SAMPLING Obtaining a Sample From a Population. A CENSUS is a sample of an entire Population…. They...
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Transcript of SAMPLING Obtaining a Sample From a Population. A CENSUS is a sample of an entire Population…. They...
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SAMPLING
Obtaining a Sample From a Population
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A CENSUS is a sample of an entire Population….
They are seldom done because…..
1. Impossible2. Unprofitable3. Less accurate
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Sampling is the process of discovering what a populationis like….. but
You can never look directly at the population!
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The population is like a large container… you can pull things outbut you are NEVER allowed to look at all its contents.
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Sampling is a five step process
Each step is important
5
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Sampling is a five step processEach step is important
Or the sample will not givean accurate estimate of the
population.
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1.Before a sample can be taken from a population: that population must be defined.
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1. Before a sample can be taken from a population that population must be defined.
A population: The total member of objects orpersons that are of interest for a study.
Male Female Male Female
France India
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1. Before a sample can be taken from a population that population must be defined.
A population: The total member of objects orpersons that are of interest for a study.
The characteristics of a population are called:
Parameters.
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Many business problems can be resolvedby simply looking at population parameters.
http://en.wikipedia.org/wiki/Demographics_of_the_United_States
https://www.cia.gov/library/publications/the-world-factbook/
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2. Identify the sampling frame
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2. Identify the sampling frame
A sampling frame is a list of the units of apopulation:
telephone numbersaddressesemail addresses
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3. Select a sampling procedure
Two kinds:1. Nonprobability samples2. Probability samples
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3. Select a sampling procedure
1. Nonprobability samplesConvenience Sample (Accidental Sample)
Judgmental SampleQuota sample
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3. Select a sampling procedure
2. Probability samplesSimple Random Sample (SRS)
Special case of the convenience sample…..
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3. Select a sampling procedure
2. Probability samplesSimple Random Sample (SRS)
Stratified Sample
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3. Select a sampling procedure
2. Probability samplesSimple Random Sample (SRS)
Stratified SampleCluster Sample
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3. Select a sampling procedure
2. Probability samplesSimple Random Sample (SRS)
Stratified SampleCluster SampleSystematic Sample
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Note: Important!
The human mind will not randomize!
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4. Determine a sample size
What is the correct sample size?
The correct answer is always the same.
It depends!
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4. Determine a sample size
And what does it depend upon? 1. Sampling error
http://elections.huffingtonpost.com/pollster/obama-favorable-rating
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4. Determine a sample size
And what does it depend upon? 1. Sampling error
National Survey of 1,000 Likely VotersConducted September 20-21, 2010By Rasmussen Reports 1* Is the current structure of the Social Security system a Ponzi scheme? 27% Yes36% No37% Not sure
NOTE: Margin of Sampling Error, +/- 3 percentage points with a 95% level of confidence
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4. Determine a sample size
And what does it depend upon? 1. Sampling error2. Precision3. Degree of confidence4. Other factors
a. timeb. costc. type of scalesd. number of cross-classifications
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4. Determine a sample size
And what does it depend upon? 1. Sampling error2. Precision3. Degree of confidence4. Other factors
f. historical and secondary datag. statistical considerationsh. political considerations
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4. Determine a sample size
Since any given interval on the normal curve can be calculated by:
HZ
n
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4. Determine a sample size
Since any given interval on the normal curve can be calculated by:
HZ
n
x
xxZ
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HZ
n
H = ZSE
SEn
nZ
H
2 2
2
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Since any given interval on the normal curve can be calculated by:
HZ
n
The sample size can then be seen as:
nZ
H
2 2
2
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The sample size for nominal and ordinal datacan then be seen as:
nZ pq
H
2
2
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H Zpq
n
H = ZSE
SEpq
n
nZ pq
H
2
2
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What size sample would be needed if you wished to make a decision to within 2 IQ point with 95% accuracy?
IQ has a standard deviation of 15…… therefore:n
Z
H
2 2
2
With Z = 2, H = 2; therefore….
nZ
H
2 2
2
2 15
2225
2 2
2
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It is assumed that 55% of all students are women, what size sample would beneeded to test this assumption to a 95% accuracy at 2%?
nZ pq
H
2
2
p = .55, q = .45; H = ,02, Z = 2
n 2 55 45
022475
2
2
(. )( . )
(. )
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The largest sample size that will ever be needed for any given H is when nominal data is beingused and p = q = 0.5. Therefore the largest sampleEVER needed is:
nH
12
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What size sample would be needed to:
1. Use a GPA scale with a SD = 15 to an accuracy of 95% at 3 IQ points?
2. A Likert scale to a 95% accuracy of 0.4?
3. Income scale with a SD = $15,000 to within a 95% accuracy of $5,000?
4. The largest sample that would ever be needed to do an over night politicalpoll with a 95% accuracy of 2%?
5. Test a hypothesis that 80% of all customers will buy a product again to within 95% accuracy at 3%?
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National Survey of 1,000 Likely VotersConducted September 20-21, 2010By Rasmussen Reports 1* Is the current structure of the Social Security system a Ponzi scheme? 27% Yes36% No37% Not sure
NOTE: Margin of Sampling Error, +/- 3 percentage points with a 95% level of confidence
Why is it +/- 3 percent at 95% confidence?
What is the sample size?
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4. Determine a sample size
What about the size of the population?
Does that change the size of the sampleneeded?
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4. Determine a sample size
Surprisingly so,
Usually not!!
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4. Determine a sample size
Pragmatically, the sample size is independentof the population size!
Except for very small populations, or very, very big samples.
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5. Collect data (go do it!!)
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An example of the problems in samplingand the value of demographics….
http://www.dailymail.co.uk/news/article-1315078/Race-maps-America.html