# Sample Design and Sampling Procedure

### Sample Design

A sample design is made up of two elements.

Sampling method. Sampling method refers to the rules and procedures by which some elements of the population are included in the sample. Some common sampling methods are simple random sampling, stratified sampling, and cluster sampling.

Estimator. The estimation process for calculating sample statistics is called the estimator. Different sampling methods may use different estimators. For example, the formula for computing a mean score with a simple random sample is different from the formula for computing a mean score with a stratified sample. Similarly, the formula for the standard error may vary from one sampling method to the next.

The “best” sample design depends on survey objectives and on survey resources. For example, a researcher might select the most economical design that provides a desired level of precision. Or, if the budget is limited, a researcher might choose the design that provides the greatest precision without going over budget.

### Sampling Procedure

Sampling method refers to the way that observations are selected from a population to be in the sample for a sample survey.

### Population Parameter vs. Sample Statistic

The reason for conducting a sample survey is to estimate the value of some attribute of a population.

Population parameter. A population parameter is the true value of a population attribute.

Sample statistic. A sample statistic is an estimate, based on sample data, of a population parameter.

Consider this example. A public opinion pollster wants to know the percentage of voters that favor a flat-rate income tax. The actual percentage of all the voters is a population parameter. The estimate of that percentage, based on sample data, is a sample statistic.

The quality of a sample statistic (i.e., accuracy, precision, representativeness) is strongly affected by the way that sample observations are chosen; that is., by the sampling method.

### Probability vs. Non-Probability Samples

As a group, sampling methods fall into one of two categories.

Probability samples. With probability sampling methods, each population element has a known (non-zero) chance of being chosen for the sample.

Non-probability samples. With non-probability sampling methods, we do not know the probability that each population element will be chosen, and/or we cannot be sure that each population element has a non-zero chance of being chosen.

Non-probability sampling methods offer two potential advantages – convenience and cost. The main disadvantage is that non-probability sampling methods do not allow you to estimate the extent to which sample statistics are likely to differ from population parameters. Only probability sampling methods permit that kind of analysis.

### Non-Probability Sampling Methods

Two of the main types of non-probability sampling methods are voluntary samples and convenience samples.

Voluntary sample. A voluntary sample is made up of people who self-select into the survey. Often, these folks have a strong interest in the main topic of the survey.

Suppose, for example, that a news show asks viewers to participate in an on-line poll. This would be a volunteer sample. The sample is chosen by the viewers, not by the survey administrator.

Convenience sample. A convenience sample is made up of people who are easy to reach.

Consider the following example. A pollster interviews shoppers at a local mall. If the mall was chosen because it was a convenient site from which to solicit survey participants and/or because it was close to the pollster’s home or business, this would be a convenience sample.

### Probability Sampling Methods

The main types of probability sampling methods are simple random sampling, stratified sampling, cluster sampling, multistage sampling, and systematic random sampling. The key benefit of probability sampling methods is that they guarantee that the sample chosen is representative of the population. This ensures that the statistical conclusions will be valid.

Simple random sampling. Simple random sampling refers to any sampling method that has the following properties.

The population consists of N objects.

The sample consists of n objects.

If all possible samples of n objects are equally likely to occur, the sampling method is called simple random sampling.

There are many ways to obtain a simple random sample. One way would be the lottery method. Each of the N population members is assigned a unique number. The numbers are placed in a bowl and thoroughly mixed. Then, a blind-folded researcher selects n numbers. Population members having the selected numbers are included in the sample.

Stratified sampling. With stratified sampling, the population is divided into groups, based on some characteristic. Then, within each group, a probability sample (often a simple random sample) is selected. In stratified sampling, the groups are called strata.

As a example, suppose we conduct a national survey. We might divide the population into groups or strata, based on geography – north, east, south, and west. Then, within each stratum, we might randomly select survey respondents.

Cluster sampling. With cluster sampling, every member of the population is assigned to one, and only one, group. Each group is called a cluster. A sample of clusters is chosen, using a probability method (often simple random sampling). Only individuals within sampled clusters are surveyed.

Note the difference between cluster sampling and stratified sampling. With stratified sampling, the sample includes elements from each stratum. With cluster sampling, in contrast, the sample includes elements only from sampled clusters.

Multistage sampling. With multistage sampling, we select a sample by using combinations of different sampling methods.

For example, in Stage 1, we might use cluster sampling to choose clusters from a population. Then, in Stage 2, we might use simple random sampling to select a subset of elements from each chosen cluster for the final sample.

Systematic random sampling. With systematic random sampling, we create a list of every member of the population. From the list, we randomly select the first sample element from the first k elements on the population list. Thereafter, we select every kth element on the list.

This method is different from simple random sampling since every possible sample of n elements is not equally likely.

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