SAMPLING Obtaining a Sample From a Population

A CENSUS is a sample of an entire Population…. They are seldom done because….. 1. Impossible 2. Unprofitable 3. Less accurate

Sampling is the process of discovering what a population is like….. but You can never look directly at the population!

The population is like a large container… you can pull things out but 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 process Each step is important Or the sample will not give an 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 or persons 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 or persons that are of interest for a study. The characteristics of a population are called: Parameters.

Many business problems can be resolved by simply looking at population parameters.

2. Identify the sampling frame

A sampling frame is a list of the units of a population: telephone numbers addresses addresses

3. Select a sampling procedure Two kinds: 1. Nonprobability samples 2. Probability samples

3. Select a sampling procedure 1. Nonprobability samples Convenience Sample (Accidental Sample) Judgmental Sample Quota sample

3. Select a sampling procedure 2. Probability samples Simple Random Sample (SRS) Special case of the convenience sample…..

3. Select a sampling procedure 2. Probability samples Simple Random Sample (SRS) Stratified Sample

3. Select a sampling procedure 2. Probability samples Simple Random Sample (SRS) Stratified Sample Cluster Sample

3. Select a sampling procedure 2. Probability samples Simple Random Sample (SRS) Stratified Sample Cluster Sample Systematic 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

4. Determine a sample size And what does it depend upon? 1. Sampling error National Survey of 1,000 Likely Voters Conducted September 20-21, 2010 By Rasmussen Reports 1* Is the current structure of the Social Security system a Ponzi scheme? 27% Yes 36% No 37% 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 error 2. Precision 3. Degree of confidence 4. Other factors a. time b. cost c. type of scales d. number of cross-classifications

4. Determine a sample size And what does it depend upon? 1. Sampling error 2. Precision 3. Degree of confidence 4. Other factors f. historical and secondary data g. statistical considerations h. political considerations

4. Determine a sample size Since any given interval on the normal curve can be calculated by:

4. Determine a sample size Since any given interval on the normal curve can be calculated by:

H = ZSE

Since any given interval on the normal curve can be calculated by: The sample size can then be seen as:

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

H = ZSE

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: With Z = 2, H = 2; therefore….

It is assumed that 55% of all students are women, what size sample would be needed to test this assumption to a 95% accuracy at 2%? p =.55, q =.45; H =,02, Z = 2

The largest sample size that will ever be needed for any given H is when nominal data is being used and p = q = 0.5. Therefore the largest sample EVER needed is:

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 political poll 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 Voters Conducted September 20-21, 2010 By Rasmussen Reports 1* Is the current structure of the Social Security system a Ponzi scheme? 27% Yes 36% No 37% 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 sample needed?

4. Determine a sample size Surprisingly so, Usually not!!

4. Determine a sample size Pragmatically, the sample size is independent of 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 sampling and the value of demographics….