CHAPTER 12

DETERMINING THE SAMPLE PLAN

Important Topics of This Chapter

Differences between population and sample.Sampling frame and frame error.Developing sampling plan. Basic sampling methods.Strength and Weaknesses of Basic Sampling techniques. Choosing Probability Vs. non-probability sampling.

Definitions of Important Terms

Population or Universe The total group of people from whom information is needed.

Census Data obtained from or about every member of the population of

interest.

Sample A subset of the population of interest

Sampling Error: Selection error Sampling size

Sample Frame and Frame Error:

Sample vs. CensusSample vs. Census

Types of Study Conditions Favoring the Use of

Sample Census

1. Budget

Small

Large

2. Time available

Short Long

3. Population size

Large Small

4. Variance in the characteristic

Small Large

5. Cost of sampling errors

Low High

6. Cost of nonsampling errors

High Low

7. Nature of measurement

Destructive Nondestructive

8. Attention to individual cases Yes No

The Sampling Design ProcessThe Sampling Design Process

Define the Population

Determine the Sampling Frame

Select Sampling Technique(s)

Determine the Sample Size

Execute the Sampling Process

Steps in Developing a Sampling Plan

Step 1: Defining the Population: Bases for defining the population of interest include:

Geography Demographics Use Awareness

Step 2: Choosing a Sampling Frame Sampling frame

List of population elements from which to select units to be sampled.

Steps in Developing a Sampling Plan (cont.)

Step 3: Selecting the Sampling Technique(s): Probability samples:

Samples in which every element of the population has a known, nonzero probability of selection.

Non-probability samples: Include the selection of specific elements from the population

in a nonrandom manner.

Sampling error: The difference between the sample value and the true value of

the population mean.

Steps in Developing a Sampling Plan (cont.)

Advantages of probability samples

Disadvantages of probability samples

- The researcher can be sure of obtaining information from a representative cross section of the population of interest.

- Sampling error can be computed.

- The survey results are projectable to the total population.

- They are more expensive than non-probability samples of the sample size in most cases. The rules for selection increase interviewing costs and professional time must be spent in developing the sample design.

- Probability samples take more time to design and execute than non- probability samples.

Steps in Developing a Sampling Plan (cont.)

Advantages of non-probability samples

Disadvantages of non-probability samples

- Non-probability samples cost less than probability samples. This characteristic of non-probability samples may have considerable appeal in those situations where accuracy is not of critical importance.

-Non-probability samples ordinarily can be conducted more quickly than probability samples.

- - Sampling error cannot be computed.

- The researcher does not know the degree to which the sample is representative of the population from which it was drawn.

- The results of non-probability samples cannot and should not be projected to the total population.

Steps in Developing a Sampling Plan (cont.)

Step 4: Determine the Sample Size: Once the sampling method has been chosen, the

next step is to determine the appropriate sample size.

Developing Operational Procedures: Involves determining whether a probability or non-

probability sample is being used.

Steps in Developing a Sampling Plan (cont.)

Step 5: Execute the Sampling Process: The final step in the sampling process involves

execution of the operational sampling plan discussed in the previous steps.

It is important that this step include adequate checking to make sure that specified procedures are adhered to.

Sampling Techniques

Classification of Sampling TechniquesClassification of Sampling Techniques

Non-probabilitySampling Techniques

ConvenienceSampling

ProbabilitySampling Techniques

JudgmentSamples

QuotaSampling

SnowballSampling

SystematicSampling

StratifiedSampling

ClusterSampling

Simple randomSampling

Probability Sampling Methods

Simple Random Sampling Is considered to be the purest form of

probability sampling. A probability sample is a sample in which every element of the population has a known and equal probability of being selected into the sample.

Probability of Selection = Sample Size

Population Size

Procedures for DrawingProcedures for DrawingProbability SamplesProbability Samples

1. Select a suitable sampling frame

2. Each element is assigned a number from 1 to N (pop. size)

3. Generate n (sample size) different random numbers between 1 and N

4. The numbers generated denote the elements that should be included in the sample

Simple Random Sampling

Probability Sampling Methods (cont.)

Systematic Sampling Probability sampling in which the entire

population is numbered, and elements are drawn using a skip interval.

Skip Interval = Population Size

Sample Size

Systematic Sampling

1. Select a suitable sampling frame

2. Each element is assigned a number from 1 to N (pop. size)

3. Determine the sample interval i:i=N/n. If i is a fraction, round to the nearest integer

4. Select a random number, r, between 1 and i, as explained in simple random sampling

5. The elements with the following numbers will comprise the systematic random sample: r, r+i,r+2i,r+3i,r+4i,...,r+(n-1)i

Probability Sampling Methods (cont.)

Stratified Samples Stratified samples are probability samples that

are distinguished by the following procedural steps:

First, the original or parent population is divided into two or more mutually exclusive and exhaustive subsets (e.g., male and female).

Second, simple random samples of elements from the two or more subsets are chosen independently from each other.

nh = nh=1

H

1. Select a suitable frame

2. Select the stratification variable(s) and the number of strata, H

3. Divide the entire population into H strata. Based on the classification variable, each element of the population is assigned to one of the H strata

4. In each stratum, number the elements from 1 to Nh (the pop. size of stratum h)

5. Determine the sample size of each stratum, nh, based on proportionate or disproportionate stratified sampling, where

6. In each stratum select a simple random sample of size nh

StratifiedSampling

Probability Sampling Methods(cont.)

Cluster Samples In the case of cluster samples, the sampling

units are selected in groups. There are two basic steps in cluster sampling:

First, the population of interest is divided into mutually exclusive and exhaustive subsets.

Second, a random sample of the subsets is selected.

Cluster Sampling

1. Assign a number from 1 to N to each element in the population

2. Divide the population in C clusters of which c will be included in the sample

3. Calculate the sampling interval i, i=N/c (round to nearest integer)

4. Select a random number r between 1 and i, as explained in simple random sampling

5. Identify elements with the following numbers: r,r+i,r+2i,... r+(c-1)i

6. Select the clusters that contain the identified elements

7. Select sampling units within each selected cluster based on SRS or systematic sampling

8. Remove clusters exceeding sampling interval i. Calculate new population size N*, number of clusters to be selected C*= C-1, and new sampling interval i*.

Cluster Sampling

Types of Cluster SamplingTypes of Cluster Sampling

One-StepApproach

MultistageApproach

Two-StepApproach

Simple ClusterSampling

ProbabilityProportionate

to Size Sampling

Non-probability Sampling Methods

Convenience Samples Non-probability samples used primarily

because they are easy to collect.

Judgment Samples Non-probability samples in which the selection

criteria are based on personal judgment that the element is representative of the population under study.

Non-probability Sampling Methods (cont.)

Quota Samples Non-probability samples in which population

subgroups are classified on the basis of researcher judgment.

Snowball Samples Non-probability samples in which selection of

additional respondents is based on referrals from the initial respondents.

Technique Strengths WeaknessesNonprobability Sampling Convenience sampling

Least expensive, leasttime-consuming, mostconvenient

Selection bias, sample notrepresentative, not recommended fordescriptive or causal research

Judgmental sampling Low cost, convenient,not time-consuming

Does not allow generalization,subjective

Quota sampling Sample can be controlledfor certain characteristics

Selection bias, no assurance ofrepresentativeness

Snowball sampling Can estimate rarecharacteristics

Time-consuming

Probability sampling Simple random sampling(SRS)

Easily understood,results projectable

Difficult to construct samplingframe, expensive, lower precision,no assurance of representativeness.

Systematic sampling Can increaserepresentativeness,Easier to implement thanSRS, sampling frame notnecessary

Can decrease representativeness

Stratified sampling Include all importantsubpopulations,precision

Difficult to select relevantstratification variables, not feasible tostratify on many variables, expensive

Cluster sampling Easy to implement, costeffective

Imprecise, difficult to compute andinterpret results

Strengths and Weaknesses of Basic Sampling TechniquesStrengths and Weaknesses of Basic Sampling Techniques

Conditions Favoring the Use ofFactors Nonprobability

samplingProbabilitysampling

Nature of research Exploratory Conclusive

Relative magnitude of sampling andnonsampling errors

Nonsamplingerrors arelarger

Samplingerrors arelarger

Variability in the population Homogeneous(low)

Heterogeneous(high)

Statistical considerations Unfavorable Favorable

Operational considerations Favorable Unfavorable

Choosing Non-probability vs. Choosing Non-probability vs. Probability SamplingProbability Sampling

Table 11.4Table 11.4