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1、2007會計資訊系統計學(一)上課投影片Data Collection and Data Collection and SamplingSamplingChapter 5Chapter 512007會計資訊系統計學(一)上課投影片RecallStatistics is a tool for converting data into information:DataStatisticsInformationButWhere then does data come from? How is it gathered? How do we ensure its accurate（正確）? Is the
2、 data reliable（可靠）? Is it representative（代表性） of the population from which it was drawn? This chapter explores some of these issues.22007會計資訊系統計學(一)上課投影片5.1 Methods of Collecting DataThe reliability and accuracy of the data affect the validity of the results of a statistical analysis.The reliability
3、 and accuracy of the data depend on the method of collection.Four of the most popular sources of statistical data are:Published data（公開資料）Observational studies（觀察）Experimental studies（實驗）Surveys（調查）32007會計資訊系統計學(一)上課投影片This is often a preferred source of data due to low cost and convenience.Publishe
4、d data is found as printed material, tapes, disks, and on the Internet.Data published by the organization that has collected it is called PRIMARY DATA（初級資料）.For example:Data published by the US Bureau of Census.Data published by an organization different than the organization that has collected it i
5、s called SECONDARY DATA（次級資料）. For example:The Statistical abstracts of the United States,compiles data from primary sources Compustat, sells variety of financial data tapescompiled from primary sourcesPublished Data42007會計資訊系統計學(一)上課投影片Observational study is one in which measurements representing a
6、 variable of interest are observed and recorded, without controlling any factor that might influence their values.Experimental study is one in which measurements representing a variable of interest are observed and recorded, while controlling factors（控制變數） that might influence their values. When pub
7、lished data is unavailable, one needs to conduct a study to generate the data.Observational and experimental studies52007會計資訊系統計學(一)上課投影片Surveys solicit information from people. e.g. pre-election polls; marketing surveys.The Response Rate（回收率） (i.e. the proportion of all people selected who complete
8、 the survey) is a key survey parameter.Surveys can be made by means of personal interview（個人訪談）telephone interview（電話訪談）self-administered questionnaire（自我管理調查）Surveys62007會計資訊系統計學(一)上課投影片Questionnaire Design（問卷設計）lKey design principles of a good questionnaire:1.Keep the questionnaire as short as pos
9、sible.2.Ask short, simple, and clearly worded questions.3.Start with demographic questions to help respondents get started comfortably.4.Use dichotomous (yes|no) and multiple choice questions.5.Use open-ended questions cautiously. 6.Avoid using leading-questions.7. Pretest a questionnaire on a small
10、 number of people.8.Think about the way you intend to use the collected data when preparing the questionnaire.72007會計資訊系統計學(一)上課投影片5.2 Sampling（抽樣）Recall that statistical inference permits us to draw conclusions about a population based on a sample.Motivation for conducting a sampling procedure:Cost
11、s. (e.g. its less expensive to sample 1,000 television viewers than 100 million TV viewers) Population size.The possible destructive nature （破壞性）of the sampling process. (e.g. performing a crash test on every automobile produced is impractical).The sampled population（抽樣母體） and the target population（
12、目標母體） should be similar to one another.82007會計資訊系統計學(一)上課投影片5.3 Sampling PlansA sampling plan is just a method or procedure for specifying how a sample will be taken from a population.We will focus our attention on these three methods:Simple random sampling（簡單隨機抽樣）Stratified random sampling（分層隨機抽樣）C
13、luster sampling（集群抽樣）92007會計資訊系統計學(一)上課投影片Simple Random SamplingIn simple random sampling all the samples with the same size are equally likely to be chosen.To conduct random sampling assign a number to each element of the chosen population (or use already given numbers),randomly select the sample n
14、umbers (members). Use a random numbers table, or a software package.102007會計資訊系統計學(一)上課投影片Example 5.1A government income-tax auditor is responsible for 1,000 tax returns.The auditor will randomly select 40 returns to audit.Use Excels random number generator to select the returns.SolutionWe generate
15、50 numbers between 1 and 1000 (we need only 40 numbers, but the extra might be used if duplicate numbers are generated.)Simple Random Sampling112007會計資訊系統計學(一)上課投影片Simple Random SamplingExample 5.1: A government income tax auditor must choose a sample of 40 of 1,000 returns to auditExtra #s may be u
16、sed if duplicate random numbers are generated.122007會計資訊系統計學(一)上課投影片Simple Random SamplingX(100)Round-up38310159790088595915408864139246.The auditor should select 40 files numbered 383, 101, .50 Random numbersbetween 0 and 1000,each has a probabilityof 1/1000 to be selected50 numbers uniformly distr
17、ibuted between 0 and 150 random uniformly distributed whole-numbers between 1 and 1000.132007會計資訊系統計學(一)上課投影片This sampling procedure separates the population into mutually exclusive sets (strata) （互斥的層別）, and then draw simple random samples from each stratum.Stratified Random Sampling142007會計資訊系統計學(
18、一)上課投影片With this procedure we can acquire information aboutthe whole populationeach stratumthe relationships among strata.Stratified Random Sampling152007會計資訊系統計學(一)上課投影片Stratified Random SamplingAfter the population has been stratified, we can use simple random sampling to generate the complete sam
19、ple. For example, keep the proportion of each stratum in the population.If we only have sufficient resources to sample 400 people total, we would draw 100 of them from the low income groupIf we are sampling 1000 people, wed draw50 of them from the high income group.162007會計資訊系統計學(一)上課投影片Cluster samp
20、ling is a simple random sample of groups or clusters of elements.This procedure is useful whenit is difficult and costly to develop a complete list of the population members (making it difficult to develop a simple random sampling procedure.the population members are widely dispersed geographically.
21、Cluster sampling may increase sampling error（抽樣誤差）, because of probable similarities among cluster members.Cluster Sampling172007會計資訊系統計學(一)上課投影片Sample Size（樣本數）Numerical techniques for determining sample sizes will be described later, but suffice it to say that the larger the sample size is, the mo
22、re accurate we can expect the sample estimates to be.182007會計資訊系統計學(一)上課投影片5.4 Sampling and Non-Sampling ErrorsTwo major types of error can arise when a sample of observations is taken from a population: Sampling error（抽樣誤差） refers to differences between the sample and the population that exist only
23、 because of the observations that happened to be selected for the sample.Nonsampling errors （非抽樣誤差） are more serious and are due to mistakes made in the acquisition of data or due to the sample observations being selected improperly.192007會計資訊系統計學(一)上課投影片Sampling ErrorSampling error refers to differ
24、ences between the sample and the population that exist only because of the observations that happened to be selected for the sample.Another way to look at this is: the differences in results for different samples (of the same size) is due to sampling error:E.g. Two samples of size 10 of 1,000 househ
25、olds. If we happened to get the highest income level data points in our first sample and all the lowest income levels in the second, this delta is due to sampling error.Increasing the sample size will reduce this type of error.202007會計資訊系統計學(一)上課投影片Population income distributionm m ( population mean
26、)Sampling errorThe sample mean falls here only because certain randomly selected observations were included in the sample.Sampling Errors212007會計資訊系統計學(一)上課投影片Nonsampling ErrorNonsampling errors are more serious and are due to mistakes made in the acquisition of data or due to the sample observation
27、s being selected improperly. Three types of nonsampling errors:Errors in data acquisitionNonresponse errors（無反應偏差）Selection bias（取樣誤差）Note: increasing the sample size will not reduce this type of error.222007會計資訊系統計學(一)上課投影片Errors in data acquisitionarises from the recording of incorrect responses,
28、due to:incorrect measurements being taken because of faulty equipment,mistakes made during transcription from primary sources,inaccurate recording of data due to misinterpretation of terms, orinaccurate responses to questions concerning sensitive issues.232007會計資訊系統計學(一)上課投影片Data Acquisition ErrorIf
29、 this observationis wrongly recorded herethen the sample mean is affectedSampling error + Data acquisition errorPopulationSample242007會計資訊系統計學(一)上課投影片Nonresponse Errorrefers to error (or bias) introduced when responses are not obtained from some members of the sample, i.e. the sample observations th
30、at are collected may not be representative of the target population.As mentioned earlier, the Response Rate (i.e. the proportion of all people selected who complete the survey) is a key survey parameter and helps in the understanding in the validity of the survey and sources of nonresponse error.252
31、007會計資訊系統計學(一)上課投影片Non-Response ErrorPopulationSampleNo response here. may lead to biased results here.262007會計資訊系統計學(一)上課投影片Selection Biasoccurs when the sampling plan is such that some members of the target population cannot possibly be selected for inclusion in the sample.272007會計資訊系統計學(一)上課投影片Se
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