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Chapter Nine Sampling: Theory, Designs and Issues in Marketing Research Copyright © 2006 McGraw-Hill/Irwin Learning Objectives 1. Discuss the concept of sampling and list reasons for sampling. 2. Identify and explain the different roles that sampling plays in the overall information research process. 3. Demonstrate the basic terminology used in sampling decisions. 4. Understand the concept of error in the context of sampling. McGraw-Hill/Irwin 2 Learning Objectives 5. Discuss and calculate sampling distributions, standard errors, and confidence intervals and how they are used in assessing the accuracy of a sample. 6. Discuss the factors that must be considered when determined sample size. 7. Discuss the methods of calculating appropriate sample sizes. McGraw-Hill/Irwin 3 Value of Sampling in Information Research • Discuss the concept of sampling and list reasons for sampling Sampling • Selection of a small number of elements from a larger defined target group—information gathered will allow judgments to be made about the larger group – Census • Includes data about every member of the defined target population – Sampling • McGraw-Hill/Irwin Used when it is impossible to conduct a census of the population 4 Value of Sampling in Information Research • Identify and explain the different roles that sampling plays in the overall information research process Role of Sampling – Identifying, developing, and understanding new marketing constructs that need to be investigated – Plays an indirect role in the design of the questionnaire – Enables the researchers to make decisions using limited information McGraw-Hill/Irwin 5 Value of Sampling in Information Research • Discuss the concept of sampling and list reasons for sampling Concept of Sampling – Making the right decision in the selection of items (i.e., people, products or services) – Feeling confident that data from the sample can be transformed into accurate information about the target population McGraw-Hill/Irwin 6 Overview: The Basics of Sampling Theory • Discuss the concept of sampling and list reasons for sampling Basic Sampling Terminology – Population • Defined target population – Element – – – – Must be unique Must be countable Target population Identify correctly – Sampling Units – Sampling Frames McGraw-Hill/Irwin 7 Overview: The Basics of Sampling Theory • Discuss the concept of sampling and list reasons for sampling Main Factors Underlying Sampling Theory – Sampling Discussions – Logic Behind this Perspective – Important Assumption • • McGraw-Hill/Irwin Probability distribution Sampling distribution 8 Exhibit 9.2 McGraw-Hill/Irwin Discuss the concept of sampling and list reasons for sampling 9 Exhibit 9.3 McGraw-Hill/Irwin Discuss the concept of sampling and list reasons for sampling 10 Overview: The Basics of Sampling Theory • Discuss the concept of sampling and list reasons for sampling Central Limit Theorem – for almost all target populations the sampling distribution of the sample mean or the percentage value derived from a simple random sample will be approximately normally distributed, provided that the sample size is sufficiently large ( i.e., when n is ≥ 30) McGraw-Hill/Irwin 11 Overview: The Basics of Sampling Theory • Discuss the concept of sampling and list reasons for sampling With an understanding the basics of the central limit theorem, the researcher can: – Draw representative samples from any target population – Obtain sample statistics from a random sample that serve as accurate estimate of the target population’s parameters – Draw one random sample instead of many, reducing the costs of data collection – Test more accurately the reliability and validity of constructs and scale measurements – Statistically analyze data and transform them into meaningful into meaningful information about the target population. McGraw-Hill/Irwin 12 Overview: The Basics of Sampling Theory • Understand the concept of error in the context of sampling Types of Errors • Classified as being either sampling or non-sampling – Random sampling errors – Sampling Error • Any type of bias that is attributable to mistakes in either drawing a sample or determining sample size – Central Limit Theorem—sampling error can be reduced by increasing the size of the sample McGraw-Hill/Irwin 13 Exhibit 9.4 McGraw-Hill/Irwin Discuss the concept of sampling and list reasons for sampling 14 Overview: The Basics of Sampling Theory • Understand the concept of error in the context of sampling Nonsampling Error – A bias that occurs in a research study regardless of whether a sample or census is used • • • • McGraw-Hill/Irwin Population frame error Measurement error Response error Errors in gathering and recording data 15 Overview: The Basics of Sampling Theory • Discuss and calculate sampling distributions, standard errors, and confidence intervals Statistical Precision – Critical Level of Error – General Precision – Precise Precision • Estimated standard Error – Measure of the sampling error and an indication of how far the sample result lies from the actual target population McGraw-Hill/Irwin 16 Estimating Standard Error-General Precision Sx s/ n [( p)(q )] Sp n • Standard error of the sample mean=Estimated standard deviation of the sample mean divided by the square root of the Sample size • Standard error of the sample percentage value = square root of [(the % of the sample possessing the characteristic times the % of the sample NOT possessing the characteristic) divided by the Sample size] McGraw-Hill/Irwin 17 Estimating Standard Error-General Precision Sx s/ n • • • • • • • [( p)(q )] Sp n A) Calculate the Standard error for the sample mean if 900 people were interviewed with a estimated sample deviation of 12.5 The sample mean was 36 B) Calculate the Standard error of sample percentage if 65% of the sample of 489 people have VCR’s q=(100-p) The sample proportion was A) = +- .406 B) = +- 2.16% We can then use estimated standard error to construct a confidence interval McGraw-Hill/Irwin 18 Confidence Interval • Confidence Interval – Statistical range of values within which the true value of the defined target population parameter is expected to be _ - Confidence Intervals range from almost zero to almost 100 percent, but the most commonly used confidence levels are the 90, 95, and 99 percent levels McGraw-Hill/Irwin 19 Confidence Interval for population mean and proportions CI x ( Sx )( ZB, CL ) CI p p ( Sp )( ZB, CL ) • • • • • Critical Z Value for 90% is 1.65, 95% is 1.96, 99% is 2.58 Calculate the Confidence interval for the population mean if the sample mean is 25 and the Standard error of the sample mean is 2 with a 90% confidence level Answer = 25 +- 3.3 Calculate the Confidence interval for a population proportion if the sample proportion is 75% and the Estimated standard error of the sample proportion is 5% with a confidence level of 95% 75% +- 9.8% McGraw-Hill/Irwin 20 Probability Sampling and Sample Sizes • Determining Sample Size – 3 Factors in Determining Sample Sizes • Variability of the population characteristic under investigation u or p • Standard deviation • Level of confidence desired in the estimate • Degree of precision desired in estimating the population characteristic McGraw-Hill/Irwin 21 Probability Sampling and Sample Sizes Discuss the methods of calculating appropriate sample size • When estimating a population mean n = (Z2B,CL)(σ2/e2) • When estimates of a population proportion are of concern n = (Z2B,CL)([P x Q]/e2) Estimate the sample size having a 95% confidence level, a estimate population standard deviation of 5 and a 3% tolerance level of error McGraw-Hill/Irwin 22 Probability Sampling and Sample Sizes Discuss the methods of calculating appropriate sample size • There is a direct relationship between the desired CL (90% 95%, 99%) and the require sample size – CL are directly associated with corresponding critical z-values – The higher the level of confidence required the larger the sample size • Acceptable tolerance level of error—amount of precision desired (2%, 5%, or 10%) McGraw-Hill/Irwin 23 Probability Sampling and Sample Sizes Discuss the methods of calculating appropriate sample size • Sample Size – Not a product of the population size, it is not a direct factor in determining sample size • Finite Correction Factor • Should be used if the sample size is greater than 5% of the population _ FCF = √N-n/N-1 McGraw-Hill/Irwin 24 Probability Sampling and Sample Sizes Discuss the methods of calculating appropriate sample size 1. Determine if the sample size is more than 5% of the population by taking the calculated sample size and dividing it by the known defined target population size 2. If it is, then calculate the appropriate finite correction factor and multiply the originally calculated sample size by it to adjust the required sample size 3. If the target population size is ≤500 should consider doing a census McGraw-Hill/Irwin 25 Sample Sizes Versus Usable Observations for Data Analysis Discuss the methods of calculating appropriate sample size • Sample Size – Researchers can estimate the number of sampling units that must be surveyed • Not all initial responses are usable – Inactive mailing addresses – Telephone number no longer in service – Incomplete responses – Factors to consider in drawing a sample • Reachable rate RR • Who is qualified to be included in the survey Overall Incidence Rate OIR • Expected completion rate ECR McGraw-Hill/Irwin 26 Calculating the Number of Contacts n Number of Contacts ( RR) * (OIR) * ( ECR) • Calculate the number of contacts you require if need a sample 1500 students but only 90% answer the phone and you have determine that 20% of students are taking marketing and do not qualify. Finally you estimate that only 90% will answer all the questions in the survey. • Number of Contacts is 2315 McGraw-Hill/Irwin 27 Summary • • • • • Value of Sampling in Marketing Research Overview: The Basics of Sampling Theory Probability Sampling and Sample Sizes Nonprobability Sampling and Sample Size Sample Sizes versus Usable Observations McGraw-Hill/Irwin 28