Obtaining a Sample From a Population SAMPLING Obtaining a Sample From a Population

A population is all the people or objects of interest in a study.

Population data can be very informative, especially in business. What can you determine about Iowa by looking at the following overlay of demographics on a map?

What do we learn about China by simply looking at population data?

Statistically, the population for a study about UNI students would be all the students at UNI.

If a study utilized everyone in a population, the sample would be called a Census.

A CENSUS is a sample of an entire Population…. They are seldom done because…..

Impossible A CENSUS is a sample of an entire Population…. They are seldom done because….. Impossible

Impossible Unprofitable A CENSUS is a sample of an entire Population…. They are seldom done because….. Impossible Unprofitable

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

So… instead of a census, a sample is taken.

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 must be done properly or sampling itself can invalidate your research!

Sampling is a five step process:

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.

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. India France Male Female Male Female

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.

2. Identify the sampling frame

2. Identify the sampling frame A sampling frame is a list of the units of a population: telephone numbers addresses email addresses commercial sources “Big” data

3. Select a sampling procedure

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

3. Select a sampling procedure 1. Nonprobability samples

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

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

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

3. Select a sampling procedure 2. Probability samples

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

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

Cluster Sample

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

The human mind will not randomize! Note: Important! The human mind will not randomize!

Select a sampling procedure

4. Determine a sample size

IT DEPENDS! 4. Determine a sample size What is the correct sample size? The answer is always the same. IT DEPENDS!

4. Determine a sample size And what does it depend upon?

4. Determine a sample size And what does it depend upon? 1. Sampling error http://www.rasmussenreports.com/public_content/politics/obama_administration/daily_presidential_tracking_poll

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

4. Determine a sample size And what does it depend upon? 1. Sampling error 2. Precision 3. Degree 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 = Z SE

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 (p + q = 1); H = .02; Z = 2

EVER needed is: 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: Use an IQ scale with a SD = 15 to an accuracy of 95% at 3 IQ points?

What size sample would be needed to: Use a GPA scale with a SD = 15 to an accuracy of 95% at 3 IQ points? A Likert scale to a 95% accuracy of 0.4?

What size sample would be needed to: Use a GPA scale with a SD = 15 to an accuracy of 95% at 3 IQ points? A Likert scale to a 95% accuracy of 0.4? Income scale with a SD = $15,000 to within a 95% accuracy of $5,000?

What size sample would be needed to: Use a GPA scale with a SD = 15 to an accuracy of 95% at 3 IQ points? A Likert scale to a 95% accuracy of 0.4? Income scale with a SD = $15,000 to within a 95% accuracy of $5,000? The largest sample that would ever be needed to do an over-night political poll with a 95% accuracy of 2%?

What size sample would be needed to: Use a GPA scale with a SD = 15 to an accuracy of 95% at 3 IQ points? A Likert scale to a 95% accuracy of 0.4? Income scale with a SD = $15,000 to within a 95% accuracy of $5,000? The largest sample that would ever be needed to do an over-night political poll with a 95% accuracy of 2%? 5. To test a hypothesis that 80% of all customers will buy a product again to within 95% accuracy at 3%?

What is the sample size? Why is it +/- 3 percent at 95% confidence? 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?

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 large samples.

5. Collect data (go do it!!)

An example of the problems in sampling and the value of demographics…. http://www.prb.org/Publications/Articles/2008/workingaroundtheclock.aspx http://www.dailymail.co.uk/news/article-1315078/Race-maps-America.html