Sampling

• ISSUES RELATED TO SAMPLING

• Why Sample?

• Probability vs. Non-Probability Samples

• Population of Interest

• Sampling Frame

Types of Random Samples

• Simple Random Sampling

• Systematic Sampling with a Random Start

• Stratified Random Sampling

• Multi-Stage Cluster Sampling

• Types of Non-Random Samples

• Purposive Sample

• Quota Samples

• Snowball Sample

• Available Subjects

Example of a Quota Matrix.Men Women

20-39 40-69 20-39 40-69< Grade 12 20 20 20 20Grade 12 20 20 20 20

B.A.+ 20 20 20 20

SAMPLE SIZE

The required sample size depends principally on two things:

1. the heterogeneity of the population in question;

2. the degree of accuracy required in conclusions.

(Gray and Guppy p. 157)

CALCULATING SAMPLE SIZE

Efficient sample sizes can be calculated if you know how accurate the results must be as well as how much variation exists in the population.

The necessary level of accuracy depends on the kinds of consequences or decisions that are to be based on the research results.

Estimating the variability in a population is more difficult. The primary reason for doing a survey is to learn something about a population, and so knowledge of variability in the population is usually not readily available.

(Gray and Guppy p. 160)

There are some methods that can be used to estimate variability:

1. Ask experts. You can ask people knowledgeable about a population to estimate rates of variability for key variables.

2. Use a pilot test. From a very small, random sample of the population, you can calculate measures of variability to use in determining sample sizes.

3. Use previous results. Sometimes the results of earlier research can be used to estimate variability.

4. Make an educated guess. As a last resort, estimate the lowest and highest values (i.e. the range) on a key variable and divide this range by four.

(Gray and Guppy p. 160)

SOME PRACTICAL CONSIDERATIONS IN CALCULATING SAMPLE SIZE

1. Response rates.

2. Subgroup Analysis.

3. Cost.

nz

B ( )( )1 2

Formula for Calculating Sample Size for Estimating a Proportion ():

nz

B 2 2( )

Formula for Calculating Sample Size for Estimating a Mean ():

Two conventional Z scores that you might consider are:

Z = 1.95, which corresponds to a .05 probability of your results being due to sampling error.

Z = 2.58, which corresponds to a .01 probability of your results being due to sampling error.

There are trade-off so be made. Based on the formulas, the lower your probability of making a sampling error, the higher your sample size will need to be (e.g. Z = 2.58 vs. 1.96).

Similarly, the greater the accuracy of your estimate in having tight estimates bounds (e.g. a proportion of .03 versus .05) then the larger your sample size will need to be.

Example for Determining Sample Size to Estimate a Proportion:

Using formula for estimating a proportion (say the proportion of the population holding a certain opinion), let's say we want to have a .05 chance of the result being due to sampling error (Z = 1.96), and let's say we want to be accurate within 3 percentage points (B = .03), and for the pi symbol for proportion we will use the conventional number of .50 then plugging all of these numbers into the equation would we need to obtain a sample size of n = 1067 to satisfy our criteria.

n . * .2 5 6 5 3 3 2

n . * .2 5 6 5 3 3 2 n . *2 5 4 2 6 8 n 1 0 6 7

nz

B ( )( )1 2 n . ( . )(

.

.)5 0 1 5 0

1 9 6

0 32

Calculations for Determining Sample Size for a Proportion:

Example for Determining Sample Size to Estimate a Mean:

If we wanted to estimate a mean (say mean income) and we knew that the standard deviation was $10,000 and thus the variance was 100,000,000; and we wanted a .01 probability of our estimate being due to sampling error (Z = 2.58) and we wanted to be accurate within $1,000 then we would need to obtain a sample size of n = 666.

nz

B 2 2( )

n 1 0 0 0 02 5 8

1 0 0 02 2, (

.

,)

n 1 0 0 0 0 0 0 0 0 0 .0 0 2 5 8( ) 2 n 1 0 0 0 0 0 0 0 0 0 .0 0 0 0 0 6 6 5 6 4( )

n 6 6 5 .6 4 n 6 6 6

Calculations for Determining Sample Size for a Mean: