DOCSLIB.ORG

Stochastic Algorithms for Biochemical Processes

Total Page：16

File Type：pdf, Size：1020Kb

Download full-text PDF Read full-text
Stochastic Algorithms for Biochemical Processes UNIVERSITA` DEGLI STUDI DI MILANO BICOCCA Facolt`adi Scienze MM.FF.NN. Dottorato di Ricerca in Informatica XXII Ciclo Stochastic algorithms for biochemical processes Paolo Cazzaniga Supervisor Prof. Giancarlo Mauri Tutor Prof. Paola Bonizzoni PhD Coordinator Prof. Stefania Bandini ANNO ACCADEMICO 2008–2009 iii Acknowledgments I would like to express my sincere gratitude to Professor Giancarlo Mauri who has been my supervisor. He gave me many helpful suggestions and important advice during the course of my PhD. Special thanks are due to Daniela Besozzi for her constant encourage- ment, her useful help (on many occasions) and her friendship. I would also like to thank Dario Pescini for his assistance with writing code, his great effort to explain things and for all the last minute rushes to airports and train stations because we were always late. A particular thanks to Prof. Stephen Gilmore and Jane Hillston who hosted me for 6 months in Edinburgh. And I should also say thank you to my flatmates, the guys working at the LFCS and all the other people I met there. I wish to thank the people working at DISCo for their friendship, help and for the parties we had. I am grateful to the people who helped me during my PhD, and to my friends for the fun and laughter we shared. Indeed, I owe a special thanks to my family for its support during this period and to Laura who believed in me and supported me throughout my PhD. Contents Introduction ix 1 Stochastic algorithms for the simulation of biochemical sys- tems 1 1.1 Gillespie’s stochastic simulation algorithm . ... 2 1.2 Thenextreactionmethod . 6 1.3 The tau-leaping algorithm . 11 1.4 Thenextsubvolumemethod . 16 1.5 The binomial tau-leap spatial stochastic simulation algorithm 20 1.6 Otheralgorithms ......................... 25 2 Optimization algorithms 29 2.1 Geneticalgorithms . 30 2.2 Particle swarm optimizer . 37 3 Membrane systems 45 3.1 Basic notions of membrane systems . 46 3.2 Dynamical probabilistic P systems . 52 3.3 A DPP application: metapopulation systems . 58 3.3.1 Themodellingframework . 60 3.3.2 Simulations and results . 66 3.3.3 Discussion......................... 72 4 τ–DPP 75 4.1 Tau-leapingprocedureinDPPs . 76 4.2 τ-DPPalgorithm ......................... 80 4.3 A test case for τ-DPP ...................... 84 4.4 τ-DPP with size associated to volumes and objects . 84 4.5 A test case for Sτ-DPP ..................... 90 4.6 Implementation of the algorithms . 94 4.7 Discussion and future developments . 96 v Contents 5 Modelling chemical and biological systems 99 5.1 The Ras/cAMP/PKA signalling pathway in the yeast Sac- charomyces cerevisiae ......................101 5.1.1 The Ras/cAMP/PKA pathway description . 101 5.1.2 Thestochasticmodel. 103 5.1.3 The Ras2 • GTP generation module . 106 5.1.4 Generation of cAMP, coupling with PKA and feed- backloops.........................107 5.1.5 Discussion......................... 110 5.2 The repressilator: a genetic oscillators coupled with a quorum sensingmechanism . 113 5.2.1 A multivolume model for coupled genetic oscillators . 114 5.2.2 Results of simulations . 116 5.2.3 Discussion and future developments . 121 5.3 First steps toward a wet implementation for τ-DPP . 122 5.3.1 Chemical computing . 123 5.3.2 Definition and simulation of component reaction net- works using τ-DPP....................125 5.3.2.1 The NAND and XOR logic circuits . 126 5.3.2.2 Fredkin gates and circuits . 130 5.3.2.3 The SUB instruction . 138 5.3.2.4 The SUBADD module . 140 5.3.3 Discussion and open problems . 141 5.4 A study on the combined interplay between stochastic fluc- tuations and the number of flagella in bacterial chemotaxis . 144 5.4.1 The modeling of bacterial chemotaxis . 145 5.4.2 Stochastic simulations of chemotactic response regulator149 5.4.3 The interplay between stochastic fluctuations and the number of bacterial flagella . 153 5.4.4 Discussion......................... 157 6 The role of parameters in chemical and biological systems 161 6.1 Parameter estimation of biochemical systems . 163 6.2 Parameter sweep application . 165 6.3 Fitnessfunction. 166 6.4 A comparison of GAs and PSO for parameter estimation in stochastic biochemical systems . 169 6.4.1 Systems of biochemical reactions . 169 6.4.2 GAs and PSO settings . 171 6.4.3 Experimental results . 172 6.4.4 Discussion......................... 176 6.5 Stochastic simulations on a grid framework for parameter sweep applications in biological models . 178 6.5.1 TheEGEEgridplatform . 179 vi Contents 6.5.2 PSAoverthegrid . 180 6.5.3 Bacterial chemotaxis: a case study . 183 6.5.4 Results ..........................184 6.5.5 Performance discussion . 187 6.5.6 Conclusion ........................193 7 Conclusion and future work 195 Bibliography 201 vii Introduction Aims and motivations After the completion of the human genome sequencing (and of a lot of other genomes), the main challenge for the modern biology is to understand com- plex biological processes such as metabolic pathways, gene regulatory net- works and cell signalling pathways, which are the basis of the functioning of living cells. This goal can only be achieved by using mathematical modelling tools and computer simulation techniques, to integrate experimental data and to make predictions on the system behaviour that will be then exper- imentally checked, so as to gain insights into the working and the general principles of organization of biological systems. In fact, the formal modelling of biological systems allows the develop- ment of simulators, which can be used to understand how the described sys- tem behaves in normal conditions, and how it reacts to (simulated) changes in the environment or to alterations of some of its components. Simulations present many advantages over conventional experimental biology in terms of cost, ease to use and speed. For instance, some experiments that are infeasible in vivo can be conducted in silico, e.g. it is possible to knock out many vital genes from the cells and monitor their individual and collective impact on cellular metabolism. Evidently such experiments cannot be done in vivo because the cell may not survive. Therefore, the development of pre- dictive in silico models offers opportunities for unprecedented control over the system. In the last few years a wide variety of models of cellular processes have been proposed, based on different formalisms. For example, chemical kinetic models attempt to represent a cellular process as a system of distinct chemi- cal reactions. In this case, the network state is defined by the instantaneous quantity (or concentration) of each molecular species of interest in the cell, and different molecular species may interact via one or more reactions. Usu- ally, reactions are represented by a system of coupled differential equations that relate the quantity of reactants to the quantity of products, according to a reaction rate and other parameters. Recently, it has been pointed out that transcription, translation and other cellular processes may not behave deterministically but instead are ix Introduction: aims and motivations better modelled as random events [123]. Several models address this concern by abandoning differential equations in favour of stochastic relations that describe each chemical reaction in terms of molecular collisions [6, 74]. The use of stochastic methods for the study of biological systems is motivated by the fact that these systems are usually composed by many chemical interactions among a large number of chemical species, whereby the molecular quantities involved can be small (few tens of molecules). In systems having these characteristics, noise plays a major role in the system’s dynamics [128]. Two different kind of noise can be identified in biological systems: ex- trinsic and intrinsic [59, 176]. The first one is related to the experimental conditions; for instance, the variation of temperature, pressure, light, or fluctuations of other cellular factors, are all sources of extrinsic noise. On the other hand, there are stochastic events occurring during the processes of gene expression, at the level of transcription, translation and protein degra- dation, which result in intrinsic noise. The role of noise in biological systems has been studied and quantified [59, 176, 192], proving that the classic deterministic and continuous ap- proach (like, for instance, ordinary differential equations) is unsuitable for the modelling, simulation and analysis of phenomena like cellular pathways, especially when the gene transcription and translation machinery is involved. The deterministic approach is based on the law of mass action, an empir- ical law which provides a simple relation between reaction rates and molec- ular species concentrations. Given the initial molecular concentrations, by using the law of mass action, a temporal description of the component con- centrations can be obtained. The law of mass action considers chemical reactions to be macroscopic, continuous and deterministic. However, in the study of “small” systems, the law of mass action becomes inadequate, and it more is suitable to apply stochastic approaches, since (1) they take into account the discreteness of the quantity of the molecular species and the inherently random character of the phenomena; (2) they are in accordance with the theories of thermodynamics and stochastic processes; and (3) they are appropriate for the description of systems characterised by instability phenomena [198]. On the other hand, one major problem related to stochastic methods is that they are difficult to implement analytically; hence, they are im- plemented by means of numerical simulations whose computation time is usually very expensive. In this thesis we provide a discrete and stochastic framework for the modelling, simulation and analysis of biological and chemical systems. To this aim, we will start from the description of other techniques and meth- ods that are present in literature, as the basis to build and compare our approach.
Load more

Recommended publications
  • Ocr IB 1967 '70
    ocr IB 1967 '70 OAK RIDGE NATIONAL LABORATORY operated by UNION CARBIDE CORPORATION NUCLEAR DIVISION for the • U.S. ATOMIC ENERGY COMMISSION ORNL - TM- 1919 INDICES OF QUALITATIVE VARIATION Allen R. Wilcox NOTICE This document contains information of a preliminary natur<> and was prepared primarily far internal use at the Oak Ridge National Laboratory. It is subject to revision or correction and therefore doe> not represent o finol report. DISCLAIMER This report was prepared as an account of work sponsored by an agency of the United States Government. Neither the United States Government nor any agency Thereof, nor any of their employees, makes any warranty, express or implied, or assumes any legal liability or responsibility for the accuracy, completeness, or usefulness of any information, apparatus, product, or process disclosed, or represents that its use would not infringe privately owned rights. Reference herein to any specific commercial product, process, or service by trade name, trademark, manufacturer, or otherwise does not necessarily constitute or imply its endorsement, recommendation, or favoring by the United States Government or any agency thereof. The views and opinions of authors expressed herein do not necessarily state or reflect those of the United States Government or any agency thereof. DISCLAIMER Portions of this document may be illegible in electronic image products. Images are produced from the best available original document. .-------------------LEGAL NOTICE--------------~ This report was prepared as on account of Government sponsored work. Neither the United States, nor the Commission, nor any person acting on behalf of the Commission: A. Makes any warranty or representation, expressed or implied, with respect to the accuracy, compl""t"'n~<~~:oo;, nr ulltf!fulnes!l: of the information conto1ned in this report, or that the use of any information, apparatus, method, or process disc lased in this report may not infringe privately ownsd rights; or B.
    [Show full text]
  • Current Practices in Quantitative Literacy © 2006 by the Mathematical Association of America (Incorporated)
    Current Practices in Quantitative Literacy © 2006 by The Mathematical Association of America (Incorporated) Library of Congress Catalog Card Number 2005937262 Print edition ISBN: 978-0-88385-180-7 Electronic edition ISBN: 978-0-88385-978-0 Printed in the United States of America Current Printing (last digit): 10 9 8 7 6 5 4 3 2 1 Current Practices in Quantitative Literacy edited by Rick Gillman Valparaiso University Published and Distributed by The Mathematical Association of America The MAA Notes Series, started in 1982, addresses a broad range of topics and themes of interest to all who are in- volved with undergraduate mathematics. The volumes in this series are readable, informative, and useful, and help the mathematical community keep up with developments of importance to mathematics. Council on Publications Roger Nelsen, Chair Notes Editorial Board Sr. Barbara E. Reynolds, Editor Stephen B Maurer, Editor-Elect Paul E. Fishback, Associate Editor Jack Bookman Annalisa Crannell Rosalie Dance William E. Fenton Michael K. May Mark Parker Susan F. Pustejovsky Sharon C. Ross David J. Sprows Andrius Tamulis MAA Notes 14. Mathematical Writing, by Donald E. Knuth, Tracy Larrabee, and Paul M. Roberts. 16. Using Writing to Teach Mathematics, Andrew Sterrett, Editor. 17. Priming the Calculus Pump: Innovations and Resources, Committee on Calculus Reform and the First Two Years, a subcomit- tee of the Committee on the Undergraduate Program in Mathematics, Thomas W. Tucker, Editor. 18. Models for Undergraduate Research in Mathematics, Lester Senechal, Editor. 19. Visualization in Teaching and Learning Mathematics, Committee on Computers in Mathematics Education, Steve Cunningham and Walter S.
    [Show full text]
  • Measuring Variation for Nominal Data
    Bulletin ofthe Psychonomic Society 1988. 26 (5), 433-436 Measuring variation for nominal data TARALD O. KVALSETH University of Minnesota , Minneapolis, Minnesota This paper is concerned with the measurement of variation or dispersion for nominal categori­ cal data. A new measure of such variation is proposed. It is defined as the complement of the standard deviation of the individual category frequencies from the modal frequency. Large-sample distribution methods are developed for constructing confidence intervals and testing hypotheses for the equivalent population measure of variation. Numerical sample data are used to exem­ plify the statistical inference methods. For measuring the variation or dispersion in a set of measures, the IQV in Equation 2 appears to be the most nominal data, a number ofalternative measures have been widely accepted, especially in the social sciences (e.g., defined in the literature. Such measures are generally Ott, Mendenhall, & Larson, 1978, pp. 110-113). The functions ofthe absolute frequencies or counts nh n2, . .. , measure in Equation 3, which is based on Shannon's n, for a set of I categories that are exhaustive and mutu­ (1948) entropy in information theory, has been used quite ally exclusive. Thus, among the total number ofn = Elnl extensively in the biological sciences (Pielou, 1977). observations (individuals or items), n, observations be­ The measure MOM in Equation 1 suffers from one seri­ long to category i, with each observation belonging to one ous limitation: its value is determined exclusively by the and only one category. Among the best known variation relative modal frequency nm/n and I (the number of measures for the n, (i = 1, 2, .
    [Show full text]
  • KOF Working Papers, No
    A Service of Leibniz-Informationszentrum econstor Wirtschaft Leibniz Information Centre Make Your Publications Visible. zbw for Economics Maag, Thomas Working Paper On the accuracy of the probability method for quantifying beliefs about inflation KOF Working Papers, No. 230 Provided in Cooperation with: KOF Swiss Economic Institute, ETH Zurich Suggested Citation: Maag, Thomas (2009) : On the accuracy of the probability method for quantifying beliefs about inflation, KOF Working Papers, No. 230, ETH Zurich, KOF Swiss Economic Institute, Zurich, http://dx.doi.org/10.3929/ethz-a-005859391 This Version is available at: http://hdl.handle.net/10419/50407 Standard-Nutzungsbedingungen: Terms of use: Die Dokumente auf EconStor dürfen zu eigenen wissenschaftlichen Documents in EconStor may be saved and copied for your Zwecken und zum Privatgebrauch gespeichert und kopiert werden. personal and scholarly purposes. Sie dürfen die Dokumente nicht für öffentliche oder kommerzielle You are not to copy documents for public or commercial Zwecke vervielfältigen, öffentlich ausstellen, öffentlich zugänglich purposes, to exhibit the documents publicly, to make them machen, vertreiben oder anderweitig nutzen. publicly available on the internet, or to distribute or otherwise use the documents in public. Sofern die Verfasser die Dokumente unter Open-Content-Lizenzen (insbesondere CC-Lizenzen) zur Verfügung gestellt haben sollten, If the documents have been made available under an Open gelten abweichend von diesen Nutzungsbedingungen die in der dort Content Licence (especially Creative Commons Licences), you genannten Lizenz gewährten Nutzungsrechte. may exercise further usage rights as specified in the indicated licence. www.econstor.eu KOF Working Papers On the Accuracy of the Probability Method for Quantifying Beliefs about Inflation Thomas Maag No.
    [Show full text]
  • Media Diversity and the Analysis of Qualitative Variation
    Media diversity and the analysis of qualitative variation David Deacon & James Stanyer CENTRE FOR RESEARCH IN COMMUNICATION AND CULTURE, LOUGHBOROUGH UNIVERSITY January 2019 1 Abstract Diversity is recognised as a significant criterion for appraising the democratic performance of media systems. This article begins by considering key conceptual debates that help differentiate types and levels of diversity. It then addresses one of the core methodological challenges in measuring diversity: how do we model statistical variation and difference when many measures of source and content diversity only attain the nominal level of measurement? We identify a range of obscure statistical indices developed in other fields that measure the strength of ‘qualitative variation’. Using original data, we compare the performance of five diversity indices and, on this basis, propose the creation of a more effective diversity average measure (DIVa). The article concludes by outlining innovative strategies for drawing statistical inferences from these measures, using bootstrapping and permutation testing resampling. All statistical procedures are supported by a unique online resource developed with this article. Key word: Media diversity, diversity indices, qualitative variation, categorical data Acknowledgements We wish to thank Orange Gao and Peter Dean of Business Intelligence and Strategy Ltd and Dr Adrian Leguina, School of Social Sciences, Loughborough University for their assistance in developing the conceptual and technical aspects of this paper. 2 Introduction Concerns about diversity are at the heart of discussions about the democratic performance of all media platforms (e.g. Entman, 1989: 64, 95; Habermas, 2006: 412, 416; Sunstein, 2018:85). With mainstream media, such debates are fundamentally about plurality, namely, the extent to which these powerful opinion leading organisations are able and/or inclined to engage with and represent the disparate communities, issues and interests that sculpt modern societies.
    [Show full text]
  • The Need to Measure Variance in Experiential Learning and a New Statistic to Do So
    Developments in Business Simulation & Experiential Learning, Volume 26, 1999 THE NEED TO MEASURE VARIANCE IN EXPERIENTIAL LEARNING AND A NEW STATISTIC TO DO SO John R. Dickinson, University of Windsor James W. Gentry, University of Nebraska-Lincoln ABSTRACT concern should be given to the learning process rather than performance outcomes. The measurement of variation of qualitative or categorical variables serves a variety of essential We contend that insight into process can be gained purposes in simulation gaming: de- via examination of within-student and across-student scribing/summarizing participants’ decisions for variance in decision-making. For example, if the evaluation and feedback, describing/summarizing role of an experiential exercise is to foster trial-and- simulation results toward the same ends, and error learning, the variance in a student’s decisions explaining variation for basic research purposes. will be greatest when the trial-and-error stage is at Extant measures of dispersion are not well known. its peak. To the extent that the exercise works as Too, simulation gaming situations are peculiar in intended, greater variances would be expected early that the total number of observations available-- in the game play as opposed to later, barring the usually the number of decision periods or the game world encountering a discontinuity. number of participants--is often small. Each extant measure of dispersion has its own limitations. On the other hand, it is possible that decisions may Common limitations are that, under ordinary be more consistent early and then more variable later circumstances and especially with small numbers if the student is trying to recover from early of observations, a measure may not be defined and missteps.
    [Show full text]
  • TRACE: Tennessee Research and Creative Exchange
    University of Tennessee, Knoxville TRACE: Tennessee Research and Creative Exchange Doctoral Dissertations Graduate School 12-2016 On the quantification of complexity and diversity from phenotypes to ecosystems Zachary Harrison Marion University of Tennessee, Knoxville, [email protected] Follow this and additional works at: https://trace.tennessee.edu/utk_graddiss Part of the Biostatistics Commons, and the Other Ecology and Evolutionary Biology Commons Recommended Citation Marion, Zachary Harrison, "On the quantification of complexity and diversity from phenotypes to ecosystems. " PhD diss., University of Tennessee, 2016. https://trace.tennessee.edu/utk_graddiss/4104 This Dissertation is brought to you for free and open access by the Graduate School at TRACE: Tennessee Research and Creative Exchange. It has been accepted for inclusion in Doctoral Dissertations by an authorized administrator of TRACE: Tennessee Research and Creative Exchange. For more information, please contact [email protected]. To the Graduate Council: I am submitting herewith a dissertation written by Zachary Harrison Marion entitled "On the quantification of complexity and diversity from phenotypes to ecosystems." I have examined the final electronic copy of this dissertation for form and content and recommend that it be accepted in partial fulfillment of the equirr ements for the degree of Doctor of Philosophy, with a major in Ecology and Evolutionary Biology. Benjamin M. Fitzpatrick, Major Professor We have read this dissertation and recommend its acceptance: James A. Fordyce, Nathan J. Sanders, Shawn R. Campagna Accepted for the Council: Carolyn R. Hodges Vice Provost and Dean of the Graduate School (Original signatures are on file with official studentecor r ds.) On the quantification of complexity and diversity from phenotypes to ecosystems A Dissertation Presented for the Doctor of Philosophy Degree The University of Tennessee, Knoxville Zachary Harrison Marion December 2016 c by Zachary Harrison Marion, 2016 All Rights Reserved.
    [Show full text]
  • Measures of Dispersion and Serial Dependence in Categorical Time Series
    econometrics Article Measures of Dispersion and Serial Dependence in Categorical Time Series Christian H. Weiß Department of Mathematics and Statistics, Helmut Schmidt University, 22043 Hamburg, Germany; [email protected] Received: 21 December 2018; Accepted: 17 April 2019; Published: 22 April 2019 Abstract: The analysis and modeling of categorical time series requires quantifying the extent of dispersion and serial dependence. The dispersion of categorical data is commonly measured by Gini index or entropy, but also the recently proposed extropy measure can be used for this purpose. Regarding signed serial dependence in categorical time series, we consider three types of k-measures. By analyzing bias properties, it is shown that always one of the k-measures is related to one of the above-mentioned dispersion measures. For doing statistical inference based on the sample versions of these dispersion and dependence measures, knowledge on their distribution is required. Therefore, we study the asymptotic distributions and bias corrections of the considered dispersion and dependence measures, and we investigate the finite-sample performance of the resulting asymptotic approximations with simulations. The application of the measures is illustrated with real-data examples from politics, economics and biology. Keywords: Cohen’s k; extropy; nominal variation; signed serial dependence; asymptotic distribution 1. Introduction In many applications, the available data are not of quantitative nature (e.g., real numbers or counts) but consist of observations from a given finite set of categories. In the present article, we are concerned with data about political goals in Germany, fear states in the stock market, and phrases in a bird’s song.
    [Show full text]
  • Elementary Statistics for Social Planners
    Elementary Statistics for Social Planners Hayden Brown Social Policy Unit 2013 1 | P a g e 2 | P a g e CONTENTS Tables ....................................................................................................... 5 Types of social data .................................................................................. 5 Characteristics of Social Measures ............................................................................... 5 Contents of these notes................................................................................................ 7 Measures of Central Tendency ................................................................. 7 Mode ........................................................................................................................... 7 Median ......................................................................................................................... 7 Arithmetic Mean .......................................................................................................... 7 Measures of Dispersion ............................................................................ 7 Nominal Data ............................................................................................................... 7 Variation ratio ......................................................................................................................7 Index of Qualitative Variation ..............................................................................................7 Index of Diversity
    [Show full text]
  • Phonological Variation and the Construction of Regional Identities in New Zealand English
    Phonological variation and the construction of regional identities in New Zealand English by Sharon Marsden A thesis submitted to Victoria University of Wellington in fulfilment of the requirements for the degree of Doctor of Philosophy Victoria University of Wellington 2013 i Abstract This thesis addresses the ongoing evolution of New Zealand English phonology. In particular it explores the links between phonological variation and the social identities of speakers. The thesis investigates the possible emergence of regional dialects in the ongoing development of the variety. The investigation contributes to theories of dialect development, especially in relation to linguistic varieties described as “postcolonial” English. Since the onset of linguistic research on New Zealand English, scholars have highlighted the remarkable geographical uniformity of the variety. However, recent research concerning the development of postcolonial Englishes suggests that regional diversity is inevitable, but that its occurrence is tied to the construction of sociocultural identities. In this thesis I apply a holistic approach to investigating phonological variation and the construction of regional identities in modern New Zealand English. My aim in this thesis is twofold: firstly, to investigate current trends in 21st century New Zealand English phonology and secondly, to gain insights into the linguistic, social and cultural processes associated with the birth of new regional dialects. I view the ongoing evolution of Englishes as involving a composite of wide-ranging factors from the linguistic, historical, social, cultural and ideological domains. In order to address the full complexities of the issues I track variation and change in one influential and important dimension of English phonological systems: rhoticity.
    [Show full text]
  • Social Statistics
    SOCIAL STATISTICS Németh, Renáta Simon, Dávid Created by XMLmind XSL-FO Converter. SOCIAL STATISTICS írta Németh, Renáta és Simon, Dávid Publication date 2011 Created by XMLmind XSL-FO Converter. Tartalom Introduction ........................................................................................................................................ v 1. Lecture 1 ......................................................................................................................................... 1 1. What is social statistics? Why do we need it? ....................................................................... 1 2. Interpretation pitfall I: Ecological fallacy ............................................................................. 1 3. Interpretation pitfall II: An empirical relationship does not imply causation ........................ 2 4. Interpretation pitfall III: Simpson‟s paradox ......................................................................... 2 2. Lecture 2 ......................................................................................................................................... 6 1. Role of statistics in social research ....................................................................................... 6 2. Levels of measurement ......................................................................................................... 8 3. Unit of analysis ..................................................................................................................... 9 3. Lecture
    [Show full text]
  • Understanding the Index of Qualitative Variation
    Chapter 5: The Importance of Measuring Why is Variability important? Variability Simple Example: Suppose you wanted to • Measures of Central Tendency - know how satisfied CNAs are with their Numbers that describe what is typical or job and you found that the average average (central) in a distribution (e.g., mean, mode, median). score (on a five point scal)le) was “3”. • Measures of Variability - Numbers that describe diversity or variability in the How would knowing the variability help distribution (e.g., range, index of qualitative you to understand how satisfied CNAs variation, interquartile range, box plot, are with their job? variance, standard deviation). Answer: It would help you to see whether the average score of “3” means that the majority of CNAs are neutral about their jobs or that there is a split with CNAs either feeling very good (score of 5) or very bad (score of 1) about their job (average of 1’s and 5’s = 3). Another example. A measure of variability: Understanding the Index of Index of Qualitative Variation Qualitative Variation (IQV) • The IQV is a single number that expresses – A measure of variability for nominal variables. the diversity of a distribution. - A measure that shows how diverse a particular category •The IQV ranges from 0 to 1 of a variable is. • An IQV of 0 would indicate that the distribution has NO diversity at all. For example, when looking at ethnic diversity among •An IQV of 1 would indicate that the states, some states are very diverse with multiple ethnic distribution is maximally diverse. groups and lots of people in each group.
    [Show full text]