Chapter 10 Determining the Size of the Sample PDF

Determining the Size of the Sample Midterm - Average = 74% Highest Score = 47/50 Added 3 points to each exam Jeopardy participants received an extra two points Final Exam Reminder - Saturday, March 16th at 9:30AM - THERE WILL BE NO MAKEUP EXAMS! - Same room Reminder - Case 3 - Campbell Soup due 2/15...

Determining the Size of the Sample Midterm - Average = 74% Highest Score = 47/50 Added 3 points to each exam Jeopardy participants received an extra two points Final Exam Reminder - Saturday, March 16th at 9:30AM - THERE WILL BE NO MAKEUP EXAMS! - Same room Reminder - Case 3 - Campbell Soup due 2/15 4:59PM Advantages of Using Survey Methods Standardization Ease of administration Ability to tap the “unseen” Suitability to tabulation and statistical analysis Sensitivity to subgroup differences Copyright © 2020, 2017, 2014 Pearson Education, Inc. All Rights Reserved Important Points about Sampling Sampling method (not sample size) is related to representativeness Only a probability sample (random sample) is truly representative of a population Selection method not sample size determines sample representativeness Sample size determines accuracy of findings Copyright © 2020, 2017, 2014 Pearson Education, Inc. All Rights Reserved The Axioms of Random Sample Size and Sample Accuracy 1. The only perfectly accurate sample is a census. 2. A random sample will always have some inaccuracy, which is referred to as margin of sample error or simply sample error. 3. The larger a random sample is, the more accurate it is, meaning the less sample error it has. 4. Margin of sample error can be calculated with a simple formula and expressed as a number. 5. You can take any finding in the survey, replicate the survey with a random sample of the same size, and be “very likely” to find the same finding within the range of the original sample’s finding. 6. In almost all cases, the margin of sample error of a random sample is independent of the size of the population. 7. A random sample size can be a tiny percent of the population size and still have a small margin of sample error. 8. The size of a random sample depends on the client’s desired accuracy (acceptable margin of sample error) balanced against the cost of data collection for that sample size. Plus or minus percentage. Plus or minus percentage. Copyright © 2020, 2017, 2014 Pearson Education, Inc. All Rights Reserved Sample Accuracy Sample accuracy: refers to how close a random sample’s statistic is to the true population’s value it represents Copyright © 2020, 2017, 2014 Pearson Education, Inc. All Rights Reserved Two Types of Error Nonsampling error: pertains to all sources of error other than sample selection method and sample size - Ex: question bias, problem specification mistakes, data recording errors Sampling error: involves sample selection and sample size Copyright © 2020, 2017, 2014 Pearson Education, Inc. All Rights Reserved Sample Size and Accuracy Which of these is more accurate? – A large probability sample, or – A small probability sample? The larger a probability sample is, the more accurate it is (less sample error). Copyright © 2020, 2017, 2014 Pearson Education, Inc. All Rights Reserved Figure Copyright © 2020, 2017, 2014 Pearson Education, Inc. All Rights Reserved Sample Sizes and Margin of Sample Error Sample Size (n) Margin of Sample Error (Accuracy Level) Plus or minus 31.0 percentage. 10 Plus or minus 13.9 percentage. 50 Plus or minus 9.8 percentage. 100 Plus or minus 6.9 percentage. 200 Plus or minus 4.9 percentage. 400 Plus or minus 4.4 percentage. 500 Plus or minus 3.6 percentage. 750 Plus or minus 3.1 percentage. 1,000 Plus or minus 2.5 percentage. 1,500 Plus or minus 2.2 percentage. 2,000 Plus or minus 1.4 percentage. 5,000 Plus or minus 1.0 percentage. 10,000 Copyright © 2020, 2017, 2014 Pearson Education, Inc. All Rights Reserved Sample Error Margin of sample error formula n = sample size p = estimated percent of the population on answering an answer to a variable of interest q = 100 - p Copyright © 2020, 2017, 2014 Pearson Education, Inc. All Rights Reserved Variability Variability refers to how similar or dissimilar responses are to a given question. If most respondents indicate the same answer on the response scale, the distribution has little variability because respondents are highly similar. If respondents are evenly spread across the question’s response options, there is much variability because respondents are quite dissimilar. So, the 100% and the 0% agreement cases have little variability because everyone answers the same, while the 50% in-between case has a great deal of variability because with any two respondents, one answers “yes” while the other one answers “no.” Copyright © 2020, 2017, 2014 Pearson Education, Inc. All Rights Reserved Figure Copyright © 2020, 2017, 2014 Pearson Education, Inc. All Rights Reserved Example of Maximum Margin of Sample Error Sample error formula with and Copyright © 2020, 2017, 2014 Pearson Education, Inc. All Rights Reserved Confidence Interval Approach The confidence interval is a range whose endpoints define a certain percentage of the responses to a question. This approach is based upon the normal distribution. We can use the normal distribution because of the central limit theorem. The confidence interval Copyright © 2020, 2017, 2014 Pearson Education, Inc. All Rights Reserved Figure Copyright © 2020, 2017, 2014 Pearson Education, Inc. All Rights Reserved Example: 1 Sample error formula with and Copyright © 2020, 2017, 2014 Pearson Education, Inc. All Rights Reserved Figure Copyright © 2020, 2017, 2014 Pearson Education, Inc. All Rights Reserved What Does this Translate to? The researcher can say, “I found that 50% of the sample intends to order Domino’s the next time. I am very confident that the true population percent is between 40.2% and 59.8%; in fact, I am confident that if I did this survey over 1,000 times, 95% of the findings will fall in this range.” The confidence interval gives the range of findings if the survey were replicated many times with the identical sample size. Copyright © 2020, 2017, 2014 Pearson Education, Inc. All Rights Reserved Figure Copyright © 2020, 2017, 2014 Pearson Education, Inc. All Rights Reserved Sample Size Formula Need to know – Variability: – Acceptable margin of sample error: e – Level of confidence: z The standard sample size formula is applicable if you are concerned with the nominally scaled questions in the survey, such as yes or no questions. Copyright © 2020, 2017, 2014 Pearson Education, Inc. All Rights Reserved Sample Size Formula Acceptable margin of sample error is represented by the term e, which is the amount of sample error the researcher will permit to be associated with the survey. Level of confidence = the percentage of area under the normal curve described by our calculated confidence intervals. ○ Marketing researchers typically worry only about the 95% or 99% level of confidence. ○ 95% confidence level, z = 1.96 ○ 99% confidence level, z = 2.58 Copyright © 2020, 2017, 2014 Pearson Education, Inc. All Rights Reserved Sample Size Formula where n = the sample size z = standard error associated with the chosen level of confidence (typically, 1.96) p = estimated percent in the population q = 100 − p e = acceptable sample error expressed as a percent Copyright © 2020, 2017, 2014 Pearson Education, Inc. All Rights Reserved Example: 2 Sample size computed with and Copyright © 2020, 2017, 2014 Pearson Education, Inc. All Rights Reserved Example: 2 99% confidence interval sample size computed with and Copyright © 2020, 2017, 2014 Pearson Education, Inc. All Rights Reserved Estimating Variability How to estimate variability – Use data from a previous study on the target population. – Conduct a pilot study of the target population. – Assume worst case maximum variability (p and q – Guesstimate Copyright © 2020, 2017, 2014 Pearson Education, Inc. All Rights Reserved Practical Considerations How to determine the amount of acceptable sample error? – Researchers should work with managers to make this decision. – What are the implications? – How much error is the manager willing to tolerate? Copyright © 2020, 2017, 2014 Pearson Education, Inc. All Rights Reserved Practical Considerations How to decide on the level of confidence to use? – Marketing researchers typically use 95% or 99%. – The 99% level of confidence means that if the survey were replicated many times with the sample size determined by using 2.58 in the sample size formula, 99% of the sample p’s would fall in the sample error range, or e. Copyright © 2020, 2017, 2014 Pearson Education, Inc. All Rights Reserved Practical Considerations How to balance sample size with cost of data collection? – Researchers should work with managers to take cost into consideration in this decision. Copyright © 2020, 2017, 2014 Pearson Education, Inc. All Rights Reserved Example: 3 Sample size computed with and Copyright © 2020, 2017, 2014 Pearson Education, Inc. All Rights Reserved Other Methods of Sample Size Determination Arbitrary “percentage rule of thumb” - “A sample should be 5% of the population” Conventional sample size - Researcher generally knows what size samples it collects data on “Credibility interval” approach - Usually, used in online panel studies. - Pull from a specific table to determine sample size. - Not recommended Copyright © 2020, 2017, 2014 Pearson Education, Inc. All Rights Reserved Other Methods of Sample Size Determination Statistical analysis approach requirements - Used with subgroups - Determine the sample size of each subgroup and apply it to the larger population Cost basis (“all you can afford”) Copyright © 2020, 2017, 2014 Pearson Education, Inc. All Rights Reserved Special Sample Size Determination Situations Sample size: when sampling from small populations – Correction factor is used to modify sample size when using non-probability sampling – Must weigh value of information against cost of gathering information when sampling from panels – Panels are unique and may not be truly representative Copyright © 2020, 2017, 2014 Pearson Education, Inc. All Rights Reserved Sampling from Small Populations With small populations, use the finite population multiplier to determine small size. Copyright © 2020, 2017, 2014 Pearson Education, Inc. All Rights Reserved Example: 4 Sample size computed with p = 50%, q = 50%, and e = 5% Copyright © 2020, 2017, 2014 Pearson Education, Inc. All Rights Reserved Example: 5 Example: Sample size formula to adjust for a small population size Copyright © 2020, 2017, 2014 Pearson Education, Inc. All Rights Reserved