Manual GrowingKnowingcom 2011 1 GrowingKnowingcom 2011 Sample size How big should a sample be for a valid study Why phone 10000 students if phoning 50 is enough Large samples take longer and cost more ID: 581505
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Sample SizeManual
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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 moreWhat 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.
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Formula
Sample size for means:Sample size for proportion:
Wheren = sample sizez = normal table σ = standard deviation
E = allowed error
p = population proportion
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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
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Calculating z
Example: confidence level is 96%Calculate z the same way as Confidence Levels.Alpha = 1 - .96 = .04Z Table formula (confidence level + alpha/2)
(.96% + .04/2 ) = .9800Lookup .9800 probability, z = 2.055
Link to Normal table
http://www.growingknowing.com/GKStatsBookNormalTable2.html
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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.
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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 = .9700Lookup z in table = 1.88n = (1.88 x 43.7 / 15.73)
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= 27.3
Sample size, always round up. Answer n = 28.
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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)
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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 ) = .9600Lookup .9600, z = 1.75
n = .59(1 - .59)(1.75 / .17)
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= .59 x .41 x 105.9688581 = 25.63Answer = 26
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Practise
Go to the website, do Sample Size.GrowingKnowing.com © 2011
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