Sample Size Manual Growing Knowing com 2011 1

Sample Size Manual Growing. Knowing. com © 2011 1

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. Growing. Knowing. com © 2011 2

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 Growing. Knowing. com © 2011 3

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 Growing. Knowing. com © 2011 4

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/GKStats. Book. Normal. Table 2. html Growing. Knowing. com © 2013 5

�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. Growing. Knowing. com © 2011 6

�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. Growing. Knowing. com © 2013 7

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) Growing. Knowing. com © 2011 8

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 Growing. Knowing. com © 2013 9

Practise �Go to the website, do Sample Size. Growing. Knowing. com © 2011 10