1. Sample Size Manual
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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.
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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
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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
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5. Calculating z Example: confidence level is 96%
Calculate z the same way as Confidence Levels.
Alpha = = .04
Z Table formula (confidence level + alpha/2)
(.96% /2 ) = .9800
Lookup probability, z = 2.055
Link to Normal table
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6. 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 / 3.01)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.
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7. 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 minutes with 94% confidence. Standard deviation is 43.7 minutes.
What is the error?
E = 15.73
What is z?
z = (confidence + alpha/2 ) = /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.
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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 (1st is Means, 2nd is proportion)
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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( )(z / .17)2
z = (confidence + alpha/2 ) = ( /2 ) = .9600
Lookup .9600, z = 1.75
n = .59( )(1.75 / .17)2
= .59 x .41 x = 25.63
Answer = 26
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10. Practise
Go to the website, do Sample Size.
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