. mohammad@ mayo. edu 9 epidemiological studies is a study, not a patient. The statement for reporting systematic reviews and outcomes of meta-epidemiological studies are usually meta-analysis to fit the setting of meta- epidemiological not clinical outcomes. -
Simple Linear Regression: Straight Line Regression Between an Outcome Variable (Y ) and a Single Explanatory Or Predictor Variable (X)
1 Introduction to Regression \Regression" is a generic term for statistical methods that attempt to fit a model to data, in order to quantify the relationship between the dependent (outcome) variable and the predictor (independent) variable(s). Assuming it fits the data reasonable well, the estimated model may then be used either to merely describe the relationship between the two groups of variables (explanatory), or to predict new values (prediction). There are many types of regression models, here are a few most common to epidemiology: Simple Linear Regression: Straight line regression between an outcome variable (Y ) and a single explanatory or predictor variable (X). E(Y ) = α + β × X Multiple Linear Regression: Same as Simple Linear Regression, but now with possibly multiple explanatory or predictor variables. E(Y ) = α + β1 × X1 + β2 × X2 + β3 × X3 + ::: A special case is polynomial regression. 2 3 E(Y ) = α + β1 × X + β2 × X + β3 × X + ::: Generalized Linear Model: Same as Multiple Linear Regression, but with a possibly transformed Y variable. This introduces considerable flexibil- ity, as non-linear and non-normal situations can be easily handled. G(E(Y )) = α + β1 × X1 + β2 × X2 + β3 × X3 + ::: In general, the transformation function G(Y ) can take any form, but a few forms are especially common: • Taking G(Y ) = logit(Y ) describes a logistic regression model: E(Y ) log( ) = α + β × X + β × X + β × X + ::: 1 − E(Y ) 1 1 2 2 3 3 2 • Taking G(Y ) = log(Y ) is also very common, leading to Poisson regression for count data, and other so called \log-linear" models.