HMH ASSESSMENTS Glossary of Testing, Measurement, and Statistical Terms
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Multiple Linear Regression
Multiple Linear Regression The MULTIPLE LINEAR REGRESSION command performs simple multiple regression using least squares. Linear regression attempts to model the linear relationship between variables by fitting a linear equation to observed data. One variable is considered to be an explanatory variable (RESPONSE), and the others are considered to be dependent variables (PREDICTORS). How To Run: STATISTICS->REGRESSION->MULTIPLE LINEAR REGRESSION... Select DEPENDENT (RESPONSE) variable and INDEPENDENT variables (PREDICTORS). To force the regression line to pass through the origin use the CONSTANT (INTERCEPT) IS ZERO option from the ADVANCED OPTIONS. Optionally, you can add following charts to the report: o Residuals versus predicted values plot (use the PLOT RESIDUALS VS. FITTED option); o Residuals versus order of observation plot (use the PLOT RESIDUALS VS. ORDER option); o Independent variables versus the residuals (use the PLOT RESIDUALS VS. PREDICTORS option). For the univariate model, the chart for the predicted values versus the observed values (LINE FIT PLOT) can be added to the report. Use THE EMULATE EXCEL ATP FOR STANDARD RESIDUALS option to get the same standard residuals as produced by Excel Analysis Toolpak. Results Regression statistics, analysis of variance table, coefficients table and residuals report are produced. Regression Statistics 2 R (COEFFICIENT OF DETERMINATION, R-SQUARED) is the square of the sample correlation coefficient between 2 the PREDICTORS (independent variables) and RESPONSE (dependent variable). In general, R is a percentage of response variable variation that is explained by its relationship with one or more predictor variables. In simple words, the R2 indicates the accuracy of the prediction. The larger the R2 is, the more the total 2 variation of RESPONSE is explained by predictors or factors in the model. -
The Statistical Analysis of Distributions, Percentile Rank Classes and Top-Cited
How to analyse percentile impact data meaningfully in bibliometrics: The statistical analysis of distributions, percentile rank classes and top-cited papers Lutz Bornmann Division for Science and Innovation Studies, Administrative Headquarters of the Max Planck Society, Hofgartenstraße 8, 80539 Munich, Germany; [email protected]. 1 Abstract According to current research in bibliometrics, percentiles (or percentile rank classes) are the most suitable method for normalising the citation counts of individual publications in terms of the subject area, the document type and the publication year. Up to now, bibliometric research has concerned itself primarily with the calculation of percentiles. This study suggests how percentiles can be analysed meaningfully for an evaluation study. Publication sets from four universities are compared with each other to provide sample data. These suggestions take into account on the one hand the distribution of percentiles over the publications in the sets (here: universities) and on the other hand concentrate on the range of publications with the highest citation impact – that is, the range which is usually of most interest in the evaluation of scientific performance. Key words percentiles; research evaluation; institutional comparisons; percentile rank classes; top-cited papers 2 1 Introduction According to current research in bibliometrics, percentiles (or percentile rank classes) are the most suitable method for normalising the citation counts of individual publications in terms of the subject area, the document type and the publication year (Bornmann, de Moya Anegón, & Leydesdorff, 2012; Bornmann, Mutz, Marx, Schier, & Daniel, 2011; Leydesdorff, Bornmann, Mutz, & Opthof, 2011). Until today, it has been customary in evaluative bibliometrics to use the arithmetic mean value to normalize citation data (Waltman, van Eck, van Leeuwen, Visser, & van Raan, 2011). -
(QQ-Plot) and the Normal Probability Plot Section
MAT 2377 (Winter 2012) Quantile-Quantile Plot (QQ-plot) and the Normal Probability Plot Section 6-6 : Normal Probability Plot Goal : To verify the underlying assumption of normality, we want to compare the distribution of the sample to a normal distribution. Normal Population : Suppose that the population is normal, i.e. X ∼ N(µ, σ2). Thus, X − µ 1 µ Z = = X − ; σ σ σ where Z ∼ N(0; 1). Hence, there is a linear association between a normal variable and a standard normal random variable. If our sample is randomly selected from a normal population, then we should be able to observer this linear association. Consider a random sample of size n : x1; x2; : : : ; xn. We will obtain the order statistics (i.e. order the values in an ascending order) : y1 ≤ y2 ≤ ::: ≤ yn: We will compare the order statistics (called sample quantiles) to quantiles from a standard normal distribution N(0; 1). We rst need to compute the percentile rank of the ith order statistic. In practice (within the context of QQ-plots), it is computed as follows i − 3=8 i − 1=2 p = or (alternatively) p = : i n + 1=4 i n Consider yi, we will compare it to a lower quantile zi of order pi from N(0; 1). We get −1 zi = Φ (pi) : 1 The plot of zi against yi (or alternatively of yi against zi) is called a quantile- quantile plot or QQ-plot If the data are normal, then it should exhibit a linear tendency. To help visualize the linear tendency we can overlay the following line 1 x z = x + ; s s where x is the sample mean and s is the sample standard deviation. -
Test Scores Explanation for Parents and Teachers: Youtube Video Script by Lara Langelett July 2019 1
Test Scores Explanation for Parents and Teachers: YouTube Video Script By Lara Langelett July 2019 1 Introduction: Hello Families and Teachers. My name is Lara Langelett and I would like to teach you about how to read your child’s or student’s test scores. The purpose of this video message is to give you a better understanding of standardized test scores and to be able to apply it to all normed assessment tools. First I will give a definition of what the bell curve is by using a familiar example. Then I will explain the difference between a percentile rank and percentage. Next, I will explain Normed-Referenced Standard test scores. In addition, the MAPs percentile rank and the RIT scores will be explained. Finally, I will explain IQ scores on the bell curve. 2 Slide 1: Let’s get started: here is a bell curve; it is shaped like a bell. 3 Slide 2: To understand the Bell Curve, we will look at a familiar example of basketball players in the U.S.A. Everyone, on this day, who plays basketball fits into this bell curve around the United States. I’m going to emphasis “on this day” as this is important piece information of for explaining standardized scores. 4 Slide 3: On the right side of the bell curve we can section off a part of the bell curve (2.1 % blue area). Inside this section are people who play basketball at the highest skill level, like the U.S. Olympic basketball team. These athletes are skilled athletes who have played basketball all their life, practice on a daily basis, have extensive knowledge of the game, and are at a caliber that the rest of the basketball population have not achieved. -
Measures of Center
Statistics is the science of conducting studies to collect, organize, summarize, analyze, and draw conclusions from data. Descriptive statistics consists of the collection, organization, summarization, and presentation of data. Inferential statistics consist of generalizing form samples to populations, performing hypothesis tests, determining relationships among variables, and making predictions. Measures of Center: A measure of center is a value at the center or middle of a data set. The arithmetic mean of a set of values is the number obtained by adding the values and dividing the total by the number of values. (Commonly referred to as the mean) x x x = ∑ (sample mean) µ = ∑ (population mean) n N The median of a data set is the middle value when the original data values are arranged in order of increasing magnitude. Find the center of the list. If there are an odd number of data values, the median will fall at the center of the list. If there is an even number of data values, find the mean of the middle two values in the list. This will be the median of this data set. The symbol for the median is ~x . The mode of a data set is the value that occurs with the most frequency. When two values occur with the same greatest frequency, each one is a mode and the data set is bimodal. Use M to represent mode. Measures of Variation: Variation refers to the amount that values vary among themselves or the spread of the data. The range of a data set is the difference between the highest value and the lowest value. -
How to Use MGMA Compensation Data: an MGMA Research & Analysis Report | JUNE 2016
How to Use MGMA Compensation Data: An MGMA Research & Analysis Report | JUNE 2016 1 ©MGMA. All rights reserved. Compensation is about alignment with our philosophy and strategy. When someone complains that they aren’t earning enough, we use the surveys to highlight factors that influence compensation. Greg Pawson, CPA, CMA, CMPE, chief financial officer, Women’s Healthcare Associates, LLC, Portland, Ore. 2 ©MGMA. All rights reserved. Understanding how to utilize benchmarking data can help improve operational efficiency and profits for medical practices. As we approach our 90th anniversary, it only seems fitting to celebrate MGMA survey data, the gold standard of the industry. For decades, MGMA has produced robust reports using the largest data sets in the industry to help practice leaders make informed business decisions. The MGMA DataDive® Provider Compensation 2016 remains the gold standard for compensation data. The purpose of this research and analysis report is to educate the reader on how to best use MGMA compensation data and includes: • Basic statistical terms and definitions • Best practices • A practical guide to MGMA DataDive® • Other factors to consider • Compensation trends • Real-life examples When you know how to use MGMA’s provider compensation and production data, you will be able to: • Evaluate factors that affect compensation andset realistic goals • Determine alignment between medical provider performance and compensation • Determine the right mix of compensation, benefits, incentives and opportunities to offer new physicians and nonphysician providers • Ensure that your recruitment packages keep pace with the market • Understand the effects thatteaching and research have on academic faculty compensation and productivity • Estimate the potential effects of adding physicians and nonphysician providers • Support the determination of fair market value for professional services and assess compensation methods for compliance and regulatory purposes 3 ©MGMA. -
The Normal Distribution Introduction
The Normal Distribution Introduction 6-1 Properties of the Normal Distribution and the Standard Normal Distribution. 6-2 Applications of the Normal Distribution. 6-3 The Central Limit Theorem The Normal Distribution (b) Negatively skewed (c) Positively skewed (a) Normal A normal distribution : is a continuous ,symmetric , bell shaped distribution of a variable. The mathematical equation for the normal distribution: 2 (x)2 2 f (x) e 2 where e ≈ 2 718 π ≈ 3 14 µ ≈ population mean σ ≈ population standard deviation A normal distribution curve depend on two parameters . µ Position parameter σ shape parameter Shapes of Normal Distribution 1 (1) Different means but same standard deviations. Normal curves with μ1 = μ2 and 2 σ1<σ2 (2) Same means but different standard deviations . (3) Different 3 means and different standard deviations . Properties of the Normal Distribution The normal distribution curve is bell-shaped. The mean, median, and mode are equal and located at the center of the distribution. The normal distribution curve is unimodal (single mode). The curve is symmetrical about the mean. The curve is continuous. The curve never touches the x-axis. The total area under the normal distribution curve is equal to 1 (or 100%). The area under the normal curve that lies within Empirical Rule one standard deviation of the mean is approximately 0.68 (68%). two standard deviations of the mean is approximately 0.95 (95%). three standard deviations of the mean is approximately 0.997 (99.7%). ** Suppose that the scores on a history exam have a mean of 70. If these scores are normally distributed and approximately 95% of the scores fall in (64,76), then the standard deviation is …. -
Understanding Test Scores a Primer for Parents
Understanding Test Scores A primer for parents... Norm-Referenced Tests Norm-referenced tests compare an individual child's performance to that of his or her classmates or some other, larger group. Such a test will tell you how your child compares to similar children on a given set of skills and knowledge, but it does not provide information about what the child does and does not know. Scores on norm-referenced tests indicate the student's ranking relative to that group. Typical scores used with norm-referenced tests include: Percentiles. Percentiles are probably the most commonly used test score in education. A percentile is a score that indicates the rank of the student compared to others (same age or same grade), using a hypothetical group of 100 students. A percentile of 25, for example, indicates that the student's test performance equals or exceeds 25 out of 100 students on the same measure; a percentile of 87 indicates that the student equals or surpasses 87 out of 100 (or 87% of) students. Note that this is not the same as a "percent"-a percentile of 87 does not mean that the student answered 87% of the questions correctly! Percentiles are derived from raw scores using the norms obtained from testing a large population when the test was first developed. Standard scores. A standard score is derived from raw scores using the norming information gathered when the test was developed. Instead of reflecting a student's rank compared to others, standard scores indicate how far above or below the average (the "mean") an individual score falls, using a common scale, such as one with an "average" of 100. -
Ch6: the Normal Distribution
Ch6: The Normal Distribution Introduction Review: A continuous random variable can assume any value between two endpoints. Many continuous random variables have an approximately normal distribution, which means we can use the distribution of a normal random variable to make statistical inference about the variable. CH6: The Normal Distribution Santorico - Page 175 Example: Heights of randomly selected women CH6: The Normal Distribution Santorico - Page 176 Section 6-1: Properties of a Normal Distribution A normal distribution is a continuous, symmetric, bell-shaped distribution of a variable. The theoretical shape of a normal distribution is given by the mathematical formula (x)2 e 2 2 y , 2 where and are the mean and standard deviations of the probability distribution, respectively. Review: The and are parameters and hence describe the population . CH6: The Normal Distribution Santorico - Page 177 The shape of a normal distribution is fully characterized by its mean and standard deviation . specifies the location of the distribution. specifies the spread/shape of the distribution. CH6: The Normal Distribution Santorico - Page 178 CH6: The Normal Distribution Santorico - Page 179 Properties of the Theoretical Normal Distribution A normal distribution curve is bell-shaped. The mean, median, and mode are equal and are located at the center of the distribution. A normal distribution curve is unimodal. The curve is symmetric about the mean. The curve is continuous (no gaps or holes). The curve never touches the x-axis (just approaches it). The total area under a normal distribution curve is equal to 1.0 or 100%. Review: The Empirical Rule applies (68%-95%-99.7%) CH6: The Normal Distribution Santorico - Page 180 CH6: The Normal Distribution Santorico - Page 181 The Standard Normal Distribution Since each normally distributed variable has its own mean and standard deviation, the shape and location of these curves will vary. -
4. Descriptive Statistics
4. Descriptive statistics Any time that you get a new data set to look at one of the first tasks that you have to do is find ways of summarising the data in a compact, easily understood fashion. This is what descriptive statistics (as opposed to inferential statistics) is all about. In fact, to many people the term “statistics” is synonymous with descriptive statistics. It is this topic that we’ll consider in this chapter, but before going into any details, let’s take a moment to get a sense of why we need descriptive statistics. To do this, let’s open the aflsmall_margins file and see what variables are stored in the file. In fact, there is just one variable here, afl.margins. We’ll focus a bit on this variable in this chapter, so I’d better tell you what it is. Unlike most of the data sets in this book, this is actually real data, relating to the Australian Football League (AFL).1 The afl.margins variable contains the winning margin (number of points) for all 176 home and away games played during the 2010 season. This output doesn’t make it easy to get a sense of what the data are actually saying. Just “looking at the data” isn’t a terribly effective way of understanding data. In order to get some idea about what the data are actually saying we need to calculate some descriptive statistics (this chapter) and draw some nice pictures (Chapter 5). Since the descriptive statistics are the easier of the two topics I’ll start with those, but nevertheless I’ll show you a histogram of the afl.margins data since it should help you get a sense of what the data we’re trying to describe actually look like, see Figure 4.2. -
Norms and Scores Sharon Cermak
Chapter 5 Norms and Scores Sharon Cermak There are three kinds of lies: lies, damned lies, and statistics. - Disraeli INTRODUCTION Suppose that on the Bayley Scales of Infant Development,' Ken- dra, age 14 months, received a score of 97 on the Mental Scale and 44 on the Motor Scale. Does this mean that her mental abilities are in the average range? Does it mean that she is motorically retarded? Does it mean that her mental abilities are twice as good as her motor abilities? The numbers reported are raw scores and reflect the number of items that Kendra passed. Since there are many more items on the Mental Scale than on the Motor Scale, it is expected that her raw score on this scale would be higher. These numbers are called raw scores and cannot be interpreted. It is not known what their relation- ship is to each other, or what they signify relative to the average child of comparable age. Raw scores can be interpreted only in terms of a clearly defined and uniform frame of reference. The frame of reference in interpreting a child's scores is based upon the scoring system which is used on the test. Scores on psychological, educational, developmental, and per- Sharon Cerrnak, EdD, OTR, is Associate Professor of Occupational Therapy at Sargent College of Allied Health Professions, Boston University, University Road, Boston, MA 02215. O 1989 by The Haworth Press, Inc. All rights reserved. 91 92 DEVELOPING NORM-REFERENCED STANDARDIZED TESTS ceptual tests are generally interpreted by reference to nom. Norms represent the test performance of the standardization sample. -
Which Percentile-Based Approach Should Be Preferred for Calculating
Accepted for publication in the Journal of Informetrics Which percentile-based approach should be preferred for calculating normalized citation impact values? An empirical comparison of five approaches including a newly developed citation-rank approach (P100) Lutz Bornmann,# Loet Leydesdorff,* and Jian Wang§+ # Division for Science and Innovation Studies Administrative Headquarters of the Max Planck Society Hofgartenstr. 8, 80539 Munich, Germany. E-mail: [email protected] * Amsterdam School of Communication Research (ASCoR), University of Amsterdam, Kloveniersburgwal 48, 1012 CX Amsterdam, The Netherlands. Email: [email protected] § Institute for Research Information and Quality Assurance (iFQ) Schützenstraße 6a, 10117 Berlin, Germany. + Center for R&D Monitoring (ECOOM) and Department of Managerial Economics, Strategy and Innovation, Katholieke Universiteit Leuven, Waaistraat 6, 3000 Leuven, Belgium. Email: [email protected] Abstract For comparisons of citation impacts across fields and over time, bibliometricians normalize the observed citation counts with reference to an expected citation value. Percentile-based approaches have been proposed as a non-parametric alternative to parametric central-tendency statistics. Percentiles are based on an ordered set of citation counts in a reference set, whereby the fraction of papers at or below the citation counts of a focal paper is used as an indicator for its relative citation impact in the set. In this study, we pursue two related objectives: (1) although different percentile-based approaches have been developed, an approach is hitherto missing that satisfies a number of criteria such as scaling of the percentile ranks from zero (all other papers perform better) to 100 (all other papers perform worse), and solving the problem with tied citation ranks unambiguously.