Chapter 1: Data Collection and Sampling PDF

Chapter 1: Data Collection and Sampling 1. Surveys 2. Sampling 3. Sampling Plans 4. Sampling and non-...

Chapter 1: Data Collection and Sampling 1. Surveys 2. Sampling 3. Sampling Plans 4. Sampling and non- sampling Errors 1 Copyright © 2009 Cengage Learning  …Recall Statistics is a tool for converting data into information: Statistics Data Information But where then does data come from? How is it gathered? How do we ensure it is accurate? Is the data reliable? Is it representative of the population from which it was drawn? This chapter explores some of these issues. 2 Copyright © 2009 Cengage Learning  …Surveys  A survey solicits information from people.  The Response Rate (i.e. the proportion of all people selected who complete the survey) is a key survey parameter.  Surveys may be administered in a variety of ways, e.g. – Personal interview – Telephone interview – Self- administered questionnaire (mailed to a sample of people) – Online surveys 3 Copyright © 2009 Cengage Learning  …Questionnaire Design The questionnaire must be well designed. Some basic points to consider:  Keep the questionnaire as short as possible. (to encourage respondents to complete it.)  Ask short, simple, and clearly worded questions. (to answer quickly.)  Use yes|no and multiple choice questions. (useful because of their simplicity.)  Avoid using leading-questions. (wouldn’t you agree that the statistics exam was too difficult? ----- lead to a particular answer. )  Pretest a questionnaire on a small number of people.(to uncover potential problems such as ambiguous questions) 4 Copyright © 2009 Cengage Learning  Errors to avoid during data collection https://www.youtube.com/watch? v=7onVHIkS1YY 5 Copyright © 2009 Cengage Learning  …Sampling  Sampling is a process used in statistical analysis in which a predetermined number of observations are taken from a larger population.  The methodology used to sample from a larger population depends on the type of analysis being performed but may include simple random sampling or other methods. 6 Copyright © 2009 Cengage Learning  …Sampling  Recall that statistical inference allows us to draw conclusions about a population based on a sample. Sampling (i.e. selecting a sub-set of a whole  population) is often done for reasons of cost (it is less expensive to sample 1,000 television viewers than 100 million TV viewers).  The sampled population and the target population should be similar to one another. 7 Copyright © 2009 Cengage Learning  …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: 1) Simple random sampling, 2) Stratified random sampling 3) Cluster sampling 8 Copyright © 2009 Cengage Learning  …Simple Random Sampling )1  A simple random sample is a sample selected in such a way that every possible sample of the same size is equally likely to be chosen. (each object in the population has an equal chance of being chosen.) - One way to conduct a simple random sample is to assign a number to each element in the population, write these numbers on individual slips of paper, toss them into a hat, and draw the required number of slips (the sample size n) from that. 9 Copyright © 2009 Cengage Learning  Simple Random Sampling Example  An organization has 500 employees. We want to extract a sample of 100 from them.  Step 1: Make a list of all the employees working in the organization. (the list must contain 500 names).  Step 2: Assign a sequential number to each employee (1,2,3…500). This is your sampling frame (the list from which you draw your simple random sample). 1 Copyright © 2009 Cengage Learning  Simple Random Sampling Example  Step 3: Figure out what your sample size is going to be. (In this case, the sample size is 100).  Step 4: Write these numbers on individual slips of paper.  Step 5: Toss these slips of paper (500) into a hat, and draw the required number of slips (100) from that.  Note: We can also use a table of random numbers or a random number generator to select the required number of slips. 1 Copyright © 2009 Cengage Learning  Table of Random Numbers (Example) 1 Copyright © 2009 Cengage Learning  Simple Random Sampling  In making inferences about a population, we attempt to extract as much information as possible from a sample.  The simple random sampling often accomplishes this goal at low cost. Other methods, however, can be used to increase the amount of information about the population.  This process is relatively easy for small population but relatively difficult and time consuming for a large population. 1 Copyright © 2009 Cengage Learning  …Stratified Random Sampling )2  Stratified sampling technique is generally applied in order to obtain a representative sample, if a population from which a sample is to be selected does not constitute a homogeneous group.  A stratified random sample is obtained by separating the population into mutually exclusive sets, or strata (layers), and then drawing simple random samples from each stratum. 1 Copyright © 2009 Cengage Learning  …Stratified Random Sampling  Examples of criteria for separating a population into strata: 1) 2) 3) Gender Age Occupation Male < 20 professional Female 20-30 clerical 31-40 blue collar 41-50 other Make comparisons across 51-60 strata 1 Copyright © 2009 Cengage Learning > 60  Example 1: Stratified Random Sampling Gender Population Sample Size Proportion n=100 n=1000 Stratum 1: Female 60% 100*0.6= 60 1000*0.6=600 students Stratum 2: Male students 40% 100*0.4=40 1000*0.4=400  After the population has been stratified, we can use simple random sampling to generate the complete sample: 1 Copyright © 2009 Cengage Learning  Stratified Random Sampling (Example 2) Stratum 1 Stratum 2 Stratum 3 After the population has been stratified, we can use simple random sampling to generate the complete sample: 1 Copyright © 2009 Cengage Learning  Advantages and disadvantages of stratified random sampling - Advantage: The aim of the stratified random sample is to reduce the potential for human bias in the selection of cases to be included in the sample. - Disadvantage: A stratified random sample can only be carried out if a complete list of the population is available. 1 Copyright © 2009 Cengage Learning  …Cluster Sampling )3  A cluster sample is a simple random sample of groups or clusters of elements (vs. a simple random sample of individual objects).  This method is useful when the population elements are widely dispersed geographically.  A list of elements of the population is not available but it is easy to obtain a list of clusters.  The clusters are constructed such that the sampling units are heterogeneous within the clusters and homogeneous among the clusters. This is opposite to the construction of the strata in the stratified sampling. 1 Copyright © 2009 Cengage Learning  Example: Cluster Sampling  A firm is interested in estimating the average per capita income in a certain city. There is not an available list of resident adults.  The city is marked off into rectangular blocks (60 blocks).  The researchers decide that each of the city blocks will be considered a cluster.  The clusters are numbered from 1 to 60 and there is budget for sampling n = 20 clusters and to interview every household within each cluster. 2 Copyright © 2009 Cengage Learning  …Sample Size Numerical techniques for determining sample sizes will be described in Business Stat II, but suffice it to say that the larger the sample size is, the more accurate we can expect the sample estimates to be. 2 Copyright © 2009 Cengage Learning  Sampling and Non-Sampling …Errors  Two major types of error can arise when a sample of observations is taken from a population: – sampling error and non-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. Increasing the sample size will reduce this error. 2 Copyright © 2009 Cengage Learning  …Nonsampling Error  Non-Sampling errors are more serious and are due to mistakes made in the collection of data or due to the sample observations being selected improperly.  Three types of non-sampling errors: – Errors in data collection – Nonresponse errors – Selection bias  Note: increasing the sample size will not reduce this type of error. 2 Copyright © 2009 Cengage Learning  Errors in data collection  …arise from the recording of incorrect responses, due to: — incorrect measurements being taken because of faulty equipment, — inaccurate recording of data — inaccurate responses to questions 2 Copyright © 2009 Cengage Learning  …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. 2 Copyright © 2009 Cengage Learning  …Selection Bias Selection bias is the bias that occurs in a survey or experimental data when the selection of data points isn't sufficiently random to draw a general conclusion. (I.e. voters without telephones were excluded from possible inclusion in the sample taken)  If you survey your friends, they may not be representative of the population. 2 6 Copyright © 2009 Cengage Learning