Determining the Size of a Sample Ch 13 2 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 3 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 4 A Picture Says 1,000 Words ± Probability sample accuracy (error) can be calculated with a simple formula, and expressed as a ± % number. n 550 - 2000 = 1,450 4% - 2% = ±2% Ch 13 5 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 6 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 7 Sample Size Axioms • To properly understand how to determine sample size, it helps to understand the following axioms… Ch 13 8 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 9 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 population. Ch 13 10 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). [...]... percentage Ch of the population size and still be very accurate (have 12 13 little sample error) Sample Size Axiom • The size of the probability sample depends on the client’s desired accuracy (acceptable sample error) balanced against the cost of data collection for that sample size Ch 13 13 Putting It All Together • • • • • • • • • • Ch 13 MR – What level accuracy do you want? MM – I don’t have a clue... involves sample selection and sample size Ch 13 17 The Confidence Interval Method of Determining Sample Size • Sample error formula: Ch 13 18 The Confidence Interval Method of Determining Sample Size • The relationship between sample size and sample error: Ch 13 19 Computations Help Page 1.96 e=z pq n 50 times 50 Let’s try 3 n’s 1000 Answers this way… 500 Ch 13 100 20 And the answers are… 1.96 e=z pq... (via our formula) – So 37% - 43% like our brand Ch 13 23 The Confidence Interval Method of Determining Sample Size • Variability: refers to how similar or dissimilar responses are to a given question • P: percent • Q: 100%-P • Important point: the more variability in the population being studied, the higher the sample size needed to achieve a stated level of accuracy Ch 13 24 • With nominal data (i.e... following statement… Ch 13 27 • If we conducted our study over and over, 1,000 times, we would expect our result to fall within a known range Based upon this, we say that we are 95% confident that the true population range value falls within this range Ch 13 28 The Confidence Interval Method of Determining Sample Size • 1.96 x s.d defines the endpoints of the distribution Ch 13 29 • We also know that,... want Ch 13 – When we specify the above, the formula tells us what sample we need to use…n 32 Sample Size Formula • Standard sample size formula for estimating a percentage: Ch 13 33 Practical Considerations in Sample Size Determination • How to estimate variability (p times q) in the population – Expect the worst cast (p=50; q=50) – Estimate variability: Previous studies? Conduct a pilot study? Ch 13 34... variability is 50/50 Ch 13 25 Confidence Interval Approach • The confidence interval approach is based upon the normal curve distribution • We can use the normal distribution because of the CENTRAL LIMITS THEOREM…regardless of the shape of the population’s distribution, the distribution of samples (of n at least =30) drawn from that population will form a normal distribution Ch 13 26 Central Limits Theorem... 100 20 And the answers are… 1.96 e=z pq n 50 times 50 Let’s try 3 n’s 1000 500 Ch 13 ±3.1% ±4.4% 21 Review: What does sample accuracy mean? • 95% Accuracy – Calculate your sample’s finding, p% – Calculate your sample’s accuracy, ± e% – You will be 95% confident that the population percentage (π) lies between p% ± e% Ch 13 22 Review: What does sample accuracy mean? • Example – Sample size of 1,000 –... distribution Ch 13 29 • We also know that, given the amount of variability in the population, the sample size will affect the size of the confidence interval Ch 13 30 So, what have we learned thus far? • There is a relationship between: Ch 13 – The level of confidence we wish to have that our results would be repeated within some known range if we were to conduct the study again, and… – Variability... sample results… The Confidence Interval Method of Determining Sample Size Ch 13 15 The Confidence Interval Method of Determining Sample Size • This method is based upon the Confidence Interval and the Central Limit Theorem… • Confidence interval: range whose endpoints define a certain percentage of the response to a question Ch 13 16 The Confidence Interval Method of Determining Sample Size • Confidence... (smaller number) the Ch 13 sample error 35 Practical Considerations in Sample Size Determination • How to decide on the level of confidence desired – Researchers should work with managers to make this decision The more confidence, the larger the sample size – Convention is 95% (z=1.96) – The more important the decision, the more likely the manager will want more confidence 99% Ch 13 confidence, z=2.58 . Ch 13 4 A Picture Says 1,000 Words ± Probability sample accuracy (error) can be calculated with a simple formula, and expressed as a ± % number. n 550 - 2000 = 1,450 4% - 2% = ±2% Ch 13 5 How. accuracy of this survey is ± 7%… Ch 13 6 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 7 Sample Size Axioms • To properly understand how to determine sample size, it helps to understand the following axioms… Ch 13 8 Sample Size Axioms • The only