Sample Size Manual GrowingKnowing.com © 2011 GrowingKnowing.com © 2011

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. GrowingKnowing.com © 2011

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 © 2011

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 © 2011

Calculating z Example: confidence level is 96% Calculate z the same way as Confidence Levels. Alpha = 1 - .96 = .04 Z Table formula (confidence level + alpha/2) (.96% + .04/2 ) = .9800 Lookup .9800 probability, z = 2.055 Link to Normal table http://www.growingknowing.com/GKStatsBookNormalTable2.html GrowingKnowing.com © 2013

Rule: Always round up in Sample Size. 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 = 7.885452 = 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 © 2011

Sample size, always round up. Answer n = 28. 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 + alpha/2 ) = .94 + .06/2 = .9700 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 © 2013

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 (1st is Means, 2nd is proportion) GrowingKnowing.com © 2011

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 + alpha/2 ) = (.92 + .08/2 ) = .9600 Lookup .9600, z = 1.75 n = .59(1 - .59)(1.75 / .17)2 = .59 x .41 x 105.9688581 = 25.63 Answer = 26 GrowingKnowing.com © 2013

Practise Go to the website, do Sample Size. GrowingKnowing.com © 2011