Post on 21-Jul-2016
description
abid@iubat.edu
Lecture - 20Syed Far Abid Hossain
Determining the Size of a Sample
Sample Accuracy
abid@iubat.edu
Sample accuracy: refers to how close a random sample’s statistic (sign) is to the true population’s value it representsSample size is related to accuracy
How to Interpret Sample Accuracy
abid@iubat.edu
From a report…The sample is accurate ± 7% at the 95% level of confidence…
From a news articleThe accuracy of this survey is ± 7%…
How to Interpret Sample Accuracy
abid@iubat.edu
Interpretation Finding: 60% are aware of our brand
So… between 53% (60%-7%) and 67% (60%+7%) of the entire population is aware of our brand
abid@iubat.edu
There is only one method of determining sample size that allows the researcher to PREDETERMINE the accuracy of the sample results…
The Confidence The Confidence Interval Method of Interval Method of
Determining Sample Determining Sample SizeSize
The Confidence Interval Method of Determining Sample Size
abid@iubat.edu
This method is based upon the Confidence Interval and the Central Limit Theorem…
Confidence interval: range whose endpoints define a certain percentage of the response to a question
Review: What does sample accuracy mean?
abid@iubat.edu
ExampleSample size of 1,000Finding: 40% of respondents like our brand
Sample accuracy is ± 3% (via our formula)
Sample Size Formula
abid@iubat.edu
Fortunately, statisticians have given us a formula which is based upon these relationships.The formula requires that we
Specify the amount of confidence we wish (95%)
Estimate the variance in the populationSpecify the amount of desired accuracy
we want.When we specify the above, the formula
tells us what sample we need to use…
Question
abid@iubat.edu
***What is Sample Accuracy? How to Interpret Sample Accuracy? Give an example assuming 95% confidence level.
Lecture – 21Syed Far Abid HossainSample Size Formula
abid@iubat.edu
Sample Size Formula
abid@iubat.edu
Standard sample size formula for estimating a percentage:
Estimating a Percentage: What is n?
abid@iubat.edu
Z=1.96 (95% confidence)p=42q=100-p=58e=5What is n?
Special Sample Size Determination Situations
abid@iubat.edu
Sampling from small populations:Small population: sample exceeds 5% of total population size
Special Sample Size Determination Situations
abid@iubat.edu
Sample size using nonprobability sampling:When using nonprobability sampling, sample size is unrelated to accuracy, so cost-benefit considerations must be used.
Practice Examples
abid@iubat.edu
5a. Using the formula provided in your text, determine the approximate sample sizes for each of the following cases, all with precision (allowable error) of ±5%:Variability of 30%, confidence level of 95%
(323) 322.6 =25
8064 =
252100 x 3.84 =
570) x (30961. =
e(pq)z = n
2
2
2
2
Practice Examples
abid@iubat.edu
5b. Using the formula provided in your text, determine the approximate sample sizes for each of the following cases, all with precision (allowable error) of ±5%:Variability of 60%, confidence level of 99%
(639) 639.4 =25
15,984 =
252400 x 6.66 =
540) x (60582. =
e(pq)z = n
2
2
2
2
Practice Examples
abid@iubat.edu
5c. Using the formula provided in your text, determine the approximate sample sizes for each of the following cases, all with precision (allowable error) of ±5%:Unknown variability, confidence level of 95%
384 =25
9600 =
252500 x 3.84 =
550) x (50961. =
e(pq)z = n
2
2
2
2