Physical Sciences and Mathematics Commons^™

City Life - Inquiry And Problem Solving Exercise, Milena Cuellar

Open Educational Resources

No abstract provided.

What’S Brewing? A Statistics Education Discovery Project, Marla A. Sole, Sharon L. Weinberg

Publications and Research

We believe that students learn best, are actively engaged, and are genuinely interested when working on real-world problems. This can be done by giving students the opportunity to work collaboratively on projects that investigate authentic, familiar problems. This article shares one such project that was used in an introductory statistics course. We describe the steps taken to investigate why customers are charged more for iced coffee than hot coffee, which included collecting data and using descriptive and inferential statistical analysis. Interspersed throughout the article, we describe strategies that can help teachers implement the project and scaffold material to assist students …

Technology Design: The Movement Of Means, Yu Gu

Open Educational Resources

In order to promote students’ conceptual understanding and learning experience in introductory statistics, a technology task, which focuses on the probability distribution in which means are defined, was created using TinkerPlots, an exploratory dataanalysis and modeling software. The targeted audiences range from senior high school grade levels to college freshmen who are starting their introductory course in statistics. Students will be guided to explore and discover the movement behaviors of means of a set of numbers randomly generated from a fixed range of values characterized by a predetermined probability distribution. The cognitive, mathematical, technological and pedagogical natures of the task, …

Teaching Size And Power Properties Of Hypothesis Tests Through Simulations, Suleyman Taspinar, Osman Dogan

Publications and Research

In this study, we review the graphical methods suggested in Davidson and MacKinnon (Davidson, Russell, and James G. MacKinnon. 1998. “Graphical Methods for Investigating the Size and Power of Hypothesis Tests.” The Manchester School 66 (1): 1–26.) that can be used to investigate size and power properties of hypothesis tests for undergraduate and graduate econometrics courses. These methods can be used to assess finite sample properties of various hypothesis tests through simulation studies. In addition, these methods can be effectively used in classrooms to reinforce students’ understanding of basic hypothesis testing concepts such as Type I error, Type II error, …

Generalized Least-Powers Regressions I: Bivariate Regressions, Nataniel Greene

Publications and Research

The bivariate theory of generalized least-squares is extended here to least-powers. The bivariate generalized least-powers problem of order p seeks a line which minimizes the average generalized mean of the absolute pth power deviations between the data and the line. Least-squares regressions utilize second order moments of the data to construct the regression line whereas least-powers regressions use moments of order p to construct the line. The focus is on even values of p, since this case admits analytic solution methods for the regression coefficients. A numerical example shows generalized least-powers methods performing comparably to generalized least-squares methods, …

Implementing Some Basic Simuation Designs Using The Simsem Package In R, Keith A. Markus

Open Educational Resources

The purpose of this tutorial is to provide a very basic introduction to implementing three simple research designs using the simsem package in R. R is an open source statistical computing environment (R Core Team, 2015). For more information about R, see the R Project homepage (https://www.r-project.org/) and the Comprehensive R Archive Network (CRAN) web page (https://cran.r-project.org/). The lavaan package provides functions for fitting and evaluating structural equation models (Rosseel, 2012). For further information about the lavaan package including tutorials, see the lavaan Project web page (http://lavaan.ugent.be/). The simsem package (Pornprasertmanit, Miller & Schoemann, 2016) provides functions to facilitate structural …

An Early Assessment Of Medium Range Monsoon Precipitation Forecasts From The Latest High-Resolution Ncep-Gfs (T1534) Model Over South Asia, Satya Prakash, Imaranali M. Momin, Ashis K. Mitra, Partha S. Bhattacharjee, Fanglin Yang, Vijay Tallapragada

Publications and Research

Reliable prediction of the South Asian monsoon rainfall and its variability is crucial for various hydrological applications and early warning systems. The National Centers for Environmental Prediction – Global Forecast System (NCEP–GFS) is one of the popular global deterministic numerical weather prediction models, which is recently upgraded from T574 to T1534. In this paper, medium range monsoon precipitation forecasts from both the T1534 and T574 models are critically evaluated over the South Asia for the peak monsoon months (July and August) of 2015. Although both the versions of GFS model show similar large-scale monsoon rainfall patterns, the dry bias over …

A Preliminary Assessment Of Gpm-Based Multi-Satellite Precipitation Estimates Over A Monsoon Dominated Region, Satya Prakash, Ashis K. Mitra, Amir Aghakouchak, Zhong Liu, Hamidreza Norouzi, D. S. Pai

Publications and Research

Following the launch of the Global Precipitation Measurement (GPM) Core Observatory, two advanced high resolution multi-satellite precipitation products namely, Integrated Multi-satellitE Retrievals for GPM (IMERG) and Global Satellite Mapping of Precipitation (GSMaP) version 6 are released. A critical evaluation of these newly released precipitation data sets is very important for both the end users and data developers. This study provides a comprehensive assessment of IMERG research product and GSMaP estimates over India at a daily scale for the southwest monsoon season (June to September 2014). The GPM-based precipitation products are inter-compared with widely used TRMM Multi-satellite Precipitation Analysis (TMPA), and …

An Evolutionary Vaccination Game In The Modified Activity Driven Network By Considering The Closeness, Dun Han, Mei Sun

Publications and Research

In this paper, we explore an evolutionary vaccination game in the modified activity driven network by considering the closeness. We set a closeness parameter p which is used to describe the way of connection between two individuals. The simulation results show that the closeness p may have an active role in weakening both the spreading of epidemic and the vaccination. Besides, when vaccination is not allowed, the final recovered density increases with the value of the ratio of the infection rate to the recovery rate λ/μ. However, when vaccination is allowed the final density of recovered individual first increases and …

Time Series Analysis For Psychological Research: Examining And Forecasting Change, Andrew T. Jebb, Louis Tay, Wei Wang, Qiming Huang

Publications and Research

Psychological research has increasingly recognized the importance of integrating temporal dynamics into its theories, and innovations in longitudinal designs and analyses have allowed such theories to be formalized and tested. However, psychological researchers may be relatively unequipped to analyze such data, given its many characteristics and the general complexities involved in longitudinal modeling. The current paper introduces time series analysis to psychological research, an analytic domain that has been essential for understanding and predicting the behavior of variables across many diverse fields. First, the characteristics of time series data are discussed. Second, different time series modeling techniques are surveyed that …

Generalized Least-Squares Regressions V: Multiple Variables, Nataniel Greene

Publications and Research

The multivariate theory of generalized least-squares is formulated here using the notion of generalized means. The multivariate generalized least-squares problem seeks an m dimensional hyperplane which minimizes the average generalized mean of the square deviations between the data and the hyperplane in m + 1 variables. The numerical examples presented suggest that a multivariate generalized least-squares method can be preferable to ordinary least-squares especially in situations where the data are ill- conditioned.

Protein Sectors: Statistical Coupling Analysis Versus Conservation, Tiberiu Teşileanu, Lucy J. Colwell, Stanislas Leibler

Publications and Research

Statistical coupling analysis (SCA) is a method for analyzing multiple sequence alignments that was used to identify groups of coevolving residues termed “sectors”. The method applies spectral analysis to a matrix obtained by combining correlation information with sequence conservation. It has been asserted that the protein sectors identified by SCA are functionally significant, with different sectors controlling different biochemical properties of the protein. Here we reconsider the available experimental data and note that it involves almost exclusively proteins with a single sector. We show that in this case sequence conservation is the dominating factor in SCA, and can alone be …

Variation In Rheumatoid Hand And Wrist Surgery Among Medicare Beneficiaries: A Population-Based Cohort Study, Lin Zhong, Kevin C. Chung, Onur Baser, David A. Fox, Huseyin Yuce, Jennifer F. Waljee

Publications and Research

Objective. To examine the rate and variation in rheumatoid arthritis (RA)-related hand and wrist surgery among Medicare (elderly) beneficiaries in the United States, and to identify the patient and provider factors that influence surgical rates.

Methods. Using the 2006–2010 100% Medicare claims data of beneficiaries with RA diagnosis, we examined rates of rheumatoid hand and wrist arthroplasty, arthrodesis, and hand tendon reconstruction in the United States. We used multivariate logistic regression models to examine variation in receipt of surgery by patient and regional characteristics (density of providers, intensity of use of biologic disease-modifying antirheumatic drugs).

Results. Between 2006 and 2010, …

Generalized Least-Squares Regressions Iv: Theory And Classification Using Generalized Means, Nataniel Greene

Publications and Research

The theory of generalized least-squares is reformulated here using the notion of generalized means. The generalized least-squares problem seeks a line which minimizes the average generalized mean of the square deviations in x and y. The notion of a generalized mean is equivalent to the generating function concept of the previous papers but allows for a more robust understanding and has an already existing literature. Generalized means are applied to the task of constructing more examples, simplifying the theory, and further classifying generalized least-squares regressions.

Generalized Least-Squares Regressions Iii: Further Theory And Classification, Nataniel Greene

Publications and Research

This paper continues the work of this series with two results. The first is an exponential equivalence theorem which states that every generalized least-squares regression line can be generated by an equivalent exponential regression. It follows that every generalized least-squares line has an effective normalized exponential parameter between 0 and 1 which classifies the line on the spectrum between ordinary least-squares and the extremal line for a given set of data. The second result is the presentation of fundamental formulas for the generalized least-squares slope and y-intercept.

Stochastic Dea With A Perfect Object And Its Application To Analysis Of Environmental Efficiency, Alexander Vaninsky

Publications and Research

The paper introduces stochastic DEA with a Perfect Object (SDEA PO). The Perfect Object (PO) is a virtual Decision Making Unit (DMU) that has the smallest inputs and greatest outputs. Including the PO in a collection of actual objects yields an explicit formula of the efficiency index. Given the distributions of DEA inputs and outputs, this formula allows us to derive the probability distribution of the efficiency score, to find its mathematical expectation, and to deliver common (group–related) and partial (object-related) efficiency components. We apply this approach to a prospective analysis of environmental efficiency of the major national and regional …

Simulation Insights Using R, Boyan Kostadinov

Publications and Research

This article attempts to introduce the reader to computational thinking and solving problems involving randomness. The main technique being employed is the Monte Carlo method, using the freely available software R for Statistical Computing. The author illustrates the computer simulation approach by focusing on several problems of increasing difficulty. The simulation techniques and the specific problems discussed in this article would be of interest to STEM students and instructors, teaching courses in Monte Carlo simulations, stochastic modeling, probability and statistics. The R code for all problems is discussed in full detail so that the reader can get a taste of …

Generalized Least-Squares Regressions I: Efficient Derivations, Nataniel Greene

Publications and Research

Ordinary least-squares regression suffers from a fundamental lack of symmetry: the regression line of y given x and the regression line of x given y are not inverses of each other. Alternative symmetric regression methods have been developed to address this concern, notably: orthogonal regression and geometric mean regression. This paper presents in detail a variety of least squares regression methods which may not have been known or fully explicated. The derivation of each method is made efficient through the use of Ehrenberg's formula for the ordinary least-squares error and through the extraction of a weight function g(b) which characterizes …

Generalized Least-Squares Regressions Ii: Theory And Classification, Nataniel Greene

Publications and Research

In the first paper of this series, a variety of known and new symmetric and weighted least-squares regression methods were presented with efficient derivations. This paper continues and generalizes the previous work with a theory for deriving, analyzing, and classifying all symmetric and weighted least-squares regression methods.

Computational Insight With Monte Carlo Simulations, Boyan Kostadinov

Publications and Research

We introduce Monte Carlo simulations for estimating areas by playing a game of "darts". We also introduce simulations of random walks. We use compact, vectorized programming, based on the R language, for all computer simulations and visualizations, aimed at high school students. This presentation is based on the Invited, prime time lecture given at the summer camp for gifted high school students at City College of New York, July 13, 2011.

Neath Studies, Teaches The Uncertainties Of Life, Aldemaro Romero Jr.

Publications and Research

No abstract provided.

Statistician Recommends A Dose Of Skepticism, Aldemaro Romero Jr.

Publications and Research

No abstract provided.

Methods Of Assessing And Ranking Probable Sources Of Error, Nataniel Greene

Publications and Research

A classical method for ranking n potential events as sources of error is Bayes' theorem. However, a ranking based on Bayes' theorem lacks a fundamental symmetry: the ranking in terms of blame for error will not be the reverse of the ranking in terms of credit for lack of error. While this is not a flaw in Bayes' theorem, it does lead one to inquire whether there are related methods which have such symmetry. Related methods explored here include the logical version of Bayes' theorem based on probabilities of conditionals, probabilities of biconditionals, and ratios or differences of credit to …

An Overview Of Conditionals And Biconditionals In Probability, Nataniel Greene

Publications and Research

Conditional and biconditional statements are a standard part of symbolic logic but they have only recently begun to be explored in probability for applications in artificial intelligence. Here we give a brief overview of the major theorems involved and illustrate them using two standard model problems from conditional probability.

A Dynamic-Trend Exponential Smoothing Model, Don Miller, Dan Williams

Publications and Research

Forecasters often encounter situations in which the local pattern of a time series is not expected to persist over the forecasting horizon. Since exponential smoothing models emphasize recent behavior, their forecasts may not be appropriate over longer horizons. In this paper, we develop a new model in which the local trend line projected by exponential smoothing converges asymptotically to an assumed future long-run trend line, which might be an extension of a historical long-run trend line. The rapidity of convergence is governed by a parameter. A familiar example is an economic series exhibiting persistent long-run trend with cyclic variation. This …

Hierarchical Linear Modeling In Organizational Research: Longitudinal Data Outside The Context Of Growth Modeling, Irvin Sam Schonfeld, David Rindskopf

Publications and Research

Organizational researchers, including those carrying out occupational stress research, often conduct longitudinal studies. Hierarchical linear modeling (HLM; also known as multilevel modeling and random regression) can efficiently organize analyses of longitudinal data by including within- and between-person levels of analysis. A great deal of longitudinal research has been conducted in the context of growth studies in which change in the dependent variable is examined in relation to the passage of time. HLM can treat longitudinal data, including data outside the context of the growth study, as nested data, reducing the problem of censoring. Within-person equation coefficients can represent the impact …

Level Adjusted Exponential Smoothing: A Method For Judgmentally Adjusting Exponential Smoothing Models For Planned Discontinuities, Dan Williams, Don Miller

Publications and Research

Forecasters often make judgmental adjustments to exponential smoothing forecasts to account for the effects of a future planned change. While this approach may produce sound initial forecasts, it can result in diminished accuracy for forecast updates. A proposed technique lets the forecaster include policy change adjustments within an exponential smoothing model. For 20 real data series representing Virginia Medicaid expenses, initial forecasts and forecast updates are developed using the proposed technique and several alternatives, and they are updated through various simulated level shifts. The proposed technique was more accurate than the alternatives in updating forecasts when a shift in level …

Performance Indices For On-Ice Hockey Statistics, William (Bill) H. Williams

Publications and Research

No abstract provided.

Generating Unbiased Ratio And Regression Estimators, William (Bill) H. Williams

Publications and Research

Standard ratio and regression are only conditionally unbiased. The paper uses split sample techniques to develop unbiased versions.

How Bad Can Good Data Really Be?, William (Bill) H. Williams

Publications and Research

Bias has different sources. Measurement errors create "bad" data and biased estimates. But selection biases occur even with "good" data and can be both subtle and large in magnitude.