1. GrowingKnowing.com © 2011 1

2. Sample size How big should a sample be for a valid study? Why phone 10,000 students if phoning 50 is enough? Large samples take longer and cost more What if a sample of 50 is not enough, you need 51 for a valid study? We will learn how to calculate the needed sample size. 2GrowingKnowing.com © 2011

3. Formula Sample size for means: Sample size for proportion: Where n = sample size z = normal table σ = standard deviation E = allowed error p = population proportion GrowingKnowing.com © 20113

4. Sample Size for Means Example: what is the sample size required if the standard deviation (S.D.) is 11.55, error is within 3.01, and confidence level is 96%? Notice error (E) is 3.01 Some students have trouble detecting E. Look for words like ‘within’ if it does not say ‘error’ Always use z, never use t in sample size calculations GrowingKnowing.com © 20114

5. Calculating z Example: confidence level is 96% Calculate z the same way as Confidence Levels. Alpha = 1 -.96 =.04 Z Table formula (confidence level /2) (96% /2 ) =.4800 Lookup.4800 probability, z = 2.055 Link to Normal table http://www.growingknowing.com/GKStatsBook.php?topic=NormalTable1 GrowingKnowing.com © 20115

6. What is the sample size required if the standard deviation (S.D.) is 11.55, error is within 3.01, and confidence level is 96%? Formula n = (2.055 x 11.55 / 3.01) 2 = 7.88545 2 = 62.1 Round up to 63 Why round to 63 from 62.1? Not what we were taught rounding in arithmetic! You cannot talk to.1 of a person, so to have a valid study with 62.1 or more in your sample, you are forced to round up. Rule: Always round up in Sample Size. GrowingKnowing.com © 20116

7. What sample size is needed for a survey of the time to fly to Basra, Iraq from New York. You want the time to be within 15.73 minutes with 94% confidence. Standard deviation is 43.7 minutes. What is the error? E = 15.73 What is z? z = (confidence /2 ) =.94 /2 =.4700 Lookup z in table = 1.88 n = (1.88 x 43.7 / 15.73) 2 = 27.3 Sample size, always round up. Answer n = 28. GrowingKnowing.com © 20117

8. Common errors Most common error is to forget the last step: power of 2. If the number looks small, double check power of 2. You don’t see the error value. Look for ‘within’ In a test, after doing many probability questions, you may be looking for a probability question when you are being asked for a Sample Size calculation! Last common error, you don’t understand there are 2 formulas for sample size (1 st is Means, 2 nd is proportion) GrowingKnowing.com © 20118

9. Sample size for proportion What should the sample size be if proportion is 59%, error is 0.17, and confidence level is 0.92? Formula = n =.59(1 -.59)(z /.17) 2 z = (confidence /2 ) = (.92 /2 ) =.4600 Lookup.4600, z = 1.75 n =.59(1 -.59)(1.75 /.17) 2 =.59 x.41 x 105.9688581 = 25.63 Answer = 26 GrowingKnowing.com © 20119

10. Practise Go to the website, do Sample Size. GrowingKnowing.com © 201110