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Determining the Size of a Sample Sample Accuracy • Sample accuracy: refers to how close a random sample’s statistic is to the true population’s value it represents • Important points: – Sample size is not related to representativeness – Sample size is related to accuracy Ch 13 2 Sample Size and Accuracy • Intuition: Which 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). Ch 13 3 A Picture Says 1,000 Words ± 16% 14% 12% 10% 8% 6% 4% 2% 0% 2000 1850 1700 1550 1400 1250 1100 950 800 650 500 350 n 550 - 2000 = 1,450 4% - 2% = ±2% 200 50 Accuracy Sample Size and Accuracy Sample Size Ch 13 Probability sample accuracy (error) can be calculated with a simple formula, and expressed as a ± % number. 4 How to Interpret Sample Accuracy • From a report… – The sample is accurate ± 7% at the 95% level of confidence… • From a news article – The accuracy of this survey is ± 7%… Ch 13 5 How to Interpret Sample Accuracy • Interpretation – Finding: 60% are aware of our brand – So… between 53% (60%-7%) and 67% (60%+7%) of the entire population is aware of our brand Ch 13 6 Sample Size Axioms • To properly understand how to determine sample size, it helps to understand the following axioms… Ch 13 7 Sample Size Axioms • The only perfectly accurate sample is a census. • A probability sample will always have some inaccuracy (sample error). • The larger a probability sample is, the more accurate it is (less sample error). • Probability sample accuracy (error) can be calculated with a simple formula, and expressed as a +- % number. Ch 13 8 Sample Size Axioms • You can take any finding in the survey, replicate the survey with the same probability sample size, and you will be “very likely” to find the same finding within the +- range of the original finding. • In almost all cases, the accuracy (sample error) of a probability sample is independent of the size of the Ch 13 population. 9 Sample Size Axioms • A probability sample can be a very tiny percentage of the population size and still be very accurate (have little sample error). Ch 13 10