Timeline of Statistics
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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. -
An Introduction to Psychometric Theory with Applications in R
What is psychometrics? What is R? Where did it come from, why use it? Basic statistics and graphics TOD An introduction to Psychometric Theory with applications in R William Revelle Department of Psychology Northwestern University Evanston, Illinois USA February, 2013 1 / 71 What is psychometrics? What is R? Where did it come from, why use it? Basic statistics and graphics TOD Overview 1 Overview Psychometrics and R What is Psychometrics What is R 2 Part I: an introduction to R What is R A brief example Basic steps and graphics 3 Day 1: Theory of Data, Issues in Scaling 4 Day 2: More than you ever wanted to know about correlation 5 Day 3: Dimension reduction through factor analysis, principal components analyze and cluster analysis 6 Day 4: Classical Test Theory and Item Response Theory 7 Day 5: Structural Equation Modeling and applied scale construction 2 / 71 What is psychometrics? What is R? Where did it come from, why use it? Basic statistics and graphics TOD Outline of Day 1/part 1 1 What is psychometrics? Conceptual overview Theory: the organization of Observed and Latent variables A latent variable approach to measurement Data and scaling Structural Equation Models 2 What is R? Where did it come from, why use it? Installing R on your computer and adding packages Installing and using packages Implementations of R Basic R capabilities: Calculation, Statistical tables, Graphics Data sets 3 Basic statistics and graphics 4 steps: read, explore, test, graph Basic descriptive and inferential statistics 4 TOD 3 / 71 What is psychometrics? What is R? Where did it come from, why use it? Basic statistics and graphics TOD What is psychometrics? In physical science a first essential step in the direction of learning any subject is to find principles of numerical reckoning and methods for practicably measuring some quality connected with it. -
Cluster Analysis for Gene Expression Data: a Survey
Cluster Analysis for Gene Expression Data: A Survey Daxin Jiang Chun Tang Aidong Zhang Department of Computer Science and Engineering State University of New York at Buffalo Email: djiang3, chuntang, azhang @cse.buffalo.edu Abstract DNA microarray technology has now made it possible to simultaneously monitor the expres- sion levels of thousands of genes during important biological processes and across collections of related samples. Elucidating the patterns hidden in gene expression data offers a tremen- dous opportunity for an enhanced understanding of functional genomics. However, the large number of genes and the complexity of biological networks greatly increase the challenges of comprehending and interpreting the resulting mass of data, which often consists of millions of measurements. A first step toward addressing this challenge is the use of clustering techniques, which is essential in the data mining process to reveal natural structures and identify interesting patterns in the underlying data. Cluster analysis seeks to partition a given data set into groups based on specified features so that the data points within a group are more similar to each other than the points in different groups. A very rich literature on cluster analysis has developed over the past three decades. Many conventional clustering algorithms have been adapted or directly applied to gene expres- sion data, and also new algorithms have recently been proposed specifically aiming at gene ex- pression data. These clustering algorithms have been proven useful for identifying biologically relevant groups of genes and samples. In this paper, we first briefly introduce the concepts of microarray technology and discuss the basic elements of clustering on gene expression data. -
Reliability Engineering: Today and Beyond
Reliability Engineering: Today and Beyond Keynote Talk at the 6th Annual Conference of the Institute for Quality and Reliability Tsinghua University People's Republic of China by Professor Mohammad Modarres Director, Center for Risk and Reliability Department of Mechanical Engineering Outline – A New Era in Reliability Engineering – Reliability Engineering Timeline and Research Frontiers – Prognostics and Health Management – Physics of Failure – Data-driven Approaches in PHM – Hybrid Methods – Conclusions New Era in Reliability Sciences and Engineering • Started as an afterthought analysis – In enduing years dismissed as a legitimate field of science and engineering – Worked with small data • Three advances transformed reliability into a legitimate science: – 1. Availability of inexpensive sensors and information systems – 2. Ability to better described physics of damage, degradation, and failure time using empirical and theoretical sciences – 3. Access to big data and PHM techniques for diagnosing faults and incipient failures • Today we can predict abnormalities, offer just-in-time remedies to avert failures, and making systems robust and resilient to failures Seventy Years of Reliability Engineering – Reliability Engineering Initiatives in 1950’s • Weakest link • Exponential life model • Reliability Block Diagrams (RBDs) – Beyond Exp. Dist. & Birth of System Reliability in 1960’s • Birth of Physics of Failure (POF) • Uses of more proper distributions (Weibull, etc.) • Reliability growth • Life testing • Failure Mode and Effect Analysis -
On Popularization of Scientific Education in Italy Between 12Th and 16Th Century
PROBLEMS OF EDUCATION IN THE 21st CENTURY Volume 57, 2013 90 ON POPULARIZATION OF SCIENTIFIC EDUCATION IN ITALY BETWEEN 12TH AND 16TH CENTURY Raffaele Pisano University of Lille1, France E–mail: [email protected] Paolo Bussotti University of West Bohemia, Czech Republic E–mail: [email protected] Abstract Mathematics education is also a social phenomenon because it is influenced both by the needs of the labour market and by the basic knowledge of mathematics necessary for every person to be able to face some operations indispensable in the social and economic daily life. Therefore the way in which mathe- matics education is framed changes according to modifications of the social environment and know–how. For example, until the end of the 20th century, in the Italian faculties of engineering the teaching of math- ematical analysis was profound: there were two complex examinations in which the theory was as impor- tant as the ability in solving exercises. Now the situation is different. In some universities there is only a proof of mathematical analysis; in others there are two proves, but they are sixth–month and not annual proves. The theoretical requirements have been drastically reduced and the exercises themselves are often far easier than those proposed in the recent past. With some modifications, the situation is similar for the teaching of other modern mathematical disciplines: many operations needing of calculations and math- ematical reasoning are developed by the computers or other intelligent machines and hence an engineer needs less theoretical mathematics than in the past. The problem has historical roots. In this research an analysis of the phenomenon of “scientific education” (teaching geometry, arithmetic, mathematics only) with respect the methods used from the late Middle Ages by “maestri d’abaco” to the Renaissance hu- manists, and with respect to mathematics education nowadays is discussed. -
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. -
Biostatistics (BIOSTAT) 1
Biostatistics (BIOSTAT) 1 This course covers practical aspects of conducting a population- BIOSTATISTICS (BIOSTAT) based research study. Concepts include determining a study budget, setting a timeline, identifying study team members, setting a strategy BIOSTAT 301-0 Introduction to Epidemiology (1 Unit) for recruitment and retention, developing a data collection protocol This course introduces epidemiology and its uses for population health and monitoring data collection to ensure quality control and quality research. Concepts include measures of disease occurrence, common assurance. Students will demonstrate these skills by engaging in a sources and types of data, important study designs, sources of error in quarter-long group project to draft a Manual of Operations for a new epidemiologic studies and epidemiologic methods. "mock" population study. BIOSTAT 302-0 Introduction to Biostatistics (1 Unit) BIOSTAT 429-0 Systematic Review and Meta-Analysis in the Medical This course introduces principles of biostatistics and applications Sciences (1 Unit) of statistical methods in health and medical research. Concepts This course covers statistical methods for meta-analysis. Concepts include descriptive statistics, basic probability, probability distributions, include fixed-effects and random-effects models, measures of estimation, hypothesis testing, correlation and simple linear regression. heterogeneity, prediction intervals, meta regression, power assessment, BIOSTAT 303-0 Probability (1 Unit) subgroup analysis and assessment of publication -
Big Data for Reliability Engineering: Threat and Opportunity
Reliability, February 2016 Big Data for Reliability Engineering: Threat and Opportunity Vitali Volovoi Independent Consultant [email protected] more recently, analytics). It shares with the rest of the fields Abstract - The confluence of several technologies promises under this umbrella the need to abstract away most stormy waters ahead for reliability engineering. News reports domain-specific information, and to use tools that are mainly are full of buzzwords relevant to the future of the field—Big domain-independent1. As a result, it increasingly shares the Data, the Internet of Things, predictive and prescriptive lingua franca of modern systems engineering—probability and analytics—the sexier sisters of reliability engineering, both statistics that are required to balance the otherwise orderly and exciting and threatening. Can we reliability engineers join the deterministic engineering world. party and suddenly become popular (and better paid), or are And yet, reliability engineering does not wear the fancy we at risk of being superseded and driven into obsolescence? clothes of its sisters. There is nothing privileged about it. It is This article argues that“big-picture” thinking, which is at the rarely studied in engineering schools, and it is definitely not core of the concept of the System of Systems, is key for a studied in business schools! Instead, it is perceived as a bright future for reliability engineering. necessary evil (especially if the reliability issues in question are safety-related). The community of reliability engineers Keywords - System of Systems, complex systems, Big Data, consists of engineers from other fields who were mainly Internet of Things, industrial internet, predictive analytics, trained on the job (instead of receiving formal degrees in the prescriptive analytics field). -
Interactive Statistical Graphics/ When Charts Come to Life
Titel Event, Date Author Affiliation Interactive Statistical Graphics When Charts come to Life [email protected] www.theusRus.de Telefónica Germany Interactive Statistical Graphics – When Charts come to Life PSI Graphics One Day Meeting Martin Theus 2 www.theusRus.de What I do not talk about … Interactive Statistical Graphics – When Charts come to Life PSI Graphics One Day Meeting Martin Theus 3 www.theusRus.de … still not what I mean. Interactive Statistical Graphics – When Charts come to Life PSI Graphics One Day Meeting Martin Theus 4 www.theusRus.de Interactive Graphics ≠ Dynamic Graphics • Interactive Graphics … uses various interactions with the plots to change selections and parameters quickly. Interactive Statistical Graphics – When Charts come to Life PSI Graphics One Day Meeting Martin Theus 4 www.theusRus.de Interactive Graphics ≠ Dynamic Graphics • Interactive Graphics … uses various interactions with the plots to change selections and parameters quickly. • Dynamic Graphics … uses animated / rotating plots to visualize high dimensional (continuous) data. Interactive Statistical Graphics – When Charts come to Life PSI Graphics One Day Meeting Martin Theus 4 www.theusRus.de Interactive Graphics ≠ Dynamic Graphics • Interactive Graphics … uses various interactions with the plots to change selections and parameters quickly. • Dynamic Graphics … uses animated / rotating plots to visualize high dimensional (continuous) data. 1973 PRIM-9 Tukey et al. Interactive Statistical Graphics – When Charts come to Life PSI Graphics One Day Meeting Martin Theus 4 www.theusRus.de Interactive Graphics ≠ Dynamic Graphics • Interactive Graphics … uses various interactions with the plots to change selections and parameters quickly. • Dynamic Graphics … uses animated / rotating plots to visualize high dimensional (continuous) data. -
Cluster Analysis Or Clustering Is a Common Technique for Statistical
IOSR Journal of Engineering Apr. 2012, Vol. 2(4) pp: 719-725 AN OVERVIEW ON CLUSTERING METHODS T. Soni Madhulatha Associate Professor, Alluri Institute of Management Sciences, Warangal. ABSTRACT Clustering is a common technique for statistical data analysis, which is used in many fields, including machine learning, data mining, pattern recognition, image analysis and bioinformatics. Clustering is the process of grouping similar objects into different groups, or more precisely, the partitioning of a data set into subsets, so that the data in each subset according to some defined distance measure. This paper covers about clustering algorithms, benefits and its applications. Paper concludes by discussing some limitations. Keywords: Clustering, hierarchical algorithm, partitional algorithm, distance measure, I. INTRODUCTION finding the length of the hypotenuse in a triangle; that is, it Clustering can be considered the most important is the distance "as the crow flies." A review of cluster unsupervised learning problem; so, as every other problem analysis in health psychology research found that the most of this kind, it deals with finding a structure in a collection common distance measure in published studies in that of unlabeled data. A cluster is therefore a collection of research area is the Euclidean distance or the squared objects which are “similar” between them and are Euclidean distance. “dissimilar” to the objects belonging to other clusters. Besides the term data clustering as synonyms like cluster The Manhattan distance function computes the analysis, automatic classification, numerical taxonomy, distance that would be traveled to get from one data point to botrology and typological analysis. the other if a grid-like path is followed.