Research Method (I) Knowledge on Sampling (Simple Random Sampling)


 Hillary Allison
 1 years ago
 Views:
Transcription
1 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 that, coclusios from the sample may be exteded to that about the etire populatio. 1.2 Advatages of samplig There are several advatages of samplig over cesus (i.e. selectio of whole populatio for aalysis). Firstly, the costs o samplig should be much lower tha that o cesus. For example, for the govermet bycesus (ote: populatio cesus is usually coducted oce every te years ad a bycesus is coducted i the middle of the itercesal period), oe fifth of the populatio is large eough to declare what the govermet wats to kow. There is o eed to sped several times of dollars to iterview the etire populatio i the society. Secodly, a quality guru (Demig, 196) argued that the quality of a study was ofte better with samplig tha with a cesus. He suggested that, Samplig possesses the possibility of better iterviewig(testig), more thorough ivestigatio of missig, wrog, or suspicious iformatio, better supervisio, ad better processig tha is possible with complete coverage. Research fidigs substatiate this opiio. More tha 9% of survey error i oe study was from osamplig error 1, ad 1% or less was from samplig error 2. (Doald et al., 1995) Thirdly, samplig ca save the time. The speed of executio reduces the time betwee the recogitio of a eed for iformatio ad the availability of that iformatio. 1 Nosamplig error is the error of research due to factors other tha the sample size ad samplig method, icludig orespose, bad commuicatio with iterviewees, measuremet error, etc. 2 Samplig error is the error durig research due to the sample size ad samplig method. Page 1
2 1.3 Importace to lear samplig Statistical applicatio is maily cocered with the collectio, presetatio of data, aalysis ad iterpretatio of iformatio. Data collectio is the first step. Most statistical aalysis methods are derived based o the assumptio of the radomizatio used i data collectio. Whe the assumptio of the radomizatio/represetatio of samplig caot hold, the applicatios of the statistical aalysis ad the respective iterpretatio from the aalysis are meaigless. Therefore, it is ecessary to acquire the kowledge o samplig before learig the statistical aalysis. 2. Type of samplig desig There are two types of samplig desig, i.e. probability samplig ad oprobability samplig. Probability samplig is based o the cocept of radom selectio  a cotrolled procedure that assures that each populatio elemet is give a kow ozero chace of selectio. Noprobability samplig is oradom ad subjective. Each member does ot have a kow ozero chace to be selected. Whe you distribute a questioaire to the customers i a restaurat to idetify Macao residets opiios o the gamig idustry i Macau, the samplig you draw is oprobability samplig because before the study, the probability of each residet draw is ukow, ad most of the populatio is ot covered i the study whose probability to be selected is zero. May people mistakely thik that the sample is represetative if people do ot kow who will be chose before the samplig. Such samplig method is oradom ad orepresetative. Ideed oly probability samplig is represetative ad radom samplig which ca determie the precisio of the estimate from the sample draw. Almost all of the statistical aalyses are derived based o the assumptio of probability samplig. This article will illustrate the simplest probability samplig simple radom sample. The remaiig probability samplig methods will be dealt with later. Page 2
3 3. Simple Radom Sample (SRS) 3.1 Itroductio SRS is the simplest form of probability samplig. Each populatio elemet of SRS has a kow ad equal chace of selectio. For example, 1% of MGRA members are selected from MGRA member listig via radom umber geeratio. It is oted that, SRS requires a samplig frame which is the list of all elemets. The sample is actually draw from the samplig frame. 3.2 Sample size calculatio of SRS What sample size should be appropriate? is a commo questio amog researchers. Ideed this questio is ot easy to aswer. From the techical poit of view, the sample size required depeds o the samplig method, the populatio size, the expected margi of error (boud of error betwee true value ad the estimated value), reliability ad stadard deviatio of the variables that we are iterested i. From the practical poit of view, it also depeds o the budget ad the time. It is oted that, there are some explaatios o the reliability ad margi of error. The followig are two examples. We wat to have a SRS providig 95% of cofidece o the gap betwee the true value ad the estimated value less tha, say $1. It represets that, we wat a sample size, such that the probability that the gap betwee the true value ad the estimated value is less tha $1 is at least 95%. The 95% represets the reliability, while the $1 represets the margi of error. A SRS is desired to provide 9% of cofidece o the maximum gap betwee the true probability ad the estimated probability of selected groups less tha.2. It represets that, the sample size ca satisfy that, the likelihood that the maximum gap is less tha.2 is at least 9%. The 9% represets the reliability, while the.2 represets the margi of error. If we oly cosider the techical poit of view, for SRS, the sample size () required ca be calculated via the followig formulatio. Page 3
4 = reliability *SD d 2 ( ) = 1+ N where: N: populatio size Reliability: critical poit (Z) of stadard ormal distributio correspodig to the value α/2 3, where we wat to have cofidece 1α. For example, the cofidece is 95% which may be the most prevailig figure, the correspodig Z value is d: Margi of error SD: Stadard deviatio of the variable we are iterested i. The idetificatio ca be referred to the followig. (i) Variables we are iterested i are cotiuous data The stadard deviatio ca be calculated from the previous study or pretest. If we have ot coducted the previous study or formal pretest, we may cosider the rough approach by takig oe sixth of the expected rage (max.mi.) of the variable. For example, a sevepoit Likert scale is ofte adopted i questioaire surveys. May treat these scales as cotiuous variables. If o previous study is coducted, we may estimate the stadard deviatio as 1 ((71)/6). (ii) Variables we are iterested i are discrete data max i i, i If there is a previous study or a pretest, the the SD is take as p (1p ) where p i represets the probability of the i th group. 3 α ca be represeted as the probability of error betwee the true value ad the estimate which is out of boud. Page 4
5 However, if o iformatio o p are kow, we may take the coservative SD=1/2, max where p (1p ) =1/2 for all i. pi 1 i i For survey study, this approach is ofte adopted. If we wat to coduct a adhoc survey which has ot bee coducted before ad for which o formal pretests have bee coducted, the sample size () ca be simply writte as: Z α/2 2 = ( ) 2d = 1+ N Note: The defiitios of Z, d, N, α are the same as that i last page. 3.3 More characteristics o SRS Pros: SRS is easy to implemet with radom umber geeratio whe the samplig frame exists, especially for the telephoe survey with automatic dialig (radom digit dialig) ad with computerized voice respose system. Cos: SRS requires a listig of populatio elemet, which is ot practical for may busiess scearios. For example, whe we coduct the visit survey, it is ot feasible to possess the listig of elemet of visitors. SRS produces larger errors tha some of other research methods, e.g. stratified samplig (which will be discussed ext time) whe the sample size is fixed. This pheomeo ca be prove by mathematics. I order to offset the lower accuracy of SRS, larger sample size is demaded, which will result i higher costs ad lower efficiecy. O the other had, comparig to cluster samplig (which will be discussed i Research Method (III)), the data collectio method of SRS is much more expesive ad more iefficiet. SRS may ot cover the segmets that we are iterested i or the subsample sizes of there segmets are ot large eough so that people caot coduct idepth Page 5
6 aalysis or make idepth iferece o these segmets. Bibliography Assael Hery ad Keo Joh. (1982). Nosamplig versus Samplig Errors i Survey Research. Joural of Market Research, Sprig Cooper Doald R., Emory C. William. (1995) 5 th ed. Busiess Research Methods. Richard D. Irwi, INC. Demig W.E.. (196) Sample Desig i Busiess Research. New York: Joh Wiley & Sos. Page 6
Confidence Intervals for One Mean with Tolerance Probability
Chapter 421 Cofidece Itervals for Oe Mea with Tolerace Probability Itroductio This procedure calculates the sample size ecessary to achieve a specified distace from the mea to the cofidece limit(s) with
More informationConfidence 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 informationStat 104 Lecture 16. Statistics 104 Lecture 16 (IPS 6.1) Confidence intervals  the general concept
Statistics 104 Lecture 16 (IPS 6.1) Outlie for today Cofidece itervals Cofidece itervals for a mea, µ (kow σ) Cofidece itervals for a proportio, p Margi of error ad sample size Review of mai topics for
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 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 informationMath C067 Sampling Distributions
Math C067 Samplig Distributios Sample Mea ad Sample Proportio Richard Beigel Some time betwee April 16, 2007 ad April 16, 2007 Examples of Samplig A pollster may try to estimate the proportio of voters
More informationSection 73 Estimating a Population. Requirements
Sectio 73 Estimatig a Populatio Mea: σ Kow Key Cocept This sectio presets methods for usig sample data to fid a poit estimate ad cofidece iterval estimate of a populatio mea. A key requiremet i this sectio
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 informationDefinition. Definition. 72 Estimating a Population Proportion. Definition. Definition
7 stimatig a Populatio Proportio I this sectio we preset methods for usig a sample proportio to estimate the value of a populatio proportio. The sample proportio is the best poit estimate of the populatio
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 informationCHAPTER 8: CONFIDENCE INTERVAL ESTIMATES for Means and Proportions
CHAPTER 8: CONFIDENCE INTERVAL ESTIMATES for Meas ad Proportios Itroductio: We wat to kow the value of a parameter for a populatio. We do t kow the value of this parameter for the etire populatio because
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 informationThe following example will help us understand The Sampling Distribution of the Mean. C1 C2 C3 C4 C5 50 miles 84 miles 38 miles 120 miles 48 miles
The followig eample will help us uderstad The Samplig Distributio of the Mea Review: The populatio is the etire collectio of all idividuals or objects of iterest The sample is the portio of the populatio
More informationStandard Errors and Confidence Intervals
Stadard Errors ad Cofidece Itervals Itroductio I the documet Data Descriptio, Populatios ad the Normal Distributio a sample had bee obtaied from the populatio of heights of 5yearold boys. If we assume
More informationConfidence Intervals and Sample Size
8/7/015 C H A P T E R S E V E N Cofidece Itervals ad Copyright 015 The McGrawHill Compaies, Ic. Permissio required for reproductio or display. 1 Cofidece Itervals ad Outlie 71 Cofidece Itervals for the
More informationEconomics 140A Confidence Intervals and Hypothesis Testing
Ecoomics 140A Cofidece Itervals ad Hypothesis Testig Obtaiig a estimate of a parameter is ot the al purpose of statistical iferece because it is highly ulikely that the populatio value of a parameter is
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 information7.1 Inference for a Population Proportion
7.1 Iferece for a Populatio Proportio Defiitio. The statistic that estimates the parameter p is the sample proportio cout of successes i the sample ˆp = cout of observatios i the sample. Assumptios for
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 informationHypothesis Tests Applied to Means
The Samplig Distributio of the Mea Hypothesis Tests Applied to Meas Recall that the samplig distributio of the mea is the distributio of sample meas that would be obtaied from a particular populatio (with
More informationPractice Problems for Test 3
Practice Problems for Test 3 Note: these problems oly cover CIs ad hypothesis testig You are also resposible for kowig the samplig distributio of the sample meas, ad the Cetral Limit Theorem Review all
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 informationSampling Distribution And Central Limit Theorem
() Samplig Distributio & Cetral Limit Samplig Distributio Ad Cetral Limit Samplig distributio of the sample mea If we sample a umber of samples (say k samples where k is very large umber) each of size,
More informationConfidence Intervals
Cofidece Itervals Cofidece Itervals are a extesio of the cocept of Margi of Error which we met earlier i this course. Remember we saw: The sample proportio will differ from the populatio proportio by more
More informationKey Ideas Section 81: Overview hypothesis testing Hypothesis Hypothesis Test Section 82: Basics of Hypothesis Testing Null Hypothesis
Chapter 8 Key Ideas Hypothesis (Null ad Alterative), Hypothesis Test, Test Statistic, Pvalue Type I Error, Type II Error, Sigificace Level, Power Sectio 81: Overview Cofidece Itervals (Chapter 7) are
More informationStatistical Methods. Chapter 1: Overview and Descriptive Statistics
Geeral Itroductio Statistical Methods Chapter 1: Overview ad Descriptive Statistics Statistics studies data, populatio, ad samples. Descriptive Statistics vs Iferetial Statistics. Descriptive Statistics
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 information9.8: THE POWER OF A TEST
9.8: The Power of a Test CD91 9.8: THE POWER OF A TEST I the iitial discussio of statistical hypothesis testig, the two types of risks that are take whe decisios are made about populatio parameters based
More informationConfidence Intervals for the Mean of Nonnormal Data Class 23, 18.05, Spring 2014 Jeremy Orloff and Jonathan Bloom
Cofidece Itervals for the Mea of Noormal Data Class 23, 8.05, Sprig 204 Jeremy Orloff ad Joatha Bloom Learig Goals. Be able to derive the formula for coservative ormal cofidece itervals for the proportio
More informationMeasures of Central Tendency
Measures of Cetral Tedecy A studet s grade will be determied by exam grades ( each exam couts twice ad there are three exams, HW average (couts oce, fial exam ( couts three times. Fid the average if the
More informationConfidence Intervals for the Population Mean
Cofidece Itervals Math 283 Cofidece Itervals for the Populatio Mea Recall that from the empirical rule that the iterval of the mea plus/mius 2 times the stadard deviatio will cotai about 95% of the observatios.
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 informationStatistics Lecture 14. Introduction to Inference. Administrative Notes. Hypothesis Tests. Last Class: Confidence Intervals
Statistics 111  Lecture 14 Itroductio to Iferece Hypothesis Tests Admiistrative Notes Sprig Break! No lectures o Tuesday, March 8 th ad Thursday March 10 th Exteded Sprig Break! There is o Stat 111 recitatio
More informationReview for 1 sample CI Name. MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question.
Review for 1 sample CI Name MULTIPLE CHOICE. Choose the oe alterative that best completes the statemet or aswers the questio. Fid the margi of error for the give cofidece iterval. 1) A survey foud that
More informationAnalyzing Longitudinal Data from Complex Surveys Using SUDAAN
Aalyzig Logitudial Data from Complex Surveys Usig SUDAAN Darryl Creel Statistics ad Epidemiology, RTI Iteratioal, 312 Trotter Farm Drive, Rockville, MD, 20850 Abstract SUDAAN: Software for the Statistical
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 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 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 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 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 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 informationHypergeometric Distributions
7.4 Hypergeometric Distributios Whe choosig the startig lieup for a game, a coach obviously has to choose a differet player for each positio. Similarly, whe a uio elects delegates for a covetio or you
More informationx : X bar Mean (i.e. Average) of a sample
A quick referece for symbols ad formulas covered i COGS14: MEAN OF SAMPLE: x = x i x : X bar Mea (i.e. Average) of a sample x i : X sub i This stads for each idividual value you have i your sample. For
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 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 informationMaximum Likelihood Estimators.
Lecture 2 Maximum Likelihood Estimators. Matlab example. As a motivatio, let us look at oe Matlab example. Let us geerate a radom sample of size 00 from beta distributio Beta(5, 2). We will lear the defiitio
More informationSAMPLING NTI Bulletin 2006,42/3&4, 5562
SAMPLING NTI Bulleti 006,4/3&4, 556 Sample size determiatio i health studies VK Chadha * Summary Oe of the most importat factors to cosider i the desig of a itervetio trial is the choice of a appropriate
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 informationUsing Excel to Construct Confidence Intervals
OPIM 303 Statistics Ja Stallaert Usig Excel to Costruct Cofidece Itervals This hadout explais how to costruct cofidece itervals i Excel for the followig cases: 1. Cofidece Itervals for the mea of a populatio
More informationExplore Identifying Likely Population Proportions
COMMON CORE Locker LESSON Cofidece Itervals ad Margis of Error Commo Core Math Stadards The studet is expected to: COMMON CORE SIC.B.4 Use data from a sample survey to estimate a populatio mea or proportio;
More informationInstitute for the Advancement of University Learning & Department of Statistics
Istitute for the Advacemet of Uiversity Learig & Departmet of Statistics Descriptive Statistics for Research (Hilary Term, 00) Lecture 5: Cofidece Itervals (I.) Itroductio Cofidece itervals (or regios)
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 informationHypothesis testing: one sample
Hypothesis testig: oe sample Describig iformatios Flowchart for QMS 202 Drawig coclusios Forecastig Improve busiess processes Data Collectio Probability & Probability Distributio Regressio Aalysis Timeseries
More information23.3 Sampling Distributions
COMMON CORE Locker LESSON Commo Core Math Stadards The studet is expected to: COMMON CORE SIC.B.4 Use data from a sample survey to estimate a populatio mea or proportio; develop a margi of error through
More informationChapter 10. Hypothesis Tests Regarding a Parameter. 10.1 The Language of Hypothesis Testing
Chapter 10 Hypothesis Tests Regardig a Parameter A secod type of statistical iferece is hypothesis testig. Here, rather tha use either a poit (or iterval) estimate from a simple radom sample to approximate
More informationStatistical Inference: Hypothesis Testing for Single Populations
Chapter 9 Statistical Iferece: Hypothesis Testig for Sigle Populatios A foremost statistical mechaism for decisio makig is the hypothesis test. The cocept of hypothesis testig lies at the heart of iferetial
More informationLaboratory: CaseControl Studies. Hypothesis Testing
Laboratory: CaseCotrol Studies How may do I eed? is oe of the most commo questios addressed to a epidemiologist. The epidemiologist aswers with What questio are you attemptig to aswer? Sample size depeds
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 informationReview for Test 3. b. Construct the 90% and 95% confidence intervals for the population mean. Interpret the CIs.
Review for Test 3 1 From a radom sample of 36 days i a recet year, the closig stock prices of Hasbro had a mea of $1931 From past studies we kow that the populatio stadard deviatio is $237 a Should you
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 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 informationTHE REGRESSION MODEL IN MATRIX FORM. For simple linear regression, meaning one predictor, the model is. for i = 1, 2, 3,, n
We will cosider the liear regressio model i matrix form. For simple liear regressio, meaig oe predictor, the model is i = + x i + ε i for i =,,,, This model icludes the assumptio that the ε i s are a sample
More informationStatistics for Clinicians. 7: Sample size
J. Paediatr. Child Health (2002) 38, 300 304 Statistics for Cliicias 7: Sample size JB CARLIN 1,3 ad LW DOYLE 2,3,4 1 Cliical Epidemiology ad Biostatistics Uit, Murdoch Childre s Research Istitute, Departmets
More informationME 101 Measurement Demonstration (MD 1) DEFINITIONS Precision  A measure of agreement between repeated measurements (repeatability).
INTRODUCTION This laboratory ivestigatio ivolves makig both legth ad mass measuremets of a populatio, ad the assessig statistical parameters to describe that populatio. For example, oe may wat to determie
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 informationUniversity of California, Los Angeles Department of Statistics. Distributions related to the normal distribution
Uiversity of Califoria, Los Ageles Departmet of Statistics Statistics 100B Istructor: Nicolas Christou Three importat distributios: Distributios related to the ormal distributio Chisquare (χ ) distributio.
More informationChapter 10 Student Lecture Notes 101
Chapter 0 tudet Lecture Notes 0 Basic Busiess tatistics (9 th Editio) Chapter 0 Twoample Tests with Numerical Data 004 PreticeHall, Ic. Chap 0 Chapter Topics Comparig Two Idepedet amples Z test for
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 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 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 informationDepartment of Computer Science, University of Otago
Departmet of Computer Sciece, Uiversity of Otago Techical Report OUCS200609 Permutatios Cotaiig May Patters Authors: M.H. Albert Departmet of Computer Sciece, Uiversity of Otago Micah Colema, Rya Fly
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 informationSTA 2023 Practice Questions Exam 2 Chapter 7 sec 9.2. Case parameter estimator standard error Estimate of standard error
STA 2023 Practice Questios Exam 2 Chapter 7 sec 9.2 Formulas Give o the test: Case parameter estimator stadard error Estimate of stadard error Samplig Distributio oe mea x s t (1) oe p ( 1 p) CI: prop.
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 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 informationHypothesis testing in a Nutshell
Hypothesis testig i a Nutshell Summary by Pamela Peterso Drake Itroductio The purpose of this readig is to discuss aother aspect of statistical iferece, testig. A is a statemet about the value of a populatio
More informationChapter 14 Nonparametric Statistics
Chapter 14 Noparametric Statistics A.K.A. distributiofree statistics! Does ot deped o the populatio fittig ay particular type of distributio (e.g, ormal). Sice these methods make fewer assumptios, they
More informationChapter Gaussian Elimination
Chapter 04.06 Gaussia Elimiatio After readig this chapter, you should be able to:. solve a set of simultaeous liear equatios usig Naïve Gauss elimiatio,. lear the pitfalls of the Naïve Gauss elimiatio
More informationBASIC STATISTICS. Discrete. Mass Probability Function: P(X=x i ) Only one finite set of values is considered {x 1, x 2,...} Prob. t = 1.
BASIC STATISTICS 1.) Basic Cocepts: Statistics: is a sciece that aalyzes iformatio variables (for istace, populatio age, height of a basketball team, the temperatures of summer moths, etc.) ad attempts
More informationProperties of MLE: consistency, asymptotic normality. Fisher information.
Lecture 3 Properties of MLE: cosistecy, asymptotic ormality. Fisher iformatio. I this sectio we will try to uderstad why MLEs are good. Let us recall two facts from probability that we be used ofte throughout
More informationINTERNATIONAL BUSINESS PLAN EVENT 2016
INTERNATIONAL BUSINESS PLAN EVENT 2016 The Iteratioal Busiess Pla Evet ivolves the developmet of a proposal to start a ew busiess veture i a iteratioal settig. Ay type of busiess may be used. The purpose
More informationMESSAGE TO TEACHERS: NOTE TO EDUCATORS:
MESSAGE TO TEACHERS: NOTE TO EDUCATORS: Attached herewith, please fid suggested lesso plas for term 1 of MATHEMATICS Grade 12. Please ote that these lesso plas are to be used oly as a guide ad teachers
More informationTIEE Teaching Issues and Experiments in Ecology  Volume 1, January 2004
TIEE Teachig Issues ad Experimets i Ecology  Volume 1, Jauary 2004 EXPERIMENTS Evirometal Correlates of Leaf Stomata Desity Bruce W. Grat ad Itzick Vatick Biology, Wideer Uiversity, Chester PA, 19013
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 informationStat 104 Lecture 2. Variables and their distributions. DJIA: monthly % change, 2000 to Finding the center of a distribution. Median.
Stat 04 Lecture Statistics 04 Lecture (IPS. &.) Outlie for today Variables ad their distributios Fidig the ceter Measurig the spread Effects of a liear trasformatio Variables ad their distributios Variable:
More informationSection 7.2 Confidence Interval for a Proportion
Sectio 7.2 Cofidece Iterval for a Proportio Before ay ifereces ca be made about a proportio, certai coditios must be satisfied: 1. The sample must be a SRS from the populatio of iterest. 2. The populatio
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 informationHypothesis Testing. Definitions. H 0 : The Null Hypothesis This is the hypothesis or claim that is initially assumed to be true.
Hypothesis Testig Hypothesis testig allows us to use a sample to decide betwee two statemets made about a Populatio characteristic. These two statemets are called the Null Hypothesis ad the Alterative
More informationCHAPTER 8. Confidence Interval Estimation LEARNING OBJECTIVES. USING Saxon Home Improvement
CHAPTER 8 Cofidece Iterval Estimatio USING STATISTICS @ Saxo Home Improvemet 8.1 CONFIDENCE INTERVAL ESTIMATION FOR THE MEAN (* KNOWN) 8.2 CONFIDENCE INTERVAL ESTIMATION FOR THE MEAN (* UNKNOWN) Studet
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 informationsum of all values n x = the number of values = i=1 x = n n. When finding the mean of a frequency distribution the mean is given by
Statistics Module Revisio Sheet The S exam is hour 30 miutes log ad is i two sectios Sectio A 3 marks 5 questios worth o more tha 8 marks each Sectio B 3 marks questios worth about 8 marks each You are
More informationUnit 20 Hypotheses Testing
Uit 2 Hypotheses Testig Objectives: To uderstad how to formulate a ull hypothesis ad a alterative hypothesis about a populatio proportio, ad how to choose a sigificace level To uderstad how to collect
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 informationExample Consider the following set of data, showing the number of times a sample of 5 students check their per day:
Sectio 82: Measures of cetral tedecy Whe thikig about questios such as: how may calories do I eat per day? or how much time do I sped talkig per day?, we quickly realize that the aswer will vary from day
More informationMeasurable Functions
Measurable Fuctios Dug Le 1 1 Defiitio It is ecessary to determie the class of fuctios that will be cosidered for the Lebesgue itegratio. We wat to guaratee that the sets which arise whe workig with these
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 informationThe shaded region above represents the region in which z lies.
GCE A Level H Maths Solutio Paper SECTION A (PURE MATHEMATICS) (i) Im 3 Note: Uless required i the questio, it would be sufficiet to just idicate the cetre ad radius of the circle i such a locus drawig.
More informationGOOD PRACTICE CHECKLIST FOR INTERPRETERS WORKING WITH DOMESTIC VIOLENCE SITUATIONS
GOOD PRACTICE CHECKLIST FOR INTERPRETERS WORKING WITH DOMESTIC VIOLENCE SITUATIONS I the sprig of 2008, Stadig Together agaist Domestic Violece carried out a piece of collaborative work o domestic violece
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 informationLesson 12. Sequences and Series
Retur to List of Lessos Lesso. Sequeces ad Series A ifiite sequece { a, a, a,... a,...} ca be thought of as a list of umbers writte i defiite order ad certai patter. It is usually deoted by { a } =, or
More information