sampling obtaining a sample from a population. a census is a sample of an entire population…. they...

SAMPLING

Obtaining a Sample From a Population

A CENSUS is a sample of an entire Population….

They are seldom done because…..

1. Impossible2. Unprofitable3. Less accurate

Sampling is the process of discovering what a populationis like….. but

You can never look directly at the population!

The population is like a large container… you can pull things outbut you are NEVER allowed to look at all its contents.

Sampling is a five step process

Each step is important

5

Sampling is a five step processEach step is important

Or the sample will not givean accurate estimate of the

population.

1.Before a sample can be taken from a population: that population must be defined.

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

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.

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/

2. Identify the sampling frame

2. Identify the sampling frame

A sampling frame is a list of the units of apopulation:

telephone numbersaddressesemail addresses

3. Select a sampling procedure

Two kinds:1. Nonprobability samples2. Probability samples

3. Select a sampling procedure

1. Nonprobability samplesConvenience Sample (Accidental Sample)

Judgmental SampleQuota sample

3. Select a sampling procedure

2. Probability samplesSimple Random Sample (SRS)

Special case of the convenience sample…..

3. Select a sampling procedure

2. Probability samplesSimple Random Sample (SRS)

Stratified Sample

3. Select a sampling procedure

2. Probability samplesSimple Random Sample (SRS)

Stratified SampleCluster Sample

3. Select a sampling procedure

2. Probability samplesSimple Random Sample (SRS)

Stratified SampleCluster SampleSystematic Sample

Note: Important!

The human mind will not randomize!

4. Determine a sample size

What is the correct sample size?

The correct answer is always the same.

It depends!

4. Determine a sample size

And what does it depend upon? 1. Sampling error

http://elections.huffingtonpost.com/pollster/obama-favorable-rating

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

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

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

4. Determine a sample size

Since any given interval on the normal curve can be calculated by:

HZ

n

4. Determine a sample size

Since any given interval on the normal curve can be calculated by:

HZ

n

x

xxZ

HZ

n

H = ZSE

SEn

nZ

H

2 2

2

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

The sample size for nominal and ordinal datacan then be seen as:

nZ pq

H

2

2

H Zpq

n

H = ZSE

SEpq

n

nZ pq

H

2

2

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

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

(. )( . )

(. )

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

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%?

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?

4. Determine a sample size

What about the size of the population?

Does that change the size of the sampleneeded?

4. Determine a sample size

Surprisingly so,

Usually not!!

4. Determine a sample size

Pragmatically, the sample size is independentof the population size!

Except for very small populations, or very, very big samples.

5. Collect data (go do it!!)

An example of the problems in samplingand the value of demographics….

http://www.dailymail.co.uk/news/article-1315078/Race-maps-America.html