Observer Bias and Reliability By Xunchi Pu

Size: px
Start display at page:

Download "Observer Bias and Reliability By Xunchi Pu"

Transcription

1 Obsrvr Bias and Rliability By Xunchi Pu Introduction Clarly all masurmnts or obsrvations nd to b mad as accuratly as possibl and invstigators nd to pay carful attntion to chcking th rliability of thir masurmnts bfor undrtaking furthr analyss. Obsrvr bias is systmatic rror producd in obsrvational data by an obsrvr's xpctations or wishs. Th rror is strongly associatd with obsrvations mad on variabls that rquir jctiv assssmnt. Th goal of all masurmnt is to achiv accurat rsults. Howvr, this is not compltly possibl bcaus masurmnt rror, to som xtnt, is introducd into all masuring procdurs. In many aras of mdical rsarch, rliability studis ar frquntly conductd in ordr to assss th lvl of obsrvr variability in th masurmnt procdur. According to th collctd data, thr ar diffrnt mthods to assss th rliability of masurmnts. Rliability masurs for Catgorical data Normally, whn studying th variability of obsrvr ratings, two componnts of possibl inaccuracis must b distinguishd, thy ar intr-obsrvr bias and Intra-obsrvr bias. Th intr-obsrvr bias is rflctd by diffrnc among th marginal distribution of th rspons variabl for ach of th obsrvrs. Fliss showd that th omnibus tst of th intr-obsrvr bias can b usd by th following Q-tst: r(r 1) (y.j y.. r) j1 Q n ry.. y i. j1 Whr: r n is th numbr of jcts; r is th numbr of obsrvrs;

2 y ij is 1 if th ith jct is judgd by th jth obsrvr to hav th symptom prsnt, 0 othrwis; y i. Is th total numbr of obsrvrs who judg th ith jct to hav th symptom; y.j is th total numbr of th jcts th j th obsrvr judgs as having th symptom psnt; y.. is th total numbr of prsnt judgmnts mad. If th hypothsis of no intr-obsrvr bias is tru, thn Q has an approximatly a chisquar distribution with r-1 dgrs of frdom. Exampl 1: In th tabl, 5 psychiatrists valuat whthr th patints hav a sysmptom. If th patint has th symptom, th valu is 1; othrwis, 0. Psychiatrist total Proportion total Proportion For th data prsntd in th tabl, th tst statistic Q is givn by 5 4 ( ) Q Rfrring this to chi-squar distribution with 4 dgrs of frdom, w s that thr is som vidnc of intr-obsrvation bias for th psychiatrists on this particular symptom. Howvr, th invstigator may fl it is important to compar th diffrnt sts of obsrvrs. In this cas, w can us th paramtr of kappa to assss th obsrvr agrmnt or rliability.

3 Kappa (κ ) cofficint is usd to valuat th agrmnt of th obsrvrs. Po Pc κ 1 P Whr: c P o is dfind as th proportion of th jcts classifid into th sam catgory by th two obsrvrs; P c is dfind as th agrmnt to b xpctd by chanc. Th calculation of P o, P c and κ ar shown in xampl. Exampl : Th tabl containd th rsults that two pathologist sparatly classifid biopsy slids into on of fiv catgoris, Pathologist Row Total Pathologist P o P c κ P P o 1 P c c Kappa s possibl valus ar constraind to th intrval [0, 1]; κ 0 mans that agrmnt is not diffrnt from chanc, and κ 1 mans prfct agrmnt. Howvr, just obtaining a significantly gratr than zro is not sufficint to assss th quality of th agrmnt. Various scals to assss Kappa s significanc hav bn proposd. Landis and Koch gav som arbitrany but potntially usful valu for valuating obsrvd valu:

4 Tabl Evaluation of obsrvd kappa valus κ Strngth of agrmnt 0 Poor Slight Fair Modrat Substabtial Almost prfct Th concpt of a chanc corrctd masur of agrmnt can b xtndd to th situations involving mor than two obsrvrs. For th dtails sn Fliss and Cuzick (1979) and Schoutn (1985). Masuring Rliability of Quantitativ Variabls For th quantitativ data, any individual obsrvation x can b dscribd as: x µ Whn w assum th thr variabls t, o and indpndnt of on anothr and th varianc of an obsrvation is consquntly givn by: obs Whr: is th varianc of jcts; obs is th varianc of th obsrvrs; rr is th varianc of rror. A singl quantitativ that rflcts th rlativ magnitud of th componnts of varianc is th intraclass corrclation cofficint R, givn by: R obs

5 R can b stimatd from th man squars found by prforming a simpl two-way analysis of varianc on th data. Th gnral form of such an analysis is shown xampl 3. Exampl 3: Sourc of varianc d.f. MS Patints 19,493,469.1 Obsrvrs 3 36,481. Error 57 7,70.3 Bcaus: PMS r t RMS n EMS o So: PMS EMS ) t r ) o RMS EMS n ) EMS , R )

6 Rfrnc: 1. Evritt, B.S. Statistical Mthods for Mdical Invstigations, Oxford Univrsity Prss, Nw York, ( Barbara Di Eugnio, On th usag of Kappa to valuat agrmnt on coding tasks, Elctrical Enginring and Computr Scinc. 3. Krippndorff, Klaus, Contnt Analysis: an Introduction to its Mthodology. Bvrly Hills: Sag Publications. 4. Carolyn Fhr Waltz, Ora L. Strickland, Elizabth R. Lnz, Masurmnt in nursing rsarch, Philadlphia : F.A. Davis Co., c1991, nd d.

Task 1: Repetition - Precision & Recall

Task 1: Repetition - Precision & Recall SS 208 Exrcis 9 - July 28, 208 Task : Rptition - Prcision & Rcall Considr an information nd for which thr ar 5 rlvant documnts in th collction. Givn is th following list of rlvant ( R ) and non-rlvant

More information

Applied Statistics II - Categorical Data Analysis Data analysis using Genstat - Exercise 2 Logistic regression

Applied Statistics II - Categorical Data Analysis Data analysis using Genstat - Exercise 2 Logistic regression Applid Statistics II - Catgorical Data Analysis Data analysis using Gnstat - Exrcis 2 Logistic rgrssion Analysis 2. Logistic rgrssion for a 2 x k tabl. Th tabl blow shows th numbr of aphids aliv and dad

More information

Review Statistics review 14: Logistic regression Viv Bewick 1, Liz Cheek 1 and Jonathan Ball 2

Review Statistics review 14: Logistic regression Viv Bewick 1, Liz Cheek 1 and Jonathan Ball 2 Critical Car Fbruary 2005 Vol 9 No 1 Bwick t al. Rviw Statistics rviw 14: Logistic rgrssion Viv Bwick 1, Liz Chk 1 and Jonathan Ball 2 1 Snior Lcturr, School of Computing, Mathmatical and Information Scincs,

More information

EXST Regression Techniques Page 1

EXST Regression Techniques Page 1 EXST704 - Rgrssion Tchniqus Pag 1 Masurmnt rrors in X W hav assumd that all variation is in Y. Masurmnt rror in this variabl will not ffct th rsults, as long as thy ar uncorrlatd and unbiasd, sinc thy

More information

Search sequence databases 3 10/25/2016

Search sequence databases 3 10/25/2016 Sarch squnc databass 3 10/25/2016 Etrm valu distribution Ø Suppos X is a random variabl with probability dnsity function p(, w sampl a larg numbr S of indpndnt valus of X from this distribution for an

More information

Construction of asymmetric orthogonal arrays of strength three via a replacement method

Construction of asymmetric orthogonal arrays of strength three via a replacement method isid/ms/26/2 Fbruary, 26 http://www.isid.ac.in/ statmath/indx.php?modul=prprint Construction of asymmtric orthogonal arrays of strngth thr via a rplacmnt mthod Tian-fang Zhang, Qiaoling Dng and Alok Dy

More information

Probability and Stochastic Processes: A Friendly Introduction for Electrical and Computer Engineers Roy D. Yates and David J.

Probability and Stochastic Processes: A Friendly Introduction for Electrical and Computer Engineers Roy D. Yates and David J. Probability and Stochastic Procsss: A Frindly Introduction for Elctrical and Computr Enginrs Roy D. Yats and David J. Goodman Problm Solutions : Yats and Goodman,4.3. 4.3.4 4.3. 4.4. 4.4.4 4.4.6 4.. 4..7

More information

Addition of angular momentum

Addition of angular momentum Addition of angular momntum April, 0 Oftn w nd to combin diffrnt sourcs of angular momntum to charactriz th total angular momntum of a systm, or to divid th total angular momntum into parts to valuat th

More information

Ch. 24 Molecular Reaction Dynamics 1. Collision Theory

Ch. 24 Molecular Reaction Dynamics 1. Collision Theory Ch. 4 Molcular Raction Dynamics 1. Collision Thory Lctur 16. Diffusion-Controlld Raction 3. Th Matrial Balanc Equation 4. Transition Stat Thory: Th Eyring Equation 5. Transition Stat Thory: Thrmodynamic

More information

General Notes About 2007 AP Physics Scoring Guidelines

General Notes About 2007 AP Physics Scoring Guidelines AP PHYSICS C: ELECTRICITY AND MAGNETISM 2007 SCORING GUIDELINES Gnral Nots About 2007 AP Physics Scoring Guidlins 1. Th solutions contain th most common mthod of solving th fr-rspons qustions and th allocation

More information

Addition of angular momentum

Addition of angular momentum Addition of angular momntum April, 07 Oftn w nd to combin diffrnt sourcs of angular momntum to charactriz th total angular momntum of a systm, or to divid th total angular momntum into parts to valuat

More information

Sara Godoy del Olmo Calculation of contaminated soil volumes : Geostatistics applied to a hydrocarbons spill Lac Megantic Case

Sara Godoy del Olmo Calculation of contaminated soil volumes : Geostatistics applied to a hydrocarbons spill Lac Megantic Case wwwnvisol-canadaca Sara Godoy dl Olmo Calculation of contaminatd soil volums : Gostatistics applid to a hydrocarbons spill Lac Mgantic Cas Gostatistics: study of a PH contamination CONTEXT OF THE STUDY

More information

Dealing with quantitative data and problem solving life is a story problem! Attacking Quantitative Problems

Dealing with quantitative data and problem solving life is a story problem! Attacking Quantitative Problems Daling with quantitati data and problm soling lif is a story problm! A larg portion of scinc inols quantitati data that has both alu and units. Units can sa your butt! Nd handl on mtric prfixs Dimnsional

More information

What are those βs anyway? Understanding Design Matrix & Odds ratios

What are those βs anyway? Understanding Design Matrix & Odds ratios Ral paramtr stimat WILD 750 - Wildlif Population Analysis of 6 What ar thos βs anyway? Undrsting Dsign Matrix & Odds ratios Rfrncs Hosmr D.W.. Lmshow. 000. Applid logistic rgrssion. John Wily & ons Inc.

More information

Solution of Assignment #2

Solution of Assignment #2 olution of Assignmnt #2 Instructor: Alirza imchi Qustion #: For simplicity, assum that th distribution function of T is continuous. Th distribution function of R is: F R ( r = P( R r = P( log ( T r = P(log

More information

CS 361 Meeting 12 10/3/18

CS 361 Meeting 12 10/3/18 CS 36 Mting 2 /3/8 Announcmnts. Homwork 4 is du Friday. If Friday is Mountain Day, homwork should b turnd in at my offic or th dpartmnt offic bfor 4. 2. Homwork 5 will b availabl ovr th wknd. 3. Our midtrm

More information

ARIMA Methods of Detecting Outliers in Time Series Periodic Processes

ARIMA Methods of Detecting Outliers in Time Series Periodic Processes Articl Intrnational Journal of Modrn Mathmatical Scincs 014 11(1): 40-48 Intrnational Journal of Modrn Mathmatical Scincs Journal hompag:www.modrnscintificprss.com/journals/ijmms.aspx ISSN:166-86X Florida

More information

The van der Waals interaction 1 D. E. Soper 2 University of Oregon 20 April 2012

The van der Waals interaction 1 D. E. Soper 2 University of Oregon 20 April 2012 Th van dr Waals intraction D. E. Sopr 2 Univrsity of Orgon 20 pril 202 Th van dr Waals intraction is discussd in Chaptr 5 of J. J. Sakurai, Modrn Quantum Mchanics. Hr I tak a look at it in a littl mor

More information

Cramér-Rao Inequality: Let f(x; θ) be a probability density function with continuous parameter

Cramér-Rao Inequality: Let f(x; θ) be a probability density function with continuous parameter WHEN THE CRAMÉR-RAO INEQUALITY PROVIDES NO INFORMATION STEVEN J. MILLER Abstract. W invstigat a on-paramtr family of probability dnsitis (rlatd to th Parto distribution, which dscribs many natural phnomna)

More information

1 Minimum Cut Problem

1 Minimum Cut Problem CS 6 Lctur 6 Min Cut and argr s Algorithm Scribs: Png Hui How (05), Virginia Dat: May 4, 06 Minimum Cut Problm Today, w introduc th minimum cut problm. This problm has many motivations, on of which coms

More information

2008 AP Calculus BC Multiple Choice Exam

2008 AP Calculus BC Multiple Choice Exam 008 AP Multipl Choic Eam Nam 008 AP Calculus BC Multipl Choic Eam Sction No Calculator Activ AP Calculus 008 BC Multipl Choic. At tim t 0, a particl moving in th -plan is th acclration vctor of th particl

More information

Introduction to Arithmetic Geometry Fall 2013 Lecture #20 11/14/2013

Introduction to Arithmetic Geometry Fall 2013 Lecture #20 11/14/2013 18.782 Introduction to Arithmtic Gomtry Fall 2013 Lctur #20 11/14/2013 20.1 Dgr thorm for morphisms of curvs Lt us rstat th thorm givn at th nd of th last lctur, which w will now prov. Thorm 20.1. Lt φ:

More information

The Equitable Dominating Graph

The Equitable Dominating Graph Intrnational Journal of Enginring Rsarch and Tchnology. ISSN 0974-3154 Volum 8, Numbr 1 (015), pp. 35-4 Intrnational Rsarch Publication Hous http://www.irphous.com Th Equitabl Dominating Graph P.N. Vinay

More information

Thermodynamical insight on the role of additives in shifting the equilibrium between white and grey tin

Thermodynamical insight on the role of additives in shifting the equilibrium between white and grey tin hrmodynamical insight on th rol of additivs in shifting th quilibrium btwn whit and gry tin Nikolay Dmntv Dpartmnt of Chmistry, mpl Univrsity, Philadlphia, PA 19122 Abstract In this study mthods of statistical

More information

1 Isoparametric Concept

1 Isoparametric Concept UNIVERSITY OF CALIFORNIA BERKELEY Dpartmnt of Civil Enginring Spring 06 Structural Enginring, Mchanics and Matrials Profssor: S. Govindj Nots on D isoparamtric lmnts Isoparamtric Concpt Th isoparamtric

More information

Learning Spherical Convolution for Fast Features from 360 Imagery

Learning Spherical Convolution for Fast Features from 360 Imagery Larning Sphrical Convolution for Fast Faturs from 36 Imagry Anonymous Author(s) 3 4 5 6 7 8 9 3 4 5 6 7 8 9 3 4 5 6 7 8 9 3 3 3 33 34 35 In this fil w provid additional dtails to supplmnt th main papr

More information

Chapter 6 Student Lecture Notes 6-1

Chapter 6 Student Lecture Notes 6-1 Chaptr 6 Studnt Lctur Nots 6-1 Chaptr Goals QM353: Busnss Statstcs Chaptr 6 Goodnss-of-Ft Tsts and Contngncy Analyss Aftr compltng ths chaptr, you should b abl to: Us th ch-squar goodnss-of-ft tst to dtrmn

More information

Chapter 13 GMM for Linear Factor Models in Discount Factor form. GMM on the pricing errors gives a crosssectional

Chapter 13 GMM for Linear Factor Models in Discount Factor form. GMM on the pricing errors gives a crosssectional Chaptr 13 GMM for Linar Factor Modls in Discount Factor form GMM on th pricing rrors givs a crosssctional rgrssion h cas of xcss rturns Hors rac sting for charactristic sting for pricd factors: lambdas

More information

Transitional Probability Model for a Serial Phases in Production

Transitional Probability Model for a Serial Phases in Production Jurnal Karya Asli Lorkan Ahli Matmatik Vol. 3 No. 2 (2010) pag 49-54. Jurnal Karya Asli Lorkan Ahli Matmatik Transitional Probability Modl for a Srial Phass in Production Adam Baharum School of Mathmatical

More information

u 3 = u 3 (x 1, x 2, x 3 )

u 3 = u 3 (x 1, x 2, x 3 ) Lctur 23: Curvilinar Coordinats (RHB 8.0 It is oftn convnint to work with variabls othr than th Cartsian coordinats x i ( = x, y, z. For xampl in Lctur 5 w mt sphrical polar and cylindrical polar coordinats.

More information

Text: WMM, Chapter 5. Sections , ,

Text: WMM, Chapter 5. Sections , , Lcturs 6 - Continuous Probabilit Distributions Tt: WMM, Chaptr 5. Sctions 6.-6.4, 6.6-6.8, 7.-7. In th prvious sction, w introduc som of th common probabilit distribution functions (PDFs) for discrt sampl

More information

Estimation of odds ratios in Logistic Regression models under different parameterizations and Design matrices

Estimation of odds ratios in Logistic Regression models under different parameterizations and Design matrices Advancs in Computational Intllignc, Man-Machin Systms and Cybrntics Estimation of odds ratios in Logistic Rgrssion modls undr diffrnt paramtrizations and Dsign matrics SURENDRA PRASAD SINHA*, LUIS NAVA

More information

ph People Grade Level: basic Duration: minutes Setting: classroom or field site

ph People Grade Level: basic Duration: minutes Setting: classroom or field site ph Popl Adaptd from: Whr Ar th Frogs? in Projct WET: Curriculum & Activity Guid. Bozman: Th Watrcours and th Council for Environmntal Education, 1995. ph Grad Lvl: basic Duration: 10 15 minuts Stting:

More information

International Journal of Scientific & Engineering Research, Volume 6, Issue 7, July ISSN

International Journal of Scientific & Engineering Research, Volume 6, Issue 7, July ISSN Intrnational Journal of Scintific & Enginring Rsarch, Volum 6, Issu 7, July-25 64 ISSN 2229-558 HARATERISTIS OF EDGE UTSET MATRIX OF PETERSON GRAPH WITH ALGEBRAI GRAPH THEORY Dr. G. Nirmala M. Murugan

More information

Rational Approximation for the one-dimensional Bratu Equation

Rational Approximation for the one-dimensional Bratu Equation Intrnational Journal of Enginring & Tchnology IJET-IJES Vol:3 o:05 5 Rational Approximation for th on-dimnsional Bratu Equation Moustafa Aly Soliman Chmical Enginring Dpartmnt, Th British Univrsity in

More information

[ ] 1+ lim G( s) 1+ s + s G s s G s Kacc SYSTEM PERFORMANCE. Since. Lecture 10: Steady-state Errors. Steady-state Errors. Then

[ ] 1+ lim G( s) 1+ s + s G s s G s Kacc SYSTEM PERFORMANCE. Since. Lecture 10: Steady-state Errors. Steady-state Errors. Then SYSTEM PERFORMANCE Lctur 0: Stady-tat Error Stady-tat Error Lctur 0: Stady-tat Error Dr.alyana Vluvolu Stady-tat rror can b found by applying th final valu thorm and i givn by lim ( t) lim E ( ) t 0 providd

More information

Application of Vague Soft Sets in students evaluation

Application of Vague Soft Sets in students evaluation Availabl onlin at www.plagiarsarchlibrary.com Advancs in Applid Scinc Rsarch, 0, (6):48-43 ISSN: 0976-860 CODEN (USA): AASRFC Application of Vagu Soft Sts in studnts valuation B. Chtia*and P. K. Das Dpartmnt

More information

MCB137: Physical Biology of the Cell Spring 2017 Homework 6: Ligand binding and the MWC model of allostery (Due 3/23/17)

MCB137: Physical Biology of the Cell Spring 2017 Homework 6: Ligand binding and the MWC model of allostery (Due 3/23/17) MCB37: Physical Biology of th Cll Spring 207 Homwork 6: Ligand binding and th MWC modl of allostry (Du 3/23/7) Hrnan G. Garcia March 2, 207 Simpl rprssion In class, w drivd a mathmatical modl of how simpl

More information

Propositional Logic. Combinatorial Problem Solving (CPS) Albert Oliveras Enric Rodríguez-Carbonell. May 17, 2018

Propositional Logic. Combinatorial Problem Solving (CPS) Albert Oliveras Enric Rodríguez-Carbonell. May 17, 2018 Propositional Logic Combinatorial Problm Solving (CPS) Albrt Olivras Enric Rodríguz-Carbonll May 17, 2018 Ovrviw of th sssion Dfinition of Propositional Logic Gnral Concpts in Logic Rduction to SAT CNFs

More information

Homotopy perturbation technique

Homotopy perturbation technique Comput. Mthods Appl. Mch. Engrg. 178 (1999) 257±262 www.lsvir.com/locat/cma Homotopy prturbation tchniqu Ji-Huan H 1 Shanghai Univrsity, Shanghai Institut of Applid Mathmatics and Mchanics, Shanghai 272,

More information

INFLUENCE OF GROUND SUBSIDENCE IN THE DAMAGE TO MEXICO CITY S PRIMARY WATER SYSTEM DUE TO THE 1985 EARTHQUAKE

INFLUENCE OF GROUND SUBSIDENCE IN THE DAMAGE TO MEXICO CITY S PRIMARY WATER SYSTEM DUE TO THE 1985 EARTHQUAKE 13 th World Confrnc on Earthquak Enginring Vancouvr, B.C., Canada August 1-6, 2004 Papr No. 2165 INFLUENCE OF GROUND SUBSIDENCE IN THE DAMAGE TO MEXICO CITY S PRIMARY WATER SYSTEM DUE TO THE 1985 EARTHQUAKE

More information

CPSC 665 : An Algorithmist s Toolkit Lecture 4 : 21 Jan Linear Programming

CPSC 665 : An Algorithmist s Toolkit Lecture 4 : 21 Jan Linear Programming CPSC 665 : An Algorithmist s Toolkit Lctur 4 : 21 Jan 2015 Lcturr: Sushant Sachdva Linar Programming Scrib: Rasmus Kyng 1. Introduction An optimization problm rquirs us to find th minimum or maximum) of

More information

Continuous probability distributions

Continuous probability distributions Continuous probability distributions Many continuous probability distributions, including: Uniform Normal Gamma Eponntial Chi-Squard Lognormal Wibull EGR 5 Ch. 6 Uniform distribution Simplst charactrizd

More information

15. Stress-Strain behavior of soils

15. Stress-Strain behavior of soils 15. Strss-Strain bhavior of soils Sand bhavior Usually shard undr draind conditions (rlativly high prmability mans xcss por prssurs ar not gnratd). Paramtrs govrning sand bhaviour is: Rlativ dnsity Effctiv

More information

Data Assimilation 1. Alan O Neill National Centre for Earth Observation UK

Data Assimilation 1. Alan O Neill National Centre for Earth Observation UK Data Assimilation 1 Alan O Nill National Cntr for Earth Obsrvation UK Plan Motivation & basic idas Univariat (scalar) data assimilation Multivariat (vctor) data assimilation 3d-Variational Mthod (& optimal

More information

(Upside-Down o Direct Rotation) β - Numbers

(Upside-Down o Direct Rotation) β - Numbers Amrican Journal of Mathmatics and Statistics 014, 4(): 58-64 DOI: 10593/jajms0140400 (Upsid-Down o Dirct Rotation) β - Numbrs Ammar Sddiq Mahmood 1, Shukriyah Sabir Ali,* 1 Dpartmnt of Mathmatics, Collg

More information

Einstein Equations for Tetrad Fields

Einstein Equations for Tetrad Fields Apiron, Vol 13, No, Octobr 006 6 Einstin Equations for Ttrad Filds Ali Rıza ŞAHİN, R T L Istanbul (Turky) Evry mtric tnsor can b xprssd by th innr product of ttrad filds W prov that Einstin quations for

More information

Methods for the Analysis 1. Methods for the Analysis 2. I. Introduction. Methods for the Analysis of Change

Methods for the Analysis 1. Methods for the Analysis 2. I. Introduction. Methods for the Analysis of Change Mthods for th Analysis Mthods for th Analysis 2 I. Introduction Mthods for th Analysis of Chang Throughout th social and bhavioral scincs, rsarchrs hav incrasd thir rlianc on longitudinal dsigns to addrss

More information

Linear Non-Gaussian Structural Equation Models

Linear Non-Gaussian Structural Equation Models IMPS 8, Durham, NH Linar Non-Gaussian Structural Equation Modls Shohi Shimizu, Patrik Hoyr and Aapo Hyvarinn Osaka Univrsity, Japan Univrsity of Hlsinki, Finland Abstract Linar Structural Equation Modling

More information

On spanning trees and cycles of multicolored point sets with few intersections

On spanning trees and cycles of multicolored point sets with few intersections On spanning trs and cycls of multicolord point sts with fw intrsctions M. Kano, C. Mrino, and J. Urrutia April, 00 Abstract Lt P 1,..., P k b a collction of disjoint point sts in R in gnral position. W

More information

B. water content (WC) = 0.4 WC CSF WC GM WC WM, or WC = = mol/l.

B. water content (WC) = 0.4 WC CSF WC GM WC WM, or WC = = mol/l. 9.. A. Rlvant quation: M (TR, TE) = M ( TR /T ) TE / T M (NAA) = 38. M (cratin) = 9.6 M (cholin) = 98.4 M (watr) = 7,4 B. watr contnt (WC) =.4 WC CSF +.5 WC GM +. WC WM, or WC =.4. 55.6 +.5.87 55.6 +..83

More information

Computing and Communications -- Network Coding

Computing and Communications -- Network Coding 89 90 98 00 Computing and Communications -- Ntwork Coding Dr. Zhiyong Chn Institut of Wirlss Communications Tchnology Shanghai Jiao Tong Univrsity China Lctur 5- Nov. 05 0 Classical Information Thory Sourc

More information

5.80 Small-Molecule Spectroscopy and Dynamics

5.80 Small-Molecule Spectroscopy and Dynamics MIT OpnCoursWar http://ocw.mit.du 5.80 Small-Molcul Spctroscopy and Dynamics Fall 008 For information about citing ths matrials or our Trms of Us, visit: http://ocw.mit.du/trms. Lctur # 3 Supplmnt Contnts

More information

u r du = ur+1 r + 1 du = ln u + C u sin u du = cos u + C cos u du = sin u + C sec u tan u du = sec u + C e u du = e u + C

u r du = ur+1 r + 1 du = ln u + C u sin u du = cos u + C cos u du = sin u + C sec u tan u du = sec u + C e u du = e u + C Tchniqus of Intgration c Donald Kridr and Dwight Lahr In this sction w ar going to introduc th first approachs to valuating an indfinit intgral whos intgrand dos not hav an immdiat antidrivativ. W bgin

More information

Probability Translation Guide

Probability Translation Guide Quick Guid to Translation for th inbuilt SWARM Calculator If you s information looking lik this: Us this statmnt or any variant* (not th backticks) And this is what you ll s whn you prss Calculat Th chancs

More information

COMPLEX NUMBER PAIRWISE COMPARISON AND COMPLEX NUMBER AHP

COMPLEX NUMBER PAIRWISE COMPARISON AND COMPLEX NUMBER AHP ISAHP 00, Bal, Indonsa, August -9, 00 COMPLEX NUMBER PAIRWISE COMPARISON AND COMPLEX NUMBER AHP Chkako MIYAKE, Kkch OHSAWA, Masahro KITO, and Masaak SHINOHARA Dpartmnt of Mathmatcal Informaton Engnrng

More information

Superposition. Thinning

Superposition. Thinning Suprposition STAT253/317 Wintr 213 Lctur 11 Yibi Huang Fbruary 1, 213 5.3 Th Poisson Procsss 5.4 Gnralizations of th Poisson Procsss Th sum of two indpndnt Poisson procsss with rspctiv rats λ 1 and λ 2,

More information

Brief Introduction to Statistical Mechanics

Brief Introduction to Statistical Mechanics Brif Introduction to Statistical Mchanics. Purpos: Ths nots ar intndd to provid a vry quick introduction to Statistical Mchanics. Th fild is of cours far mor vast than could b containd in ths fw pags.

More information

22/ Breakdown of the Born-Oppenheimer approximation. Selection rules for rotational-vibrational transitions. P, R branches.

22/ Breakdown of the Born-Oppenheimer approximation. Selection rules for rotational-vibrational transitions. P, R branches. Subjct Chmistry Papr No and Titl Modul No and Titl Modul Tag 8/ Physical Spctroscopy / Brakdown of th Born-Oppnhimr approximation. Slction ruls for rotational-vibrational transitions. P, R branchs. CHE_P8_M

More information

BINOMIAL COEFFICIENTS INVOLVING INFINITE POWERS OF PRIMES. 1. Statement of results

BINOMIAL COEFFICIENTS INVOLVING INFINITE POWERS OF PRIMES. 1. Statement of results BINOMIAL COEFFICIENTS INVOLVING INFINITE POWERS OF PRIMES DONALD M. DAVIS Abstract. If p is a prim and n a positiv intgr, lt ν p (n dnot th xponnt of p in n, and u p (n n/p νp(n th unit part of n. If α

More information

Why is a E&M nature of light not sufficient to explain experiments?

Why is a E&M nature of light not sufficient to explain experiments? 1 Th wird world of photons Why is a E&M natur of light not sufficint to xplain xprimnts? Do photons xist? Som quantum proprtis of photons 2 Black body radiation Stfan s law: Enrgy/ ara/ tim = Win s displacmnt

More information

Estimation of apparent fraction defective: A mathematical approach

Estimation of apparent fraction defective: A mathematical approach Availabl onlin at www.plagiarsarchlibrary.com Plagia Rsarch Library Advancs in Applid Scinc Rsarch, 011, (): 84-89 ISSN: 0976-8610 CODEN (USA): AASRFC Estimation of apparnt fraction dfctiv: A mathmatical

More information

Evaluating Reliability Systems by Using Weibull & New Weibull Extension Distributions Mushtak A.K. Shiker

Evaluating Reliability Systems by Using Weibull & New Weibull Extension Distributions Mushtak A.K. Shiker Evaluating Rliability Systms by Using Wibull & Nw Wibull Extnsion Distributions Mushtak A.K. Shikr مشتاق عبذ الغني شخير Univrsity of Babylon, Collg of Education (Ibn Hayan), Dpt. of Mathmatics Abstract

More information

Determination of Vibrational and Electronic Parameters From an Electronic Spectrum of I 2 and a Birge-Sponer Plot

Determination of Vibrational and Electronic Parameters From an Electronic Spectrum of I 2 and a Birge-Sponer Plot 5 J. Phys. Chm G Dtrmination of Vibrational and Elctronic Paramtrs From an Elctronic Spctrum of I 2 and a Birg-Sponr Plot 1 15 2 25 3 35 4 45 Dpartmnt of Chmistry, Gustavus Adolphus Collg. 8 Wst Collg

More information

Errata. Items with asterisks will still be in the Second Printing

Errata. Items with asterisks will still be in the Second Printing Errata Itms with astrisks will still b in th Scond Printing Author wbsit URL: http://chs.unl.du/edpsych/rjsit/hom. P7. Th squar root of rfrrd to σ E (i.., σ E is rfrrd to not Th squar root of σ E (i..,

More information

In the table below, write the coordinates of each point in the figure. Point x-coordinate y-coordinate A 0 3 B 3 3 C 3 5 D 3 8 E 5 5 F 6 3 G 3 1

In the table below, write the coordinates of each point in the figure. Point x-coordinate y-coordinate A 0 3 B 3 3 C 3 5 D 3 8 E 5 5 F 6 3 G 3 1 1 TASK 1.1.1: PATTY PAPER TRANSFORMATIONS Solutions 10 D C E A B F G -5 5 10 - - In th tabl blow, writ th s of ach pot th figur. x- y- A 0 3 B 3 3 C 3 5 D 3 E 5 5 F 3 G 3 1 1. On patty papr, trac th figur

More information

Title: Vibrational structure of electronic transition

Title: Vibrational structure of electronic transition Titl: Vibrational structur of lctronic transition Pag- Th band spctrum sn in th Ultra-Violt (UV) and visibl (VIS) rgions of th lctromagntic spctrum can not intrprtd as vibrational and rotational spctrum

More information

Chemical Physics II. More Stat. Thermo Kinetics Protein Folding...

Chemical Physics II. More Stat. Thermo Kinetics Protein Folding... Chmical Physics II Mor Stat. Thrmo Kintics Protin Folding... http://www.nmc.ctc.com/imags/projct/proj15thumb.jpg http://nuclarwaponarchiv.org/usa/tsts/ukgrabl2.jpg http://www.photolib.noaa.gov/corps/imags/big/corp1417.jpg

More information

That is, we start with a general matrix: And end with a simpler matrix:

That is, we start with a general matrix: And end with a simpler matrix: DIAGON ALIZATION OF THE STR ESS TEN SOR INTRO DUCTIO N By th us of Cauchy s thorm w ar abl to rduc th numbr of strss componnts in th strss tnsor to only nin valus. An additional simplification of th strss

More information

4037 ADDITIONAL MATHEMATICS

4037 ADDITIONAL MATHEMATICS CAMBRIDGE INTERNATIONAL EXAMINATIONS GCE Ordinary Lvl MARK SCHEME for th Octobr/Novmbr 0 sris 40 ADDITIONAL MATHEMATICS 40/ Papr, maimum raw mark 80 This mark schm is publishd as an aid to tachrs and candidats,

More information

A Propagating Wave Packet Group Velocity Dispersion

A Propagating Wave Packet Group Velocity Dispersion Lctur 8 Phys 375 A Propagating Wav Packt Group Vlocity Disprsion Ovrviw and Motivation: In th last lctur w lookd at a localizd solution t) to th 1D fr-particl Schrödingr quation (SE) that corrsponds to

More information

COMPUTER GENERATED HOLOGRAMS Optical Sciences 627 W.J. Dallas (Monday, April 04, 2005, 8:35 AM) PART I: CHAPTER TWO COMB MATH.

COMPUTER GENERATED HOLOGRAMS Optical Sciences 627 W.J. Dallas (Monday, April 04, 2005, 8:35 AM) PART I: CHAPTER TWO COMB MATH. C:\Dallas\0_Courss\03A_OpSci_67\0 Cgh_Book\0_athmaticalPrliminaris\0_0 Combath.doc of 8 COPUTER GENERATED HOLOGRAS Optical Scincs 67 W.J. Dallas (onday, April 04, 005, 8:35 A) PART I: CHAPTER TWO COB ATH

More information

Assessment Schedule 2013 Chemistry: Demonstrate understanding of the properties of selected organic compounds (91165)

Assessment Schedule 2013 Chemistry: Demonstrate understanding of the properties of selected organic compounds (91165) NCEA Lvl 2 Chmistry (91165) 2013 pag 1 of 5 Assssmnt Schdul 2013 Chmistry: Dmonstrat undrstanding of th proprtis of slctd organic compounds (91165) Assssmnt Critria Achivmnt Achivmnt with Mrit Achivmnt

More information

International Journal of Mathematical Archive-5(1), 2014, Available online through ISSN

International Journal of Mathematical Archive-5(1), 2014, Available online through   ISSN ntrnational Journal of Mathmatical rchiv-51 2014 263-272 vailabl onlin through www.ijma.info SSN 2229 5046 ON -CU UZZY NEUROSOPHC SO SES. rockiarani* &. R. Sumathi* *Dpartmnt of Mathmatics Nirmala Collg

More information

Hydrogen Atom and One Electron Ions

Hydrogen Atom and One Electron Ions Hydrogn Atom and On Elctron Ions Th Schrödingr quation for this two-body problm starts out th sam as th gnral two-body Schrödingr quation. First w sparat out th motion of th cntr of mass. Th intrnal potntial

More information

Function Spaces. a x 3. (Letting x = 1 =)) a(0) + b + c (1) = 0. Row reducing the matrix. b 1. e 4 3. e 9. >: (x = 1 =)) a(0) + b + c (1) = 0

Function Spaces. a x 3. (Letting x = 1 =)) a(0) + b + c (1) = 0. Row reducing the matrix. b 1. e 4 3. e 9. >: (x = 1 =)) a(0) + b + c (1) = 0 unction Spacs Prrquisit: Sction 4.7, Coordinatization n this sction, w apply th tchniqus of Chaptr 4 to vctor spacs whos lmnts ar functions. Th vctor spacs P n and P ar familiar xampls of such spacs. Othr

More information

Unit 30: Inference for Regression

Unit 30: Inference for Regression Unit 30: Infrnc for Rgrssion Summary of Vido In Unit 11, Fitting Lins to Data, w xamind th rlationship btwn wintr snowpack and spring runoff. Colorado rsourc managrs mad prdictions about th sasonal watr

More information

First derivative analysis

First derivative analysis Robrto s Nots on Dirntial Calculus Chaptr 8: Graphical analysis Sction First drivativ analysis What you nd to know alrady: How to us drivativs to idntiy th critical valus o a unction and its trm points

More information

3-2-1 ANN Architecture

3-2-1 ANN Architecture ARTIFICIAL NEURAL NETWORKS (ANNs) Profssor Tom Fomby Dpartmnt of Economics Soutrn Mtodist Univrsity Marc 008 Artificial Nural Ntworks (raftr ANNs) can b usd for itr prdiction or classification problms.

More information

Voltage, Current, Power, Series Resistance, Parallel Resistance, and Diodes

Voltage, Current, Power, Series Resistance, Parallel Resistance, and Diodes Lctur 1. oltag, Currnt, Powr, Sris sistanc, Paralll sistanc, and Diods Whn you start to dal with lctronics thr ar thr main concpts to start with: Nam Symbol Unit oltag volt Currnt ampr Powr W watt oltag

More information

A Prey-Predator Model with an Alternative Food for the Predator, Harvesting of Both the Species and with A Gestation Period for Interaction

A Prey-Predator Model with an Alternative Food for the Predator, Harvesting of Both the Species and with A Gestation Period for Interaction Int. J. Opn Problms Compt. Math., Vol., o., Jun 008 A Pry-Prdator Modl with an Altrnativ Food for th Prdator, Harvsting of Both th Spcis and with A Gstation Priod for Intraction K. L. arayan and. CH. P.

More information

Analyzing Frequencies

Analyzing Frequencies Frquncy (# ndvduals) Frquncy (# ndvduals) /3/16 H o : No dffrnc n obsrvd sz frquncs and that prdctd by growth modl How would you analyz ths data? 15 Obsrvd Numbr 15 Expctd Numbr from growth modl 1 1 5

More information

Extraction of Doping Density Distributions from C-V Curves

Extraction of Doping Density Distributions from C-V Curves Extraction of Doping Dnsity Distributions from C-V Curvs Hartmut F.-W. Sadrozinski SCIPP, Univ. California Santa Cruz, Santa Cruz, CA 9564 USA 1. Connction btwn C, N, V Start with Poisson quation d V =

More information

Dynamic Modelling of Hoisting Steel Wire Rope. Da-zhi CAO, Wen-zheng DU, Bao-zhu MA *

Dynamic Modelling of Hoisting Steel Wire Rope. Da-zhi CAO, Wen-zheng DU, Bao-zhu MA * 17 nd Intrnational Confrnc on Mchanical Control and Automation (ICMCA 17) ISBN: 978-1-6595-46-8 Dynamic Modlling of Hoisting Stl Wir Rop Da-zhi CAO, Wn-zhng DU, Bao-zhu MA * and Su-bing LIU Xi an High

More information

Alpha and beta decay equation practice

Alpha and beta decay equation practice Alpha and bta dcay quation practic Introduction Alpha and bta particls may b rprsntd in quations in svral diffrnt ways. Diffrnt xam boards hav thir own prfrnc. For xampl: Alpha Bta α β alpha bta Dspit

More information

MEASURING HEAT FLUX FROM A COMPONENT ON A PCB

MEASURING HEAT FLUX FROM A COMPONENT ON A PCB MEASURING HEAT FLUX FROM A COMPONENT ON A PCB INTRODUCTION Elctronic circuit boards consist of componnts which gnrats substantial amounts of hat during thir opration. A clar knowldg of th lvl of hat dissipation

More information

ECE507 - Plasma Physics and Applications

ECE507 - Plasma Physics and Applications ECE507 - Plasma Physics and Applications Lctur 7 Prof. Jorg Rocca and Dr. Frnando Tomasl Dpartmnt of Elctrical and Computr Enginring Collisional and radiativ procsss All particls in a plasma intract with

More information

SUMMER 17 EXAMINATION

SUMMER 17 EXAMINATION (ISO/IEC - 7-5 Crtifid) SUMMER 7 EXAMINATION Modl wr jct Cod: Important Instructions to aminrs: ) Th answrs should b amind by ky words and not as word-to-word as givn in th modl answr schm. ) Th modl answr

More information

Higher order derivatives

Higher order derivatives Robrto s Nots on Diffrntial Calculus Chaptr 4: Basic diffrntiation ruls Sction 7 Highr ordr drivativs What you nd to know alrady: Basic diffrntiation ruls. What you can larn hr: How to rpat th procss of

More information

Differential Equations

Differential Equations UNIT I Diffrntial Equations.0 INTRODUCTION W li in a world of intrrlatd changing ntitis. Th locit of a falling bod changs with distanc, th position of th arth changs with tim, th ara of a circl changs

More information

Chapter 6 Folding. Folding

Chapter 6 Folding. Folding Chaptr 6 Folding Wintr 1 Mokhtar Abolaz Folding Th folding transformation is usd to systmatically dtrmin th control circuits in DSP architctur whr multipl algorithm oprations ar tim-multiplxd to a singl

More information

4. Money cannot be neutral in the short-run the neutrality of money is exclusively a medium run phenomenon.

4. Money cannot be neutral in the short-run the neutrality of money is exclusively a medium run phenomenon. PART I TRUE/FALSE/UNCERTAIN (5 points ach) 1. Lik xpansionary montary policy, xpansionary fiscal policy rturns output in th mdium run to its natural lvl, and incrass prics. Thrfor, fiscal policy is also

More information

Recursive Estimation of Dynamic Time-Varying Demand Models

Recursive Estimation of Dynamic Time-Varying Demand Models Intrnational Confrnc on Computr Systms and chnologis - CompSysch 06 Rcursiv Estimation of Dynamic im-varying Dmand Modls Alxandr Efrmov Abstract: h papr prsnts an implmntation of a st of rcursiv algorithms

More information

CHAPTER 1. Introductory Concepts Elements of Vector Analysis Newton s Laws Units The basis of Newtonian Mechanics D Alembert s Principle

CHAPTER 1. Introductory Concepts Elements of Vector Analysis Newton s Laws Units The basis of Newtonian Mechanics D Alembert s Principle CHPTER 1 Introductory Concpts Elmnts of Vctor nalysis Nwton s Laws Units Th basis of Nwtonian Mchanics D lmbrt s Principl 1 Scinc of Mchanics: It is concrnd with th motion of matrial bodis. odis hav diffrnt

More information

COHORT MBA. Exponential function. MATH review (part2) by Lucian Mitroiu. The LOG and EXP functions. Properties: e e. lim.

COHORT MBA. Exponential function. MATH review (part2) by Lucian Mitroiu. The LOG and EXP functions. Properties: e e. lim. MTH rviw part b Lucian Mitroiu Th LOG and EXP functions Th ponntial function p : R, dfind as Proprtis: lim > lim p Eponntial function Y 8 6 - -8-6 - - X Th natural logarithm function ln in US- log: function

More information

Numerical considerations regarding the simulation of an aircraft in the approaching phase for landing

Numerical considerations regarding the simulation of an aircraft in the approaching phase for landing INCAS BULLETIN, Volum, Numbr 1/ 1 Numrical considrations rgarding th simulation of an aircraft in th approaching phas for landing Ionl Cristinl IORGA ionliorga@yahoo.com Univrsity of Craiova, Alxandru

More information

VII. Quantum Entanglement

VII. Quantum Entanglement VII. Quantum Entanglmnt Quantum ntanglmnt is a uniqu stat of quantum suprposition. It has bn studid mainly from a scintific intrst as an vidnc of quantum mchanics. Rcntly, it is also bing studid as a basic

More information

Estimation of uncertainty of coordinate measurements according to the B method

Estimation of uncertainty of coordinate measurements according to the B method Estimation of uncrtainty of coordinat masurmnts according to th mthod Władysław Jakubic Univrsity of ilsko-iala (TH Dpartmnt of Manufacturing Tchnology an utomation Willowa, ilsko-iała, 43-309, Poland

More information

STATISTICAL METHODOLOGY FOR VALIDATION CALIBRATION METHODS IN HYDROMETRY Maria do Céu Ferreira 1, José Mendonça Dias 2

STATISTICAL METHODOLOGY FOR VALIDATION CALIBRATION METHODS IN HYDROMETRY Maria do Céu Ferreira 1, José Mendonça Dias 2 º ENCONTRO NACIONAL DA SOCIEDADE PORTUGUESA DE METROLOGIA A Mtrologia o Crscimnto Sustntado 7 d Novmbro d 006, Lisboa STATISTICAL METHODOLOGY FOR VALIDATION CALIBRATION METHODS IN HYDROMETRY Maria do Céu

More information

λ - Reference surface tension (at scale line), λ

λ - Reference surface tension (at scale line), λ XVIII IMEKO WORLD CONGRE Mtrology for a ustainabl Dvlopmnt ptmbr, 7, 006, Rio d Janiro, Brazil THE ROLE OF EXPERIMENTAL DEIGN IN THE HYDROMETER FIELD Maria do Céu Frrira, José Mndonça Dias Portugus Institut

More information