Doctoring Data. (1) Radboud University Nijmegen (2) UMC Utrecht (3) University of Groningen. Trento, 21 june 2005 p.1/34
|
|
|
- Andra Fisher
- 7 years ago
- Views:
Transcription
1 Doctoring Data Johan de Swart, Mart Rentmeester, Rob Timmermans (1) Radboud University Nijmegen (2) UMC Utrecht (3) University of Groningen Trento, 21 june 25 p1/34
2 Contents Part I : np backward scattering Part I : np backward scattering 1 Introduction to np cross sections 2 np backward scattering Princeton (1974) LAMPF (1978) Freiburg ( ) TRIUMF (1982) Uppsala ( now) IUCF (25) 3 Adnorm method 4 Doctoring data 5 Conclusion Trento, 21 june 25 p2/34
3 np cross sections (normalization) PWA 93 : accurate phases, thus accurate normalization, because (forget spin) exp : measured normalization, datum (1 ), should be included in data base calculated normalization, should NOT be included in data base floated normalization Difficulty : Doctoring of data eg Error bars should represent only the statistical errors, but contain almost always a systematic component Trento, 21 june 25 p3/34
4 TRIUMF: np cross section at 212 MeV 15 dσ/dω (mb) 1 np cross section at 212 MeV (TRIUMF) PWA93 N-phase P-phase 3 np cross-section at 212 MeV (TRIUMF) 5-3 N-phase P-phase n-phase: p-phase: Trento, 21 june 25 p4/34
5 TRIUMF: absolute normalization 23 april 1999 " I know from my own experience at TRIUMF how difficult it is to get the absolute normalisation right We tried very hard and analysed all sorts of effects for 2 years I hope we got it right, but it is one of those places where I have the least confidence " At TRIUMF they measured 3 total cross sections below 35 MeV absolute normalization = 1 (8) PWA93: = 954 (7) 6 sd At 319 MeV the normalization of the forward data (N-phase) needed renormalization of 85 % Trento, 21 june 25 p5/34
6 TRIUMF: doctoring data feb 21 " I am unhappy if you renormalise ALL of the data sets Our whole objective was to monitor carefully the neutron intensity, hence obtain ABSOLUTE cross sections (The monitors were ABSOLUTELY normalised) " No errors in relative normalizations can be obtained!! Only absolutely normalized data, obviously they think that they can measure normalizations without errors?! RIDICULOUS! No statistical errors are available!! Only point-to-point errors These contain systematic components Consequence: An incorrect, lower value for Trento, 21 june 25 p6/34
7 LAMPF: np cross sections Huge dataset: 162 MeV < T < 7 MeV divided over 29 energies T < 35 MeV 11 energies = 65 = = sd 12 np cross-section at 162 MeV (LAMPF) 12 np cross-section at 2115 MeV (LAMPF) T = 162 MeV N = 42 9 = 43 = 63 T = 211 MeV N = 42 9 = 43 = 31 Trento, 21 june 25 p7/34
8 LAMPF: doctoring data 29 data sets with T 11 data sets with T 7 data sets with T < 7 MeV Momentum bins of p = 2 MeV/c < 35 MeV < 27 MeV and non-overlapping angular regions Difficulties with data: Relative normalization between different angular regions not available Data in overlapping angular regions ( T > 27 MeV) were averaged Uppsala group complains about sawtooth behavior of data Trento, 21 june 25 p8/34
9 Freiburg: Hürster data (1978) 6 np cross-section at 2 MeV (SIN) -6 data doctored (Franz 2): Large data set: 2 energy bins (each 2 Mev wide) with 19 MeV < T 8 energy bins with T < 35 MeV centered at T = 2 MeV, 22 MeV,, 32 MeV, 34 MeV < 59 MeV Trento, 21 june 25 p9/34
10 Uppsala: np cross section at 162 MeV 12 np cross section at 162 MeV (Uppsala) Originally: and 6 PWA93: refit: (data) goes down 276 (rest) goes up 74 Complaint by experimentalist: " These data were rejected by applying controversial criteria " Complaint by us: data not as measured, but data were doctored! data contain LARGE systematic errors Trento, 21 june 25 p1/34
11 Uppsala: Nijmegen normalization np cross-section at 162 MeV (Uppsala) 5 = 15 = sd Trento, 21 june 25 p11/34
12 Uppsala: Nijmegen normalization np cross-section at 162 MeV (Uppsala) 5 = 16 = sd Trento, 21 june 25 p12/34
13 Uppsala: Nijmegen normalization np cross-section at 162 MeV (Uppsala) 5 = 18 = sd Trento, 21 june 25 p13/34
14 Uppsala: Nijmegen normalization np cross-section at 162 MeV (Uppsala) 5 = 21 = sd Trento, 21 june 25 p14/34
15 Uppsala: Nijmegen normalization np cross-section at 162 MeV (Uppsala) 5 = 18 = sd Trento, 21 june 25 p15/34
16 Uppsala: Nijmegen normalization 5-5 np cross-section at 162 MeV (Uppsala) = 15 = 16 = 18 = 21 = 18 = 1166 = 352 = 185 = 494 = = 88 = = sd Trento, 21 june 25 p16/34
17 Uppsala: straight lines np cross-section at 162 MeV (Uppsala) Trento, 21 june 25 p17/34
18 Uppsala: Normalization 1 Nijmegen normalization 1 Uppsala normalization Normalizations (5) were not measured, but doctored Relative normalizations (4) determined by assuming that cross section is continuous Slope is still discontinuous Data in overlapping regions were averaged Absolute normalization calculated from other sources Data are real sick They need "radical DOCTORING" Trento, 21 june 25 p18/34
19 IUCF: np cross section at 194 MeV 6 np cross-section at 194 MeV (IUCF) -6 χ 2 / N d = 273 / N = 15 PWA93: = 14 5 = 27 refit = sd = 26 is considered acceptable, when the errors are purely statistical Trento, 21 june 25 p19/34
20 What to do? Data from Princeton, Freiburg, Uppsala Garbage Pail???? How much money was involved in doing these experiments? Who wants to guess? Proposed method to save these data from oblivion Angle dependent normalization Adnorm method No positive response from experimentalists involved in these experiments Only " they propose radical DOCTORING " Conclusion : Let us do this radical doctoring Apply euthanasia to these data sets Trento, 21 june 25 p2/34
21 Adnorm Method The data are in the interval and is the middle of this interval The adnorm is then The parameters are only taken unequal to zero, when they are more than 3 sd away from zero When they are significant Notation: Only Trento, 21 june 25 p21/34
22 Doctoring the Uppsala data np cross-section at 162 MeV (Uppsala) = 15 = 16 = 18 = 2 = 18 = 117 = 35 = 18 = 35 = 38 = 2 = 15 = 15 = 9 Trento, 21 june 25 p22/34
23 Doctoring the Freiburg data 4 experiments between 1978 and 2 8 energy bins (2 MeV wide) with T < 35 MeV exp I N = 216 = 522 = 179 for 14 adnorm pars exp II N = 245 = 471 = 239 for 1 adnorm pars exp III N = 212 = 516 = 26 for 1 adnorm pars exp IV N = 186 = 63 = 153 for 11 adnorm pars Look at the problem this way In total 959 data 32 normalizations N(dof) = adnorm pars N(dof) = 882 = 2139 = 831 Information contained in 882 pieces of data is still there!! Trento, 21 june 25 p23/34
24 Doctoring the Princeton data (1974) 9 energy bins with T < 35 MeV N = adnorm pars = = = sd = sd Per adnorm parameter a drop in of about 27 Let us be lenient and doctor some more: Throw away 3 data points that deviate more than 25 sd (this limit was 3 sd) N = adnorm pars = = = sd = sd Trento, 21 june 25 p24/34
25 Doctoring the IUCF data? 6 np cross-section at 194 MeV (IUCF) 6 np cross-section at 194 MeV (IUCF) -6 χ 2 / N d = 273 / 15-6 χ 2 / N d = 82 / N = 15 PWA93: = 27 Adnorm: = 82 N = 9954 (44) N N( ) = N [ 1 + sin(4 ) ] = 9987 (45) = 27 (6) Trento, 21 june 25 p25/34
26 Conclusion 2 data (in order of quality?) Trento, 21 june 25 p26/34
27 Contents Part II : -coupling constants Part II : -coupling constants 1 Historical Introduction Situation in general Situation in Nijmegen Situation around pn coupling constants Trento, 21 june 25 p27/34
28 General situation 195 Ashkin 1954 Bernandini 1952 Lévy 1955 Gartenhaus 1958 Chew backward np 1959 Cziffra et al 6 < 1968 MacGregor et al 1987 Bergervoet et al 3 = 65 = 54 = 89 < 7 = 81 (5) = 725 (6) 1953 Chew 1957 Gilbert (NP med) 1958 Dave Jackson 1973 Bugg et al 199 Arndt et al 1958 Chew charge exchange 1991 Timmermans et al = 58 = 84 = 8 (2) = 79 (1) = 735 (15) = 751 (17) Trento, 21 june 25 p28/34
29 Situation in Nijmegen Interest mainly in YN potentials Couplings,, and " Black Forest Meetings " ( Höhler et al) and " Compilation of low-energy parameters and coupling constants " 1975 Nijmegen D potential (NN and YN) = 74 Used Livermore PWA 1968 better than for the Reid potential 1978 Start of Nijmegen PWA 1983 FB - conference in Karlsruhe " We believe that is probably more in the neighborhood of 75 than of 8 " 1987 pp PWA 87 = 725 (6) (without magn moment) = MeV ( MeV) pp PWA 91 = 751 (6) Trento, 21 june 25 p29/34
30 Situation around scattering - scattering = 79 (1) = 73 (1) Conclusion 1 : Large breaking of Charge Independence result : Large CIB : Conclusion 2 : = 73 (1) Very unlikely - result must be wrong Research topics in Nijmegen around that time 1 - PWA Stoks, de Kok 2 - PWA Bergervoet et al, Klomp 3 backward Rentmeester 4 Timmermans 5 study CIB in cc Timmermans Trento, 21 june 25 p3/34
31 pn-coupling constants Trento, 21 june 25 p31/34
32 pn-coupling constants LAMPF data: Trento, 21 june 25 p32/34
33 Part III : EFT Intermediate-range physics is treated very poorly Contributions of mesons like are frozen out The spatial extensions of the nucleons and mesons are neglected This affects the shape of the intermediate-range potential! Applying PT to calculate a good -potential is therefore doomed to failure! The coupling constants c and c, ( in PT called LEC s ), depend on the order, and on T, and c comes out too low Such potentials are perhaps good to say T 5MeV (?) These are the so called "Third (De)generation potentials"? Including higher orders like { N NLO } introduces MORE parameters (easier to get better fits), but does not necessarily introduces better physics Trento, 21 june 25 p33/34
34 Closing Remarks THANKS FOR YOUR PATIENCE NO QUESTIONS ALLOWED HAVE A NICE LUNCH Trento, 21 june 25 p34/34
Simple Regression Theory II 2010 Samuel L. Baker
SIMPLE REGRESSION THEORY II 1 Simple Regression Theory II 2010 Samuel L. Baker Assessing how good the regression equation is likely to be Assignment 1A gets into drawing inferences about how close the
36 CHAPTER 1. LIMITS AND CONTINUITY. Figure 1.17: At which points is f not continuous?
36 CHAPTER 1. LIMITS AND CONTINUITY 1.3 Continuity Before Calculus became clearly de ned, continuity meant that one could draw the graph of a function without having to lift the pen and pencil. While this
2, 8, 20, 28, 50, 82, 126.
Chapter 5 Nuclear Shell Model 5.1 Magic Numbers The binding energies predicted by the Liquid Drop Model underestimate the actual binding energies of magic nuclei for which either the number of neutrons
Week 4: Standard Error and Confidence Intervals
Health Sciences M.Sc. Programme Applied Biostatistics Week 4: Standard Error and Confidence Intervals Sampling Most research data come from subjects we think of as samples drawn from a larger population.
Domain of a Composition
Domain of a Composition Definition Given the function f and g, the composition of f with g is a function defined as (f g)() f(g()). The domain of f g is the set of all real numbers in the domain of g such
Solutions to Problems in Goldstein, Classical Mechanics, Second Edition. Chapter 7
Solutions to Problems in Goldstein, Classical Mechanics, Second Edition Homer Reid April 21, 2002 Chapter 7 Problem 7.2 Obtain the Lorentz transformation in which the velocity is at an infinitesimal angle
3. Mathematical Induction
3. MATHEMATICAL INDUCTION 83 3. Mathematical Induction 3.1. First Principle of Mathematical Induction. Let P (n) be a predicate with domain of discourse (over) the natural numbers N = {0, 1,,...}. If (1)
5.1 Radical Notation and Rational Exponents
Section 5.1 Radical Notation and Rational Exponents 1 5.1 Radical Notation and Rational Exponents We now review how exponents can be used to describe not only powers (such as 5 2 and 2 3 ), but also roots
Unit 1 Number Sense. In this unit, students will study repeating decimals, percents, fractions, decimals, and proportions.
Unit 1 Number Sense In this unit, students will study repeating decimals, percents, fractions, decimals, and proportions. BLM Three Types of Percent Problems (p L-34) is a summary BLM for the material
Awell-known lecture demonstration1
Acceleration of a Pulled Spool Carl E. Mungan, Physics Department, U.S. Naval Academy, Annapolis, MD 40-506; mungan@usna.edu Awell-known lecture demonstration consists of pulling a spool by the free end
CHI-SQUARE: TESTING FOR GOODNESS OF FIT
CHI-SQUARE: TESTING FOR GOODNESS OF FIT In the previous chapter we discussed procedures for fitting a hypothesized function to a set of experimental data points. Such procedures involve minimizing a quantity
Independent samples t-test. Dr. Tom Pierce Radford University
Independent samples t-test Dr. Tom Pierce Radford University The logic behind drawing causal conclusions from experiments The sampling distribution of the difference between means The standard error of
The aerodynamic center
The aerodynamic center In this chapter, we re going to focus on the aerodynamic center, and its effect on the moment coefficient C m. 1 Force and moment coefficients 1.1 Aerodynamic forces Let s investigate
AP CALCULUS AB 2007 SCORING GUIDELINES (Form B)
AP CALCULUS AB 2007 SCORING GUIDELINES (Form B) Question 4 Let f be a function defined on the closed interval 5 x 5 with f ( 1) = 3. The graph of f, the derivative of f, consists of two semicircles and
0.33 d down 1 1. 0.33 c charm + 2 3. 0 0 1.5 s strange 1 3. 0 0 0.5 t top + 2 3. 0 0 172 b bottom 1 3
Chapter 16 Constituent Quark Model Quarks are fundamental spin- 1 particles from which all hadrons are made up. Baryons consist of three quarks, whereas mesons consist of a quark and an anti-quark. There
WRITING PROOFS. Christopher Heil Georgia Institute of Technology
WRITING PROOFS Christopher Heil Georgia Institute of Technology A theorem is just a statement of fact A proof of the theorem is a logical explanation of why the theorem is true Many theorems have this
3. Time value of money. We will review some tools for discounting cash flows.
1 3. Time value of money We will review some tools for discounting cash flows. Simple interest 2 With simple interest, the amount earned each period is always the same: i = rp o where i = interest earned
Basic Nuclear Concepts
Section 7: In this section, we present a basic description of atomic nuclei, the stored energy contained within them, their occurrence and stability Basic Nuclear Concepts EARLY DISCOVERIES [see also Section
Elasticity. I. What is Elasticity?
Elasticity I. What is Elasticity? The purpose of this section is to develop some general rules about elasticity, which may them be applied to the four different specific types of elasticity discussed in
2 Binomial, Poisson, Normal Distribution
2 Binomial, Poisson, Normal Distribution Binomial Distribution ): We are interested in the number of times an event A occurs in n independent trials. In each trial the event A has the same probability
" Y. Notation and Equations for Regression Lecture 11/4. Notation:
Notation: Notation and Equations for Regression Lecture 11/4 m: The number of predictor variables in a regression Xi: One of multiple predictor variables. The subscript i represents any number from 1 through
f(x) = g(x), if x A h(x), if x B.
1. Piecewise Functions By Bryan Carrillo, University of California, Riverside We can create more complicated functions by considering Piece-wise functions. Definition: Piecewise-function. A piecewise-function
Ch. 11.2: Installment Buying
Ch. 11.2: Installment Buying When people take out a loan to make a big purchase, they don t often pay it back all at once in one lump-sum. Instead, they usually pay it back back gradually over time, in
2013 Satisfaction Survey. How are we doing? Easier to Read Version
2013 Satisfaction Survey How are we doing? Easier to Read Version We asked people some questions about their support. Here is some of what people said and the changes we will make. That someone who knows
Descriptive Statistics
Y520 Robert S Michael Goal: Learn to calculate indicators and construct graphs that summarize and describe a large quantity of values. Using the textbook readings and other resources listed on the web
Odds ratio, Odds ratio test for independence, chi-squared statistic.
Odds ratio, Odds ratio test for independence, chi-squared statistic. Announcements: Assignment 5 is live on webpage. Due Wed Aug 1 at 4:30pm. (9 days, 1 hour, 58.5 minutes ) Final exam is Aug 9. Review
88 CHAPTER 2. VECTOR FUNCTIONS. . First, we need to compute T (s). a By definition, r (s) T (s) = 1 a sin s a. sin s a, cos s a
88 CHAPTER. VECTOR FUNCTIONS.4 Curvature.4.1 Definitions and Examples The notion of curvature measures how sharply a curve bends. We would expect the curvature to be 0 for a straight line, to be very small
9231 FURTHER MATHEMATICS
CAMBRIDGE INTERNATIONAL EXAMINATIONS GCE Advanced Subsidiary Level and GCE Advanced Level MARK SCHEME for the October/November 2012 series 9231 FURTHER MATHEMATICS 9231/21 Paper 2, maximum raw mark 100
Family law a guide for legal consumers
Family law a guide for legal consumers Image Credit - Jim Harper A relationship breakdown is a difficult time for anyone. It is one of the most stressful experiences in life. Where you have to involve
SCHOOL OF HEALTH AND HUMAN SCIENCES DON T FORGET TO RECODE YOUR MISSING VALUES
SCHOOL OF HEALTH AND HUMAN SCIENCES Using SPSS Topics addressed today: 1. Differences between groups 2. Graphing Use the s4data.sav file for the first part of this session. DON T FORGET TO RECODE YOUR
Summary of Formulas and Concepts. Descriptive Statistics (Ch. 1-4)
Summary of Formulas and Concepts Descriptive Statistics (Ch. 1-4) Definitions Population: The complete set of numerical information on a particular quantity in which an investigator is interested. We assume
Two-sample inference: Continuous data
Two-sample inference: Continuous data Patrick Breheny April 5 Patrick Breheny STA 580: Biostatistics I 1/32 Introduction Our next two lectures will deal with two-sample inference for continuous data As
The normal approximation to the binomial
The normal approximation to the binomial The binomial probability function is not useful for calculating probabilities when the number of trials n is large, as it involves multiplying a potentially very
Normal distribution. ) 2 /2σ. 2π σ
Normal distribution The normal distribution is the most widely known and used of all distributions. Because the normal distribution approximates many natural phenomena so well, it has developed into a
Your guide to Using a solicitor
www.lawsociety.org.uk 1 Most of us need expert legal help at some time in our lives. Some of the most common issues are to do with buying a house, getting a divorce or making a will. But you might also
Three-nucleon interaction dynamics studied via the deuteron-proton breakup. Elżbieta Stephan Institute of Physics, University of Silesia
Three-nucleon interaction dynamics studied via the deuteron-proton breakup Elżbieta Stephan Institute of Physics, University of Silesia Studies of the 1 H(d,pp)n Breakup at 130 MeV University of Silesia,
Company: Balfour Beatty Conference Title: Half Year 2011 Results Presenters: Ian Tyler, Duncan Magrath Wednesday 17 th August 2011 15h00 BST
Company: Balfour Beatty Conference Title: Half Year 2011 Results Presenters: Ian Tyler, Duncan Magrath Date: Wednesday 17 th August 2011 15h00 BST Operator: Good day ladies and gentlemen and welcome to
TEACHER NOTES MATH NSPIRED
Math Objectives Students will understand that normal distributions can be used to approximate binomial distributions whenever both np and n(1 p) are sufficiently large. Students will understand that when
Chapter 10. Key Ideas Correlation, Correlation Coefficient (r),
Chapter 0 Key Ideas Correlation, Correlation Coefficient (r), Section 0-: Overview We have already explored the basics of describing single variable data sets. However, when two quantitative variables
4. Continuous Random Variables, the Pareto and Normal Distributions
4. Continuous Random Variables, the Pareto and Normal Distributions A continuous random variable X can take any value in a given range (e.g. height, weight, age). The distribution of a continuous random
2.2 Derivative as a Function
2.2 Derivative as a Function Recall that we defined the derivative as f (a) = lim h 0 f(a + h) f(a) h But since a is really just an arbitrary number that represents an x-value, why don t we just use x
Descriptive statistics Statistical inference statistical inference, statistical induction and inferential statistics
Descriptive statistics is the discipline of quantitatively describing the main features of a collection of data. Descriptive statistics are distinguished from inferential statistics (or inductive statistics),
Lesson 26: Reflection & Mirror Diagrams
Lesson 26: Reflection & Mirror Diagrams The Law of Reflection There is nothing really mysterious about reflection, but some people try to make it more difficult than it really is. All EMR will reflect
Project Management Assessment Overview
Project Management Assessment Overview Goals The goals of the assessment are to: Provide a self assessment of your company skills in nine areas of project management (e.g. Risk Management, Scope Management,
1. Degenerate Pressure
. Degenerate Pressure We next consider a Fermion gas in quite a different context: the interior of a white dwarf star. Like other stars, white dwarfs have fully ionized plasma interiors. The positively
Method To Solve Linear, Polynomial, or Absolute Value Inequalities:
Solving Inequalities An inequality is the result of replacing the = sign in an equation with ,, or. For example, 3x 2 < 7 is a linear inequality. We call it linear because if the < were replaced with
BALTIC OLYMPIAD IN INFORMATICS Stockholm, April 18-22, 2009 Page 1 of?? ENG rectangle. Rectangle
Page 1 of?? ENG rectangle Rectangle Spoiler Solution of SQUARE For start, let s solve a similar looking easier task: find the area of the largest square. All we have to do is pick two points A and B and
Graphing Parabolas With Microsoft Excel
Graphing Parabolas With Microsoft Excel Mr. Clausen Algebra 2 California State Standard for Algebra 2 #10.0: Students graph quadratic functions and determine the maxima, minima, and zeros of the function.
The Dot and Cross Products
The Dot and Cross Products Two common operations involving vectors are the dot product and the cross product. Let two vectors =,, and =,, be given. The Dot Product The dot product of and is written and
Answer: C. The strength of a correlation does not change if units change by a linear transformation such as: Fahrenheit = 32 + (5/9) * Centigrade
Statistics Quiz Correlation and Regression -- ANSWERS 1. Temperature and air pollution are known to be correlated. We collect data from two laboratories, in Boston and Montreal. Boston makes their measurements
An Introduction to Path Analysis. nach 3
An Introduction to Path Analysis Developed by Sewall Wright, path analysis is a method employed to determine whether or not a multivariate set of nonexperimental data fits well with a particular (a priori)
Introduction. Hypothesis Testing. Hypothesis Testing. Significance Testing
Introduction Hypothesis Testing Mark Lunt Arthritis Research UK Centre for Ecellence in Epidemiology University of Manchester 13/10/2015 We saw last week that we can never know the population parameters
Chapter 3 Falling Objects and Projectile Motion
Chapter 3 Falling Objects and Projectile Motion Gravity influences motion in a particular way. How does a dropped object behave?!does the object accelerate, or is the speed constant?!do two objects behave
Introduction to Quantitative Methods
Introduction to Quantitative Methods October 15, 2009 Contents 1 Definition of Key Terms 2 2 Descriptive Statistics 3 2.1 Frequency Tables......................... 4 2.2 Measures of Central Tendencies.................
Discrete Mathematics and Probability Theory Fall 2009 Satish Rao, David Tse Note 2
CS 70 Discrete Mathematics and Probability Theory Fall 2009 Satish Rao, David Tse Note 2 Proofs Intuitively, the concept of proof should already be familiar We all like to assert things, and few of us
Section 1. Inequalities -5-4 -3-2 -1 0 1 2 3 4 5
Worksheet 2.4 Introduction to Inequalities Section 1 Inequalities The sign < stands for less than. It was introduced so that we could write in shorthand things like 3 is less than 5. This becomes 3 < 5.
2 Sample t-test (unequal sample sizes and unequal variances)
Variations of the t-test: Sample tail Sample t-test (unequal sample sizes and unequal variances) Like the last example, below we have ceramic sherd thickness measurements (in cm) of two samples representing
Chapter 25: Exchange in Insurance Markets
Chapter 25: Exchange in Insurance Markets 25.1: Introduction In this chapter we use the techniques that we have been developing in the previous 2 chapters to discuss the trade of risk. Insurance markets
Kenken For Teachers. Tom Davis tomrdavis@earthlink.net http://www.geometer.org/mathcircles June 27, 2010. Abstract
Kenken For Teachers Tom Davis tomrdavis@earthlink.net http://www.geometer.org/mathcircles June 7, 00 Abstract Kenken is a puzzle whose solution requires a combination of logic and simple arithmetic skills.
First-year Statistics for Psychology Students Through Worked Examples
First-year Statistics for Psychology Students Through Worked Examples 1. THE CHI-SQUARE TEST A test of association between categorical variables by Charles McCreery, D.Phil Formerly Lecturer in Experimental
Particle Physics. Michaelmas Term 2011 Prof Mark Thomson. Handout 7 : Symmetries and the Quark Model. Introduction/Aims
Particle Physics Michaelmas Term 2011 Prof Mark Thomson Handout 7 : Symmetries and the Quark Model Prof. M.A. Thomson Michaelmas 2011 206 Introduction/Aims Symmetries play a central role in particle physics;
Introduction to the Practice of Statistics Fifth Edition Moore, McCabe
Introduction to the Practice of Statistics Fifth Edition Moore, McCabe Section 5.1 Homework Answers 5.7 In the proofreading setting if Exercise 5.3, what is the smallest number of misses m with P(X m)
Experimental Uncertainties (Errors)
Experimental Uncertainties (Errors) Sources of Experimental Uncertainties (Experimental Errors): All measurements are subject to some uncertainty as a wide range of errors and inaccuracies can and do happen.
THE FIRST SET OF EXAMPLES USE SUMMARY DATA... EXAMPLE 7.2, PAGE 227 DESCRIBES A PROBLEM AND A HYPOTHESIS TEST IS PERFORMED IN EXAMPLE 7.
THERE ARE TWO WAYS TO DO HYPOTHESIS TESTING WITH STATCRUNCH: WITH SUMMARY DATA (AS IN EXAMPLE 7.17, PAGE 236, IN ROSNER); WITH THE ORIGINAL DATA (AS IN EXAMPLE 8.5, PAGE 301 IN ROSNER THAT USES DATA FROM
Chapter 11: r.m.s. error for regression
Chapter 11: r.m.s. error for regression Context................................................................... 2 Prediction error 3 r.m.s. error for the regression line...............................................
INTRODUCTION TO MULTIPLE CORRELATION
CHAPTER 13 INTRODUCTION TO MULTIPLE CORRELATION Chapter 12 introduced you to the concept of partialling and how partialling could assist you in better interpreting the relationship between two primary
PERPETUITIES NARRATIVE SCRIPT 2004 SOUTH-WESTERN, A THOMSON BUSINESS
NARRATIVE SCRIPT 2004 SOUTH-WESTERN, A THOMSON BUSINESS NARRATIVE SCRIPT: SLIDE 2 A good understanding of the time value of money is crucial for anybody who wants to deal in financial markets. It does
Adding and Subtracting Positive and Negative Numbers
Adding and Subtracting Positive and Negative Numbers Absolute Value For any real number, the distance from zero on the number line is the absolute value of the number. The absolute value of any real number
Using Excel for inferential statistics
FACT SHEET Using Excel for inferential statistics Introduction When you collect data, you expect a certain amount of variation, just caused by chance. A wide variety of statistical tests can be applied
Interpreting GRE Scores: Reliability and Validity
Interpreting GRE Scores: Reliability and Validity Dr. Lesa Hoffman Department of Psychology University of Nebraska Lincoln All data from: GRE Guide to the Use of Scores 2010 2011 http://www.ets.org/s/gre/pdf/gre_guide.pdf
TOPIC 4: DERIVATIVES
TOPIC 4: DERIVATIVES 1. The derivative of a function. Differentiation rules 1.1. The slope of a curve. The slope of a curve at a point P is a measure of the steepness of the curve. If Q is a point on the
Integers are positive and negative whole numbers, that is they are; {... 3, 2, 1,0,1,2,3...}. The dots mean they continue in that pattern.
INTEGERS Integers are positive and negative whole numbers, that is they are; {... 3, 2, 1,0,1,2,3...}. The dots mean they continue in that pattern. Like all number sets, integers were invented to describe
Determination of g using a spring
INTRODUCTION UNIVERSITY OF SURREY DEPARTMENT OF PHYSICS Level 1 Laboratory: Introduction Experiment Determination of g using a spring This experiment is designed to get you confident in using the quantitative
Updates to Graphing with Excel
Updates to Graphing with Excel NCC has recently upgraded to a new version of the Microsoft Office suite of programs. As such, many of the directions in the Biology Student Handbook for how to graph with
family games Taking the kids swimming is a great way of making sure they re moving around and having fun. And to help you get them into
swim family games Taking the kids swimming is a great way of making sure they re moving around and having fun. And to help you get them into the pool, we ve come up with loads of great swimming games to
CALCULATIONS & STATISTICS
CALCULATIONS & STATISTICS CALCULATION OF SCORES Conversion of 1-5 scale to 0-100 scores When you look at your report, you will notice that the scores are reported on a 0-100 scale, even though respondents
LINEAR INEQUALITIES. less than, < 2x + 5 x 3 less than or equal to, greater than, > 3x 2 x 6 greater than or equal to,
LINEAR INEQUALITIES When we use the equal sign in an equation we are stating that both sides of the equation are equal to each other. In an inequality, we are stating that both sides of the equation are
1.2 Solving a System of Linear Equations
1.. SOLVING A SYSTEM OF LINEAR EQUATIONS 1. Solving a System of Linear Equations 1..1 Simple Systems - Basic De nitions As noticed above, the general form of a linear system of m equations in n variables
MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question.
STT315 Practice Ch 5-7 MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question. Solve the problem. 1) The length of time a traffic signal stays green (nicknamed
Common sense, and the model that we have used, suggest that an increase in p means a decrease in demand, but this is not the only possibility.
Lecture 6: Income and Substitution E ects c 2009 Je rey A. Miron Outline 1. Introduction 2. The Substitution E ect 3. The Income E ect 4. The Sign of the Substitution E ect 5. The Total Change in Demand
E3: PROBABILITY AND STATISTICS lecture notes
E3: PROBABILITY AND STATISTICS lecture notes 2 Contents 1 PROBABILITY THEORY 7 1.1 Experiments and random events............................ 7 1.2 Certain event. Impossible event............................
Measuring Line Edge Roughness: Fluctuations in Uncertainty
Tutor6.doc: Version 5/6/08 T h e L i t h o g r a p h y E x p e r t (August 008) Measuring Line Edge Roughness: Fluctuations in Uncertainty Line edge roughness () is the deviation of a feature edge (as
Factors affecting online sales
Factors affecting online sales Table of contents Summary... 1 Research questions... 1 The dataset... 2 Descriptive statistics: The exploratory stage... 3 Confidence intervals... 4 Hypothesis tests... 4
Exercise 1.12 (Pg. 22-23)
Individuals: The objects that are described by a set of data. They may be people, animals, things, etc. (Also referred to as Cases or Records) Variables: The characteristics recorded about each individual.
Mechanics 1: Vectors
Mechanics 1: Vectors roadly speaking, mechanical systems will be described by a combination of scalar and vector quantities. scalar is just a (real) number. For example, mass or weight is characterized
2. Discrete random variables
2. Discrete random variables Statistics and probability: 2-1 If the chance outcome of the experiment is a number, it is called a random variable. Discrete random variable: the possible outcomes can be
ECO 199 B GAMES OF STRATEGY Spring Term 2004 PROBLEM SET 4 B DRAFT ANSWER KEY 100-3 90-99 21 80-89 14 70-79 4 0-69 11
The distribution of grades was as follows. ECO 199 B GAMES OF STRATEGY Spring Term 2004 PROBLEM SET 4 B DRAFT ANSWER KEY Range Numbers 100-3 90-99 21 80-89 14 70-79 4 0-69 11 Question 1: 30 points Games
Comparing Means in Two Populations
Comparing Means in Two Populations Overview The previous section discussed hypothesis testing when sampling from a single population (either a single mean or two means from the same population). Now we
25 Integers: Addition and Subtraction
25 Integers: Addition and Subtraction Whole numbers and their operations were developed as a direct result of people s need to count. But nowadays many quantitative needs aside from counting require numbers
https://williamshartunionca.springboardonline.org/ebook/book/27e8f1b87a1c4555a1212b...
of 19 9/2/2014 12:09 PM Answers Teacher Copy Plan Pacing: 1 class period Chunking the Lesson Example A #1 Example B Example C #2 Check Your Understanding Lesson Practice Teach Bell-Ringer Activity Students
Orbits of the Lennard-Jones Potential
Orbits of the Lennard-Jones Potential Prashanth S. Venkataram July 28, 2012 1 Introduction The Lennard-Jones potential describes weak interactions between neutral atoms and molecules. Unlike the potentials
PowerScore Test Preparation (800) 545-1750
Question 1 Test 1, Second QR Section (version 1) List A: 0, 5,, 15, 20... QA: Standard deviation of list A QB: Standard deviation of list B Statistics: Standard Deviation Answer: The two quantities are
C B A T 3 T 2 T 1. 1. What is the magnitude of the force T 1? A) 37.5 N B) 75.0 N C) 113 N D) 157 N E) 192 N
Three boxes are connected by massless strings and are resting on a frictionless table. Each box has a mass of 15 kg, and the tension T 1 in the right string is accelerating the boxes to the right at a
Playing with Numbers
PLAYING WITH NUMBERS 249 Playing with Numbers CHAPTER 16 16.1 Introduction You have studied various types of numbers such as natural numbers, whole numbers, integers and rational numbers. You have also
Physical Principle of Formation and Essence of Radio Waves
Physical Principle of Formation and Essence of Radio Waves Anatoli Bedritsky Abstract. This article opens physical phenomena which occur at the formation of the radio waves, and opens the essence of the
Inequalities - Absolute Value Inequalities
3.3 Inequalities - Absolute Value Inequalities Objective: Solve, graph and give interval notation for the solution to inequalities with absolute values. When an inequality has an absolute value we will
Trigonometric functions and sound
Trigonometric functions and sound The sounds we hear are caused by vibrations that send pressure waves through the air. Our ears respond to these pressure waves and signal the brain about their amplitude
Reflection and Refraction
Equipment Reflection and Refraction Acrylic block set, plane-concave-convex universal mirror, cork board, cork board stand, pins, flashlight, protractor, ruler, mirror worksheet, rectangular block worksheet,
Maths Targets for pupils in Year 2
Maths Targets for pupils in Year 2 A booklet for parents Help your child with mathematics For additional information on the agreed calculation methods, please see the school website. ABOUT THE TARGETS