2007 會計資訊系統計學 ( 一 ) 上課投影片 5-1 Data Collection and Sampling Chapter 5

2007 會計資訊系統計學 ( 一 ) 上課投影片 5-2 Recall Statistics is a tool for converting data into information : Data Statistics Information But… –Where then does data come from? –How is it gathered? –How do we ensure its accurate （正確） ? Is the 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.

2007 會計資訊系統計學 ( 一 ) 上課投影片 Methods of Collecting Data The reliability and accuracy of the data affect the validity of the results of a statistical analysis. The reliability 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）

2007 會計資訊系統計學 ( 一 ) 上課投影片 5-4 –This is often a preferred source of data due to low cost and convenience. –Published 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. For example: Data published by the US Bureau of Census. –Data published by an organization different than the organization that has collected it is 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 tapes compiled from primary sources For example: The Statistical abstracts of the United States, compiles data from primary sources Compustat, sells variety of financial data tapes compiled from primary sources Published Data

2007 會計資訊系統計學 ( 一 ) 上課投影片 5-5 – Observational study is one in which measurements representing a 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 published data is unavailable, one needs to conduct a study to generate the data. Observational and experimental studies

2007 會計資訊系統計學 ( 一 ) 上課投影片 5-6 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 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） Surveys

2007 會計資訊系統計學 ( 一 ) 上課投影片 5-7 Questionnaire Design （問卷設計） Key design principles of a good questionnaire: 1.Keep the questionnaire as short as possible. 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 number of people. 8.Think about the way you intend to use the collected data when preparing the questionnaire.

2007 會計資訊系統計學 ( 一 ) 上課投影片 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: –Costs. (e.g. it’s 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 （目標母體） should be similar to one another.

2007 會計資訊系統計學 ( 一 ) 上課投影片 Sampling Plans A 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） –Cluster sampling （集群抽樣）

2007 會計資訊系統計學 ( 一 ) 上課投影片 5-10 Simple Random Sampling In 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 numbers (members). Use a random numbers table, or a software package.

2007 會計資訊系統計學 ( 一 ) 上課投影片 5-11 Example 5.1 –A government income-tax auditor is responsible for 1,000 tax returns. –The auditor will randomly select 40 returns to audit. –Use Excel’s random number generator to select the returns. Solution We generate 50 numbers between 1 and 1000 (we need only 40 numbers, but the extra might be used if duplicate numbers are generated.) Simple Random Sampling

2007 會計資訊系統計學 ( 一 ) 上課投影片 5-12 Simple Random Sampling Example 5.1: A government income tax auditor must choose a sample of 40 of 1,000 returns to audit Extra #’s may be used if duplicate random numbers are generated.

2007 會計資訊系統計學 ( 一 ) 上課投影片 5-13 Simple Random Sampling X(100) Round-up The auditor should select 40 files numbered 383, 101, Random numbers between 0 and 1000, each has a probability of 1/1000 to be selected 50 numbers uniformly distributed between 0 and 1 50 random uniformly distributed whole- numbers between 1 and 1000.

2007 會計資訊系統計學 ( 一 ) 上課投影片 5-14 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. Sex Male Female Age under Occupation professional clerical blue-collar Stratified Random Sampling

2007 會計資訊系統計學 ( 一 ) 上課投影片 5-15 With this procedure we can acquire information about –the whole population –each stratum –the relationships among strata. Stratified Random Sampling

2007 會計資訊系統計學 ( 一 ) 上課投影片 5-16 Stratified Random Sampling After the population has been stratified, we can use simple random sampling to generate the complete sample. 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 group… If we are sampling 1000 people, we’d draw 50 of them from the high income group.

2007 會計資訊系統計學 ( 一 ) 上課投影片 5-17 Cluster sampling is a simple random sample of groups or clusters of elements. This procedure is useful when –it 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. Cluster sampling may increase sampling error （抽樣 誤差）, because of probable similarities among cluster members. Cluster Sampling

2007 會計資訊系統計學 ( 一 ) 上課投影片 5-18 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 more accurate we can expect the sample estimates to be.

2007 會計資訊系統計學 ( 一 ) 上課投影片 Sampling and Non-Sampling Errors Two 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 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.

2007 會計資訊系統計學 ( 一 ) 上課投影片 5-20 Sampling Error Sampling error refers to differences 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 households. 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.

2007 會計資訊系統計學 ( 一 ) 上課投影片 5-21 Population income distribution  ( population mean) Sampling error The sample mean falls here only because certain randomly selected observations were included in the sample. Sampling Errors

2007 會計資訊系統計學 ( 一 ) 上課投影片 5-22 Nonsampling Error Nonsampling errors are more serious and are due to mistakes made in the acquisition of data or due to the sample observations being selected improperly. Three types of nonsampling errors: –Errors in data acquisition –Nonresponse errors （無反應偏差） –Selection bias （取樣誤差） Note: increasing the sample size will not reduce this type of error.

2007 會計資訊系統計學 ( 一 ) 上課投影片 5-23 Errors in data acquisition …arises from the recording of incorrect responses, 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, or –inaccurate responses to questions concerning sensitive issues.

2007 會計資訊系統計學 ( 一 ) 上課投影片 5-24 Data Acquisition Error If this observation… …is wrongly recorded here… …then the sample mean is affected Sampling error + Data acquisition error Population Sample

2007 會計資訊系統計學 ( 一 ) 上課投影片 5-25 Nonresponse Error …refers to error (or bias ) introduced when responses are not obtained from some members of the sample, i.e. the sample observations that 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.

2007 會計資訊系統計學 ( 一 ) 上課投影片 5-26 Non-Response Error Population Sample No response here... …may lead to biased results here.

2007 會計資訊系統計學 ( 一 ) 上課投影片 5-27 Selection Bias …occurs when the sampling plan is such that some members of the target population cannot possibly be selected for inclusion in the sample.

2007 會計資訊系統計學 ( 一 ) 上課投影片 5-28 Selection Bias Population Sample When parts of the population cannot be selected... …the sample cannot represent the whole population.