Analyzing Longitudinal Data from Complex Surveys Using SUDAAN


 Alice Osborne
 4 years ago
 Views:
Transcription
1 Aalyzig Logitudial Data from Complex Surveys Usig SUDAAN Darryl Creel Statistics ad Epidemiology, RTI Iteratioal, 312 Trotter Farm Drive, Rockville, MD, Abstract SUDAAN: Software for the Statistical Aalysis of Correlated Data (SUDAAN) ca be used to aalyze data from surveys with complex desigs. A possible feature of a complex survey desig is clusterig. Oe way i which clusterig ca occur is to have the same iformatio collected o a samplig uit at differet poits i time. This type of clusterig creates data that may be referred to as logitudial, pael, or repeated measures data. This paper provides a example of logitudial data aalysis usig SUDAAN. The example covers the structure of the data ad data set; aalytic strategies ad iterpretatio; ad the implemetatio of the aalytic strategies usig SUDAAN. Keywords: Logitudial Data Aalysis (LDA), SUDAAN. 1. Itroductio Oe of the major uses of logitudial data is to aalyze treds, or chage, over time. The SUDAAN team at RTI Iteratioal ofte receives questios about how to coduct logitudial data aalysis usig SUDAAN. This paper provides a aswer to this questio. I Sectio 2, we discuss logitudial data. I Sectio 3, we discuss various survey desigs over time. I Sectio 4, we examie the variace of a differece of two meas. I Sectio 5, we discuss the data structure SUDAAN requires for the data aalysis. I Sectio 6, we examie the SUDAAN code to aalyze logitudial data ad discuss a cautioary ote. I Sectio 7, we provide a example to illustrate the possible differeces that may occur whe oe does ad does ot accout for the logitudial structure of the data. Fially, i Sectio 8, we provide some recommedatios ad cautios. 2. Logitudial Survey Data Logitudial data measures the same characteristics of the same samplig uit over time. For example, i a logitudial health survey of childre, measuremets such height ad weight may be measured each time the survey is coducted to create the child s body mass idex (BMI). Some of the goals of collectig logitudial data are to produce populatio estimates over time, study chage over time, ad/or study variables that affect chage over time. Cotiuig the logitudial health survey childre example, researchers may be iterested i the populatio estimates of BMI for specific subgroups over time. Researchers may also be iterested i studyig the chage i BMI overtime ad what variables are related to the chage i BMI over time. Logitudial data from a survey with a complex survey desig has the added complicatio of accoutig for this complex survey desig i the aalysis. SUDAAN ca accout for differet aspects of the complex survey desig, e.g., stratificatio, clusterig, ad differetial weightig, while coductig logitudial data aalysis. 3. Survey Desigs over Time There are four commo desig for surveys coducted over time: repeated surveys, pael survey, rotatig pael survey, ad split pael survey. 1 I the repeated survey desig, similar measuremets are made o samples from a equivalet populatio at differet poits of time, but without attemptig to esure that ay elemets are icluded i more tha oe roud of data collectio. 2 Its particular stregth is that at each roud of data collectio it routiely selects a sample of the populatio existig at that time. 3 The major limitatio of a repeated survey is that it does ot yield data to satisfy objectives [of estimatig chage at the elemet level betwee two time poits ad other compoets of idividual chage] ad [aggregate data for idividuals over time]. 4 1 There is a detailed explaatio of these desigs by Greg Duca ad Graham Kalto i Issues of Desig ad Aalysis of Surveys Across Time, Iteratioal Statistical Review, Vol. 55, No. 1, pp This sectio is a brief summary of some of their discussio. 2 Duca ad Kalto Duca ad Kalto Duca ad Kalto
2 A pael survey is oe i which similar measuremets are made o the same sample at differet poits i time. 5 The major advatage of a pael survey over a repeated survey is its much greater aalytic potetial. It eables compoets of idividual chage to be measured ad also the summatio of a variable across time. 6 It ca be much more efficiet tha a repeated survey for measurig et chage. 7 [T]wo major potetial problems with pael surveys are pael losses through orespose ad the itroductio of ew elemets to the populatio as time passes. 8 I a pael survey, sample elemets are, i priciple, kept i the pael for the duratio of the survey. I a rotatio pael survey, sample elemets have a restricted pael life; as they leave the pael, ew elemets are added. The limited membership i a rotatig pael acts to reduce the problems of pael coditioig ad pael loss i compariso with orotatig pael survey, ad the cotiual itroductio of ew sample helps to maitai a uptodate sample of a chagig populatio. 9 A split pael survey is a combiatio of a pael ad a repeated or rotatig pael survey, as advocated i Kish (1983, 1986) Variace of a Differece of Two Meas The sectio focuses o the repeated crosssectioal survey, the pael survey, ad the rotatig pael survey. The split pael survey is ot discussed i the sectio, but recall that it is a combiatio of a fixed pael ad ew sample elemets from either a repeated or rotatig pael. The repeated crosssectioal survey desig uses the same survey desig each year but samples a differet group of members each year. This approach is coceptually straight forward, samples from the curret populatio, ad avoids the complexity of a pael survey, fixed or rotatig. However, it is difficult to tell if the differeces are simply due to the differet samples or are a true differece i the outcome variable. Also, whe aalyzig the differece of two meas betwee years the repeated crosssectioal survey desig is ot the most efficiet survey desig. Because of the idepedet samples, 5 Duca ad Kalto Duca ad Kalto Duca ad Kalto Duca ad Kalto Duca ad Kalto Duca ad Kalto 104. the variace of the differece of two meas is relatively large compared to other methods. Usig simplifyig assumptios that the variaces of the meas are equal for the two time 2 periods, S 1 = S2 = S, ad that the sample sizes are equal for the two time periods, 1 = 2 =, the variace for the differece of two meas, where m 1 is the mea for time period oe ad m 2 is the mea for time period two, for repeated crosssectioal surveys is var( m 2 m1 ) = S. Cotrast this with the most efficiet survey desig to measure differeces betwee time periods which is the fixed pael survey desig, i.e., a sigle sample o which data is collected at differet poits i time. The efficiecy of the fixed pael survey depeds o the correlatio betwee the outcome variable at two time periods, ρ 12. Usig the same assumptios that were used for the variace of a differece of two meas for repeated crosssectioal surveys, the variace of a differece of two meas for the fixed pael survey is var( m m ) = S (1 12). 2 1 ρ Comparig the variace of the differece of two meas for repeated crosssectioal survey ad a fixed pael survey, the variace of the differece of two meas for the fixed pael survey has a smaller variace by the factor ( 1 ρ12). Cosequetly, the higher the correlatio betwee the two time periods is the smaller the variace of the differece of two meas. Although the fixed pael survey is the most efficiet at measurig differeces betwee years, it is ot without its limitatios. Geerally, a fixed pael survey has three limitatios: the pael is selected at oe poit i time, pael attritio, ad pael coditioig. If the populatio is chagig, the selectig the sample oce ad ot every year may cause the sample to become less ad less represetative of the populatio ad bias the survey estimates. Pael attritio ca arise because of the added respose burde for pael members to provide data every year. Pael coditioig meas that pael member s resposes chage i some way because they are part of the pael. A rotatig pael survey desig ca mitigate the problems associated with the fixed pael survey 3528
3 without losig all of the beefits of the reductio i the variace of the differeces. I a rotatig pael survey desig, pael members are oly retaied i the pael for a set period of time ad ew pael members are brought ito the pael. This mitigates the pael attritio ad pael coditioig which is a cocer for a fixed pael. Also, because of the rotatio i of ew groups ito the pael at each time period, the pael is ot static ad is updated with ew pael members from the curret populatio. This will accout for ay chages i the populatio over the course of the life of the survey. Because there is ot complete overlap, there will be some loss i the efficiecy of the rotatig pael that is proportioal to the size of the pael that does ot overlap from oe time period to the ext. That is, the formula for the variace of the differece of two meas has a added term that represets the amout of overlap,λ, var( m2 m1 ) = S (1 λρ12). With λ = ½, the variaces will oly beefit by half of the correlatio of the outcome variable betwee the two time periods. If λ = 1, i.e., there is complete overlap, the the variace is equal to the fixed pael variace. If λ = 0, i.e., there is o overlap, the the variace is equal to the repeated crosssectioal survey variace. 5. Structure of the Data Sets Let us assume that there are two data sets. Oe data set is from 2004 ad the other is from The two data sets do have some overlap. That is, there are some primary samplig uits (PSU) that are o both data sets. Also, each of the data sets has a commo set of aalytic variables that are ot show i the followig tables. Table 1 shows the stratum, PSU, ad year for the 2004 data set. Table 1: 2004 Data Set Showig the Stratum, Primary Samplig Uit, ad Year Table 2 shows the same iformatio for the 2005 data set. Note that the data i Table 1 are italicized ad bolded; the data i Table 2 are ot. This distictio is carried through i the other tables. Table 2: 2005 Data Set Showig the Stratum, Primary Samplig Uit, ad Year I order to perform the logitudial data aalysis, SUDAAN requires that the two separate data sets be combied ito oe data set. The combied data set is show i Table 3. Table 3: Combied 2004 ad 2005 Data Set Showig the Stratum, Primary Samplig Uit, ad Year SUDAAN also requires that the data set is sorted by the variables o the est statemet. The est statemet that will be used i our first set of example code cotais year, stratum, ad PSU. The data set sorted by these variables i show i Table 3. This sortig used year as a stratificatio variable. Cosequetly, the results usig this data set are similar to results from a repeated crosssectioal survey. That is, there is o beefit for the correlatio betwee resposes over the two time periods. The est statemet that will be used i our secod set of example code cotais stratum ad PSU. The data 3529
4 set sorted by these variables i show i Table 4. Sortig by stratum ad PSU, ad ot usig year, creates a data set that has year clustered withi PSU. Cosequetly, the results usig this data set are similar the pael desig, although we do ot have complete overlap. We still have the advatage of the variace reductio because of the overlap that we do have ad the correlatio betwee the resposes. Table 4: Combied 2004 ad 2005 Data Set Showig the Stratum, Primary Samplig Uit, ad Year Sorted by Stratum ad PSU SUDAAN Code for Logitudial Data Aalysis ad Cautioary Note 6.1 SUDAAN Code The focus of the followig SUDAAN code is to calculate the cotrast, ad associated iformatio, betwee 2007 ad Ofte we see examples of SUDAAN code, that cotai the year variable as a stratificatio variable as show i the followig SUDAAN code: proc descript data = dataset desig = wr; est year stratum PSU / psulev = 3; 11 weight aweight; class year / ofreqs; 11 The psulev = 3 optio o the est statemet tells SUDAAN that the third variable o the est statemet is the PSU which implies that the first two variables o the est statemet are stratificatio variables. A full descriptio of the SUDAAN laguage ca be foud i the SUDAAN Laguage Maual, Release 9.0. var avar.; cotrast year = ( 1 1 ) / ame = " Cotrast"; prit sum mea semea t_mea p_mea; ru; Usig the year variable as a stratificatio variable, does ot allow us to beefit from the logitudial structure of the data. That is, the observatios for a PSU are classified across multiple years ad ot clustered withi PSU. Oe way to capture the multiple years of data collected for a PSU is ot to use year as a stratificatio variable. The followig code oly icludes the stratum variable as the stratificatio variable: proc descript data = dataset desig = wr; est stratum PSU; weight aweight; class year / ofreqs; var avar.; cotrast year = ( 1 1 ) / ame = " Cotrast"; prit sum mea semea t_mea p_mea; ru; Cosequetly, this SUDAAN code treats the years as clustered withi the PSU ad allows us to take advatage of the logitudial structure of the data. 6.2 Cautioary Note The focus of the previous SUDAAN code is usig a combied data set to produce cotrasts betwee years. The umber for the degrees of freedom (d.f.) for our simple example that SUDAAN uses is correct for this purpose; it would use 4 d.f. There is a cautio whe oe aalyzes a sigle year s data. Each sigle year data set for our simple example would have 3 d.f. ad this is what SUDAAN would use for the sigle year data sets. For the combied data set, SUDANN would use 4 d.f. eve for the sigle year aalysis. Cosequetly, oe should use the DDF = 3 optio for the combied data set for sigle year aalysis or use the sigle year data sets. 7. Example We have icluded oe example usig simulated data so that oe ca see the potetial impact of ot takig the logitudial data structure ito accout, ad possibly gettig smaller stadard errors. The simulated data set had 500 observatios i a sigle 3530
5 stratum, a λ = 1, ad ρ = The results of aalyzig that data treatig it as a repeated crosssectioal data structure ad a pael data structure are preseted i Table 5. Research Triagle Istitute (2004), SUDAAN Laguage Maual, Release 9.0, Research Triagle Park, NC: Research Triagle Istitute. Table 5: Results of Simulated Data Set Aalyzed as a Repeated CrossSectio Survey ad a Pael Survey Repeated Pael Cross Sectio Cotrast Mea (CM) SE CM Lower Limit 95% CI CM Upper Limit 95% CI CM Ttest CM PValue Ttest CM Note that the estimates for the cotrast mea are the same, but the stadard error estimates for the cotrast mea is smaller for the pael survey tha for the repeated crosssectio survey. This differece carries through to the cofidece itervals ad testig, which results i a statistically sigificat differece at the α = 0.05 level for the pael but ot for the repeated crosssectio survey. Hece, the aalytic approach has the possibility of makig a differece i your iterpretatio of the output. 8. Recommedatios The mai poit is to take advatage of the logitudial data structure ad possibly smaller stadard errors. Oe ca accout for the logitudial data structure easily usig SUDAAN to produce cotrasts. Fially, use a data set that combies years of iformatio for cotrasts or sigle year aalysis usig the DDF optio. Oe could also use the sigle year data sets for the sigle year aalysis. Refereces Duca, Greg ad Kalto, Graham (1987), Issues of Desig ad Aalysis of Surveys Across Time, Iteratioal Statistical Review, Vol. 55, No. 1, pp Kish, Leslie (1983), Data Collectio for Details over Space ad Time, Statistical Methods ad the Improvemet of Data Quality, Ed. T. Wright, New York: Academic Press, pp Kish, Leslie (1986), Timig of Surveys for Public Policy, The Australia Joural of Statistics, Vol 28, pp
Confidence Intervals for One Mean
Chapter 420 Cofidece Itervals for Oe Mea Itroductio This routie calculates the sample size ecessary to achieve a specified distace from the mea to the cofidece limit(s) at a stated cofidece level for a
More informationZTEST / ZSTATISTIC: used to test hypotheses about. µ when the population standard deviation is unknown
ZTEST / ZSTATISTIC: used to test hypotheses about µ whe the populatio stadard deviatio is kow ad populatio distributio is ormal or sample size is large TTEST / TSTATISTIC: used to test hypotheses about
More informationLesson 17 Pearson s Correlation Coefficient
Outlie Measures of Relatioships Pearso s Correlatio Coefficiet (r) types of data scatter plots measure of directio measure of stregth Computatio covariatio of X ad Y uique variatio i X ad Y measurig
More information5: Introduction to Estimation
5: Itroductio to Estimatio Cotets Acroyms ad symbols... 1 Statistical iferece... Estimatig µ with cofidece... 3 Samplig distributio of the mea... 3 Cofidece Iterval for μ whe σ is kow before had... 4 Sample
More informationOutput Analysis (2, Chapters 10 &11 Law)
B. Maddah ENMG 6 Simulatio 05/0/07 Output Aalysis (, Chapters 10 &11 Law) Comparig alterative system cofiguratio Sice the output of a simulatio is radom, the comparig differet systems via simulatio should
More informationINVESTMENT PERFORMANCE COUNCIL (IPC) Guidance Statement on Calculation Methodology
Adoptio Date: 4 March 2004 Effective Date: 1 Jue 2004 Retroactive Applicatio: No Public Commet Period: Aug Nov 2002 INVESTMENT PERFORMANCE COUNCIL (IPC) Preface Guidace Statemet o Calculatio Methodology
More informationDetermining the sample size
Determiig the sample size Oe of the most commo questios ay statisticia gets asked is How large a sample size do I eed? Researchers are ofte surprised to fid out that the aswer depeds o a umber of factors
More informationQuadrat Sampling in Population Ecology
Quadrat Samplig i Populatio Ecology Backgroud Estimatig the abudace of orgaisms. Ecology is ofte referred to as the "study of distributio ad abudace". This beig true, we would ofte like to kow how may
More informationHypothesis testing. Null and alternative hypotheses
Hypothesis testig Aother importat use of samplig distributios is to test hypotheses about populatio parameters, e.g. mea, proportio, regressio coefficiets, etc. For example, it is possible to stipulate
More informationGCSE STATISTICS. 4) How to calculate the range: The difference between the biggest number and the smallest number.
GCSE STATISTICS You should kow: 1) How to draw a frequecy diagram: e.g. NUMBER TALLY FREQUENCY 1 3 5 ) How to draw a bar chart, a pictogram, ad a pie chart. 3) How to use averages: a) Mea  add up all
More informationODBC. Getting Started With Sage Timberline Office ODBC
ODBC Gettig Started With Sage Timberlie Office ODBC NOTICE This documet ad the Sage Timberlie Office software may be used oly i accordace with the accompayig Sage Timberlie Office Ed User Licese Agreemet.
More informationConfidence Intervals. CI for a population mean (σ is known and n > 30 or the variable is normally distributed in the.
Cofidece Itervals A cofidece iterval is a iterval whose purpose is to estimate a parameter (a umber that could, i theory, be calculated from the populatio, if measuremets were available for the whole populatio).
More informationINVESTMENT PERFORMANCE COUNCIL (IPC)
INVESTMENT PEFOMANCE COUNCIL (IPC) INVITATION TO COMMENT: Global Ivestmet Performace Stadards (GIPS ) Guidace Statemet o Calculatio Methodology The Associatio for Ivestmet Maagemet ad esearch (AIM) seeks
More informationOnesample test of proportions
Oesample test of proportios The Settig: Idividuals i some populatio ca be classified ito oe of two categories. You wat to make iferece about the proportio i each category, so you draw a sample. Examples:
More information1. C. The formula for the confidence interval for a population mean is: x t, which was
s 1. C. The formula for the cofidece iterval for a populatio mea is: x t, which was based o the sample Mea. So, x is guarateed to be i the iterval you form.. D. Use the rule : pvalue
More informationCase Study. Normal and t Distributions. Density Plot. Normal Distributions
Case Study Normal ad t Distributios Bret Halo ad Bret Larget Departmet of Statistics Uiversity of Wiscosi Madiso October 11 13, 2011 Case Study Body temperature varies withi idividuals over time (it ca
More informationHypothesis testing using complex survey data
Hypotesis testig usig complex survey data A Sort Course preseted by Peter Ly, Uiversity of Essex i associatio wit te coferece of te Europea Survey Researc Associatio Prague, 5 Jue 007 1 1. Objective: Simple
More informationDomain 1: Designing a SQL Server Instance and a Database Solution
Maual SQL Server 2008 Desig, Optimize ad Maitai (70450) 18004186789 Domai 1: Desigig a SQL Server Istace ad a Database Solutio Desigig for CPU, Memory ad Storage Capacity Requiremets Whe desigig a
More informationHCL Dynamic Spiking Protocol
ELI LILLY AND COMPANY TIPPECANOE LABORATORIES LAFAYETTE, IN Revisio 2.0 TABLE OF CONTENTS REVISION HISTORY... 2. REVISION.0... 2.2 REVISION 2.0... 2 2 OVERVIEW... 3 3 DEFINITIONS... 5 4 EQUIPMENT... 7
More information1 Correlation and Regression Analysis
1 Correlatio ad Regressio Aalysis I this sectio we will be ivestigatig the relatioship betwee two cotiuous variable, such as height ad weight, the cocetratio of a ijected drug ad heart rate, or the cosumptio
More informationInference on Proportion. Chapter 8 Tests of Statistical Hypotheses. Sampling Distribution of Sample Proportion. Confidence Interval
Chapter 8 Tests of Statistical Hypotheses 8. Tests about Proportios HT  Iferece o Proportio Parameter: Populatio Proportio p (or π) (Percetage of people has o health isurace) x Statistic: Sample Proportio
More informationDefinition. A variable X that takes on values X 1, X 2, X 3,...X k with respective frequencies f 1, f 2, f 3,...f k has mean
1 Social Studies 201 October 13, 2004 Note: The examples i these otes may be differet tha used i class. However, the examples are similar ad the methods used are idetical to what was preseted i class.
More informationModified Line Search Method for Global Optimization
Modified Lie Search Method for Global Optimizatio Cria Grosa ad Ajith Abraham Ceter of Excellece for Quatifiable Quality of Service Norwegia Uiversity of Sciece ad Techology Trodheim, Norway {cria, ajith}@q2s.tu.o
More informationResearch Method (I) Knowledge on Sampling (Simple Random Sampling)
Research Method (I) Kowledge o Samplig (Simple Radom Samplig) 1. Itroductio to samplig 1.1 Defiitio of samplig Samplig ca be defied as selectig part of the elemets i a populatio. It results i the fact
More informationPSYCHOLOGICAL STATISTICS
UNIVERSITY OF CALICUT SCHOOL OF DISTANCE EDUCATION B Sc. Cousellig Psychology (0 Adm.) IV SEMESTER COMPLEMENTARY COURSE PSYCHOLOGICAL STATISTICS QUESTION BANK. Iferetial statistics is the brach of statistics
More informationMeasures of Spread and Boxplots Discrete Math, Section 9.4
Measures of Spread ad Boxplots Discrete Math, Sectio 9.4 We start with a example: Example 1: Comparig Mea ad Media Compute the mea ad media of each data set: S 1 = {4, 6, 8, 10, 1, 14, 16} S = {4, 7, 9,
More informationStatistical inference: example 1. Inferential Statistics
Statistical iferece: example 1 Iferetial Statistics POPULATION SAMPLE A clothig store chai regularly buys from a supplier large quatities of a certai piece of clothig. Each item ca be classified either
More informationI. Chisquared Distributions
1 M 358K Supplemet to Chapter 23: CHISQUARED DISTRIBUTIONS, TDISTRIBUTIONS, AND DEGREES OF FREEDOM To uderstad tdistributios, we first eed to look at aother family of distributios, the chisquared distributios.
More informationOverview. Learning Objectives. Point Estimate. Estimation. Estimating the Value of a Parameter Using Confidence Intervals
Overview Estimatig the Value of a Parameter Usig Cofidece Itervals We apply the results about the sample mea the problem of estimatio Estimatio is the process of usig sample data estimate the value of
More informationCHAPTER 3 DIGITAL CODING OF SIGNALS
CHAPTER 3 DIGITAL CODING OF SIGNALS Computers are ofte used to automate the recordig of measuremets. The trasducers ad sigal coditioig circuits produce a voltage sigal that is proportioal to a quatity
More information5.4 Amortization. Question 1: How do you find the present value of an annuity? Question 2: How is a loan amortized?
5.4 Amortizatio Questio 1: How do you fid the preset value of a auity? Questio 2: How is a loa amortized? Questio 3: How do you make a amortizatio table? Oe of the most commo fiacial istrumets a perso
More informationCHAPTER 3 THE TIME VALUE OF MONEY
CHAPTER 3 THE TIME VALUE OF MONEY OVERVIEW A dollar i the had today is worth more tha a dollar to be received i the future because, if you had it ow, you could ivest that dollar ad ear iterest. Of all
More informationSECTION 1.5 : SUMMATION NOTATION + WORK WITH SEQUENCES
SECTION 1.5 : SUMMATION NOTATION + WORK WITH SEQUENCES Read Sectio 1.5 (pages 5 9) Overview I Sectio 1.5 we lear to work with summatio otatio ad formulas. We will also itroduce a brief overview of sequeces,
More information*The most important feature of MRP as compared with ordinary inventory control analysis is its time phasing feature.
Itegrated Productio ad Ivetory Cotrol System MRP ad MRP II Framework of Maufacturig System Ivetory cotrol, productio schedulig, capacity plaig ad fiacial ad busiess decisios i a productio system are iterrelated.
More information.04. This means $1000 is multiplied by 1.02 five times, once for each of the remaining sixmonth
Questio 1: What is a ordiary auity? Let s look at a ordiary auity that is certai ad simple. By this, we mea a auity over a fixed term whose paymet period matches the iterest coversio period. Additioally,
More informationA GUIDE TO LEVEL 3 VALUE ADDED IN 2013 SCHOOL AND COLLEGE PERFORMANCE TABLES
A GUIDE TO LEVEL 3 VALUE ADDED IN 2013 SCHOOL AND COLLEGE PERFORMANCE TABLES Cotets Page No. Summary Iterpretig School ad College Value Added Scores 2 What is Value Added? 3 The Learer Achievemet Tracker
More informationCenter, Spread, and Shape in Inference: Claims, Caveats, and Insights
Ceter, Spread, ad Shape i Iferece: Claims, Caveats, ad Isights Dr. Nacy Pfeig (Uiversity of Pittsburgh) AMATYC November 2008 Prelimiary Activities 1. I would like to produce a iterval estimate for the
More informationConfidence Intervals for Linear Regression Slope
Chapter 856 Cofidece Iterval for Liear Regreio Slope Itroductio Thi routie calculate the ample ize eceary to achieve a pecified ditace from the lope to the cofidece limit at a tated cofidece level for
More informationPUBLIC RELATIONS PROJECT 2016
PUBLIC RELATIONS PROJECT 2016 The purpose of the Public Relatios Project is to provide a opportuity for the chapter members to demostrate the kowledge ad skills eeded i plaig, orgaizig, implemetig ad evaluatig
More informationSTUDENTS PARTICIPATION IN ONLINE LEARNING IN BUSINESS COURSES AT UNIVERSITAS TERBUKA, INDONESIA. Maya Maria, Universitas Terbuka, Indonesia
STUDENTS PARTICIPATION IN ONLINE LEARNING IN BUSINESS COURSES AT UNIVERSITAS TERBUKA, INDONESIA Maya Maria, Uiversitas Terbuka, Idoesia Coauthor: Amiuddi Zuhairi, Uiversitas Terbuka, Idoesia Kuria Edah
More informationMannWhitney U 2 Sample Test (a.k.a. Wilcoxon Rank Sum Test)
NoParametric ivariate Statistics: WilcoxoMaWhitey 2 Sample Test 1 MaWhitey 2 Sample Test (a.k.a. Wilcoxo Rak Sum Test) The (Wilcoxo) MaWhitey (WMW) test is the oparametric equivalet of a pooled
More informationPresent Value Tax Expenditure Estimate of Tax Assistance for Retirement Saving
Preset Value Tax Expediture Estimate of Tax Assistace for Retiremet Savig Tax Policy Brach Departmet of Fiace Jue 30, 1998 2 Preset Value Tax Expediture Estimate of Tax Assistace for Retiremet Savig This
More informationBiology 171L Environment and Ecology Lab Lab 2: Descriptive Statistics, Presenting Data and Graphing Relationships
Biology 171L Eviromet ad Ecology Lab Lab : Descriptive Statistics, Presetig Data ad Graphig Relatioships Itroductio Log lists of data are ofte ot very useful for idetifyig geeral treds i the data or the
More informationNeolane Reporting. Neolane v6.1
Neolae Reportig Neolae v6.1 This documet, ad the software it describes, are provided subject to a Licese Agreemet ad may ot be used or copied outside of the provisios of the Licese Agreemet. No part of
More information1 Computing the Standard Deviation of Sample Means
Computig the Stadard Deviatio of Sample Meas Quality cotrol charts are based o sample meas ot o idividual values withi a sample. A sample is a group of items, which are cosidered all together for our aalysis.
More informationCOMPARISON OF THE EFFICIENCY OF SCONTROL CHART AND EWMAS 2 CONTROL CHART FOR THE CHANGES IN A PROCESS
COMPARISON OF THE EFFICIENCY OF SCONTROL CHART AND EWMAS CONTROL CHART FOR THE CHANGES IN A PROCESS Supraee Lisawadi Departmet of Mathematics ad Statistics, Faculty of Sciece ad Techoology, Thammasat
More informationIs the Event Study Methodology Useful for Merger Analysis? A Comparison of Stock Market and Accounting Data
Discussio Paper No. 163 Is the Evet Study Methodology Useful for Merger Aalysis? A Compariso of Stock Market ad Accoutig Data Tomaso Duso* laus Gugler** Burci Yurtoglu*** September 2006 *Tomaso Duso Humboldt
More informationOMG! Excessive Texting Tied to Risky Teen Behaviors
BUSIESS WEEK: EXECUTIVE EALT ovember 09, 2010 OMG! Excessive Textig Tied to Risky Tee Behaviors Kids who sed more tha 120 a day more likely to try drugs, alcohol ad sex, researchers fid TUESDAY, ov. 9
More informationLearning objectives. Duc K. Nguyen  Corporate Finance 21/10/2014
1 Lecture 3 Time Value of Moey ad Project Valuatio The timelie Three rules of time travels NPV of a stream of cash flows Perpetuities, auities ad other special cases Learig objectives 2 Uderstad the timevalue
More informationNonlife insurance mathematics. Nils F. Haavardsson, University of Oslo and DNB Skadeforsikring
Nolife isurace mathematics Nils F. Haavardsso, Uiversity of Oslo ad DNB Skadeforsikrig Mai issues so far Why does isurace work? How is risk premium defied ad why is it importat? How ca claim frequecy
More informationIn nite Sequences. Dr. Philippe B. Laval Kennesaw State University. October 9, 2008
I ite Sequeces Dr. Philippe B. Laval Keesaw State Uiversity October 9, 2008 Abstract This had out is a itroductio to i ite sequeces. mai de itios ad presets some elemetary results. It gives the I ite Sequeces
More informationDomain 1  Describe Cisco VoIP Implementations
Maual ONT (6428) 18004186789 Domai 1  Describe Cisco VoIP Implemetatios Advatages of VoIP Over Traditioal Switches Voice over IP etworks have may advatages over traditioal circuit switched voice etworks.
More informationChapter 7 Methods of Finding Estimators
Chapter 7 for BST 695: Special Topics i Statistical Theory. Kui Zhag, 011 Chapter 7 Methods of Fidig Estimators Sectio 7.1 Itroductio Defiitio 7.1.1 A poit estimator is ay fuctio W( X) W( X1, X,, X ) of
More informationCS100: Introduction to Computer Science
Review: History of Computers CS100: Itroductio to Computer Sciece Maiframes Miicomputers Lecture 2: Data Storage  Bits, their storage ad mai memory Persoal Computers & Workstatios Review: The Role of
More informationCREATIVE MARKETING PROJECT 2016
CREATIVE MARKETING PROJECT 2016 The Creative Marketig Project is a chapter project that develops i chapter members a aalytical ad creative approach to the marketig process, actively egages chapter members
More informationinsight reporting solutions
reportig solutios Create ad cotrol olie customized score reports to measure studet progress ad to determie ways to improve istructio. isight Customized Reportig empowers you to make datadrive decisios.
More informationCHAPTER 7: Central Limit Theorem: CLT for Averages (Means)
CHAPTER 7: Cetral Limit Theorem: CLT for Averages (Meas) X = the umber obtaied whe rollig oe six sided die oce. If we roll a six sided die oce, the mea of the probability distributio is X P(X = x) Simulatio:
More informationChapter 7: Confidence Interval and Sample Size
Chapter 7: Cofidece Iterval ad Sample Size Learig Objectives Upo successful completio of Chapter 7, you will be able to: Fid the cofidece iterval for the mea, proportio, ad variace. Determie the miimum
More informationNormal Distribution.
Normal Distributio www.icrf.l Normal distributio I probability theory, the ormal or Gaussia distributio, is a cotiuous probability distributio that is ofte used as a first approimatio to describe realvalued
More informationIncremental calculation of weighted mean and variance
Icremetal calculatio of weighted mea ad variace Toy Fich faf@cam.ac.uk dot@dotat.at Uiversity of Cambridge Computig Service February 009 Abstract I these otes I eplai how to derive formulae for umerically
More informationWeek 3 Conditional probabilities, Bayes formula, WEEK 3 page 1 Expected value of a random variable
Week 3 Coditioal probabilities, Bayes formula, WEEK 3 page 1 Expected value of a radom variable We recall our discussio of 5 card poker hads. Example 13 : a) What is the probability of evet A that a 5
More informationThis document contains a collection of formulas and constants useful for SPC chart construction. It assumes you are already familiar with SPC.
SPC Formulas ad Tables 1 This documet cotais a collectio of formulas ad costats useful for SPC chart costructio. It assumes you are already familiar with SPC. Termiology Geerally, a bar draw over a symbol
More informationSolving Logarithms and Exponential Equations
Solvig Logarithms ad Epoetial Equatios Logarithmic Equatios There are two major ideas required whe solvig Logarithmic Equatios. The first is the Defiitio of a Logarithm. You may recall from a earlier topic:
More informationDAME  Microsoft Excel addin for solving multicriteria decision problems with scenarios Radomir Perzina 1, Jaroslav Ramik 2
Itroductio DAME  Microsoft Excel addi for solvig multicriteria decisio problems with scearios Radomir Perzia, Jaroslav Ramik 2 Abstract. The mai goal of every ecoomic aget is to make a good decisio,
More informationLECTURE 13: Crossvalidation
LECTURE 3: Crossvalidatio Resampli methods Cross Validatio Bootstrap Bias ad variace estimatio with the Bootstrap Threeway data partitioi Itroductio to Patter Aalysis Ricardo GutierrezOsua Texas A&M
More informationBaan Service Master Data Management
Baa Service Master Data Maagemet Module Procedure UP069A US Documetiformatio Documet Documet code : UP069A US Documet group : User Documetatio Documet title : Master Data Maagemet Applicatio/Package :
More informationWindWise Education. 2 nd. T ransforming the Energy of Wind into Powerful Minds. editi. A Curriculum for Grades 6 12
WidWise Educatio T rasformig the Eergy of Wid ito Powerful Mids A Curriculum for Grades 6 12 Notice Except for educatioal use by a idividual teacher i a classroom settig this work may ot be reproduced
More informationLesson 15 ANOVA (analysis of variance)
Outlie Variability betwee group variability withi group variability total variability Fratio Computatio sums of squares (betwee/withi/total degrees of freedom (betwee/withi/total mea square (betwee/withi
More informationHow to use what you OWN to reduce what you OWE
How to use what you OWN to reduce what you OWE Maulife Oe A Overview Most Caadias maage their fiaces by doig two thigs: 1. Depositig their icome ad other shortterm assets ito chequig ad savigs accouts.
More informationForecasting techniques
2 Forecastig techiques this chapter covers... I this chapter we will examie some useful forecastig techiques that ca be applied whe budgetig. We start by lookig at the way that samplig ca be used to collect
More informationSystems Design Project: Indoor Location of Wireless Devices
Systems Desig Project: Idoor Locatio of Wireless Devices Prepared By: Bria Murphy Seior Systems Sciece ad Egieerig Washigto Uiversity i St. Louis Phoe: (805) 6985295 Email: bcm1@cec.wustl.edu Supervised
More informationISPOR Population Health SIG: Health Status Survey WG Chair: Paul Kind, Principal Investigator, Quality Outcomes, York, England, UK
ISPOR Populatio Health SIG: Health Status Surve WG Chair: Paul Kid, Pricipal Ivestigator, Qualit Outcomes, York, Eglad, UK Populatio health surve: a stadard reportig template Backgroud Large 1 populatio
More informationThe Big Picture: An Introduction to Data Warehousing
Chapter 1 The Big Picture: A Itroductio to Data Warehousig Itroductio I 1977, Jimmy Carter was Presidet of the Uited States, Star Wars hit the big scree, ad Apple Computer, Ic. itroduced the world to the
More informationA Mathematical Perspective on Gambling
A Mathematical Perspective o Gamblig Molly Maxwell Abstract. This paper presets some basic topics i probability ad statistics, icludig sample spaces, probabilistic evets, expectatios, the biomial ad ormal
More information, a Wishart distribution with n 1 degrees of freedom and scale matrix.
UMEÅ UNIVERSITET Matematiskstatistiska istitutioe Multivariat dataaalys D MSTD79 PA TENTAMEN 00409 LÖSNINGSFÖRSLAG TILL TENTAMEN I MATEMATISK STATISTIK Multivariat dataaalys D, 5 poäg.. Assume that
More informationPROCEEDINGS OF THE YEREVAN STATE UNIVERSITY AN ALTERNATIVE MODEL FOR BONUSMALUS SYSTEM
PROCEEDINGS OF THE YEREVAN STATE UNIVERSITY Physical ad Mathematical Scieces 2015, 1, p. 15 19 M a t h e m a t i c s AN ALTERNATIVE MODEL FOR BONUSMALUS SYSTEM A. G. GULYAN Chair of Actuarial Mathematics
More informationG r a d e. 2 M a t h e M a t i c s. statistics and Probability
G r a d e 2 M a t h e M a t i c s statistics ad Probability Grade 2: Statistics (Data Aalysis) (2.SP.1, 2.SP.2) edurig uderstadigs: data ca be collected ad orgaized i a variety of ways. data ca be used
More informationMeasuring Magneto Energy Output and Inductance Revision 1
Measurig Mageto Eergy Output ad Iductace evisio Itroductio A mageto is fudametally a iductor that is mechaically charged with a iitial curret value. That iitial curret is produced by movemet of the rotor
More informationChapter 7  Sampling Distributions. 1 Introduction. What is statistics? It consist of three major areas:
Chapter 7  Samplig Distributios 1 Itroductio What is statistics? It cosist of three major areas: Data Collectio: samplig plas ad experimetal desigs Descriptive Statistics: umerical ad graphical summaries
More informationEstimating Probability Distributions by Observing Betting Practices
5th Iteratioal Symposium o Imprecise Probability: Theories ad Applicatios, Prague, Czech Republic, 007 Estimatig Probability Distributios by Observig Bettig Practices Dr C Lych Natioal Uiversity of Irelad,
More informationAsymptotic Growth of Functions
CMPS Itroductio to Aalysis of Algorithms Fall 3 Asymptotic Growth of Fuctios We itroduce several types of asymptotic otatio which are used to compare the performace ad efficiecy of algorithms As we ll
More information15.075 Exam 3. Instructor: Cynthia Rudin TA: Dimitrios Bisias. November 22, 2011
15.075 Exam 3 Istructor: Cythia Rudi TA: Dimitrios Bisias November 22, 2011 Gradig is based o demostratio of coceptual uderstadig, so you eed to show all of your work. Problem 1 A compay makes highdefiitio
More informationhp calculators HP 12C Statistics  average and standard deviation Average and standard deviation concepts HP12C average and standard deviation
HP 1C Statistics  average ad stadard deviatio Average ad stadard deviatio cocepts HP1C average ad stadard deviatio Practice calculatig averages ad stadard deviatios with oe or two variables HP 1C Statistics
More informationMEI Structured Mathematics. Module Summary Sheets. Statistics 2 (Version B: reference to new book)
MEI Mathematics i Educatio ad Idustry MEI Structured Mathematics Module Summary Sheets Statistics (Versio B: referece to ew book) Topic : The Poisso Distributio Topic : The Normal Distributio Topic 3:
More informationInstitute of Actuaries of India Subject CT1 Financial Mathematics
Istitute of Actuaries of Idia Subject CT1 Fiacial Mathematics For 2014 Examiatios Subject CT1 Fiacial Mathematics Core Techical Aim The aim of the Fiacial Mathematics subject is to provide a groudig i
More informationFM4 CREDIT AND BORROWING
FM4 CREDIT AND BORROWING Whe you purchase big ticket items such as cars, boats, televisios ad the like, retailers ad fiacial istitutios have various terms ad coditios that are implemeted for the cosumer
More informationPage 1. Real Options for Engineering Systems. What are we up to? Today s agenda. J1: Real Options for Engineering Systems. Richard de Neufville
Real Optios for Egieerig Systems J: Real Optios for Egieerig Systems By (MIT) Stefa Scholtes (CU) Course website: http://msl.mit.edu/cmi/ardet_2002 Stefa Scholtes Judge Istitute of Maagemet, CU Slide What
More informationStatement of cash flows
6 Statemet of cash flows this chapter covers... I this chapter we study the statemet of cash flows, which liks profit from the statemet of profit or loss ad other comprehesive icome with chages i assets
More informationUM USER SATISFACTION SURVEY 2011. Final Report. September 2, 2011. Prepared by. ers eresearch & Solutions (Macau)
UM USER SATISFACTION SURVEY 2011 Fial Report September 2, 2011 Prepared by ers eresearch & Solutios (Macau) 1 UM User Satisfactio Survey 2011 A Collaboratio Work by Project Cosultat Dr. Agus Cheog ers
More informationPreSuit Collection Strategies
PreSuit Collectio Strategies Writte by Charles PT Phoeix How to Decide Whether to Pursue Collectio Calculatig the Value of Collectio As with ay busiess litigatio, all factors associated with the process
More information0.7 0.6 0.2 0 0 96 96.5 97 97.5 98 98.5 99 99.5 100 100.5 96.5 97 97.5 98 98.5 99 99.5 100 100.5
Sectio 13 KolmogorovSmirov test. Suppose that we have a i.i.d. sample X 1,..., X with some ukow distributio P ad we would like to test the hypothesis that P is equal to a particular distributio P 0, i.e.
More informationYour organization has a Class B IP address of 166.144.0.0 Before you implement subnetting, the Network ID and Host ID are divided as follows:
Subettig Subettig is used to subdivide a sigle class of etwork i to multiple smaller etworks. Example: Your orgaizatio has a Class B IP address of 166.144.0.0 Before you implemet subettig, the Network
More informationA Guide to the Pricing Conventions of SFE Interest Rate Products
A Guide to the Pricig Covetios of SFE Iterest Rate Products SFE 30 Day Iterbak Cash Rate Futures Physical 90 Day Bak Bills SFE 90 Day Bak Bill Futures SFE 90 Day Bak Bill Futures Tick Value Calculatios
More informationFinding the circle that best fits a set of points
Fidig the circle that best fits a set of poits L. MAISONOBE October 5 th 007 Cotets 1 Itroductio Solvig the problem.1 Priciples............................... Iitializatio.............................
More informationForecasting. Forecasting Application. Practical Forecasting. Chapter 7 OVERVIEW KEY CONCEPTS. Chapter 7. Chapter 7
Forecastig Chapter 7 Chapter 7 OVERVIEW Forecastig Applicatios Qualitative Aalysis Tred Aalysis ad Projectio Busiess Cycle Expoetial Smoothig Ecoometric Forecastig Judgig Forecast Reliability Choosig the
More informationIntroducing Your New Wells Fargo Trust and Investment Statement. Your Account Information Simply Stated.
Itroducig Your New Wells Fargo Trust ad Ivestmet Statemet. Your Accout Iformatio Simply Stated. We are pleased to itroduce your ew easytoread statemet. It provides a overview of your accout ad a complete
More informationDiscrete Mathematics and Probability Theory Spring 2014 Anant Sahai Note 13
EECS 70 Discrete Mathematics ad Probability Theory Sprig 2014 Aat Sahai Note 13 Itroductio At this poit, we have see eough examples that it is worth just takig stock of our model of probability ad may
More informationEvaluating Model for B2C E commerce Enterprise Development Based on DEA
, pp.180184 http://dx.doi.org/10.14257/astl.2014.53.39 Evaluatig Model for B2C E commerce Eterprise Developmet Based o DEA Weli Geg, Jig Ta Computer ad iformatio egieerig Istitute, Harbi Uiversity of
More informationChapter 5 Unit 1. IET 350 Engineering Economics. Learning Objectives Chapter 5. Learning Objectives Unit 1. Annual Amount and Gradient Functions
Chapter 5 Uit Aual Amout ad Gradiet Fuctios IET 350 Egieerig Ecoomics Learig Objectives Chapter 5 Upo completio of this chapter you should uderstad: Calculatig future values from aual amouts. Calculatig
More informationExample: Probability ($1 million in S&P 500 Index will decline by more than 20% within a
Value at Risk For a give portfolio, ValueatRisk (VAR) is defied as the umber VAR such that: Pr( Portfolio loses more tha VAR withi time period t)
More information