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. Census

The 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 Techniques Non-probability Sampling Techniques Convenience Sampling Probability Sampling Techniques Judgment Samples Quota Sampling Snowball Sampling Systematic Sampling Stratified Sampling Cluster Sampling Simple random Sampling

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 Drawing Probability 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.

n h = n h=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 N h (the pop. size of stratum h) 5. Determine the sample size of each stratum, n h, based on proportionate or disproportionate stratified sampling, where 6. In each stratum select a simple random sample of size n h Stratified Sampling

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 Sampling One-Step Approach Multistage Approach Two-Step Approach Simple Cluster Sampling Probability Proportionate 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.

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

Choosing Non-probability vs. Probability Sampling Table 11.4