Sunday, April 12, 2009

Probability Sampling - Systematic Sampling

A sample survey design that is widely used primarily because it simplifies the sample selection process is called systematic sampling. A sample obtained by randomly selecting one element from the first k elements in the frame and every k-th element thereafter is called a 1 – in- k systematic sample, with a random start.

A systematic random sample is obtained by selecting one unit on a random basis and choosing additional elementary units at evenly spaced intervals until the desired number of units is obtained. For example, there are 100 students in your class. You want a sample of 20 from these 100 and you have their names listed on a piece of paper may be in an alphabetical order. If you choose to use systematic random sampling, divide 100 by 20, you will get 5. Randomly select any number between 1 and five. Suppose the number you have picked is 4, that will be your starting number. So student number 4 has been selected. From there you will select every 5th name until you reach the last one, number one hundred. You will end up with 20 selected students.

Systematic sampling is presented as an alternative to simple random sampling. Systematic sampling is easier to perform and, therefore, is less subject to interviewer errors than simple random sampling. Systematic sampling often provides more information per unit cost than does simple random sampling. When N is large and variance is less than 0, the variance of systematic random sampling is smaller than simple random sampling. A systematic sample is preferable when the population is ordered and N is large. When population is random, the two sampling procedures are equivalent and either design can be used.

Systematic sampling provides a useful alternative to simple random sampling for the following reasons:
1. Systematic sampling is easier to perform in the field and hence is less subject to selection errors by field-workers than are either simple random samples or stratified random samples, especially if a good frame is not available.
2. Systematic sampling can provide greater information per unit cost than simple random sampling can provide.

In general, systematic sampling involves random selection of one element from the first k elements and then selection of every k th element thereafter. This procedure is easier to perform and usually less subject to interviewer error than is simple random sampling. The accuracy of estimates from systematic sampling depend upon the order of the sampling units in the frame. Industrial quality control sampling plans are most often systematic in structure.

How to draw a systematic sample
The methods of selecting the sample data between simple random sampling and systematic sampling are different. A simple random sample is selected by using a table of random numbers. In contrast, various methods are possible in systematic sampling. The investigator can select a 1-in-3, a1-in-5, or in general a 1-in-k systematic sample.

We cannot accurately choose k when the population size is unknown. We can determine an approximate sample size n, but we must guess the value of k needed to achieve a sample of size n.

If too large a value of k is chosen, the required sample size n will not be obtained by using a 1-in-k systematic sample from population. No problem if the user can return to population and conduct another 1-in-k systematic sample until the required sample size is obtained.

In Systematic random Sampling, easier to use for large sampling frame. Select every K-th sampling unit, K is sampling interval = 1 / desired sampling ratio = 1 / (sample size/population size) = 1/(n/N). Example: 5% sample -> K = 1/(5/100) = 20; 25% sample -> K = 1/(25/100)=4

Procedure:
a. Pick random start between 1 & K
b. Select every K-th

Scheme of Systematic Random Sampling

*. Blue circle show us selected sample

We must consider the following three types of populations
1. Random population, a population is random if the elements of the population are in random order.
2. Ordered population, a population is ordered if the elements within the population are ordered magnitude according to some scheme.
3. Periodic population, a population is periodic if the elements of the elements of the population have cyclical variation.

Summary
Systematic Sampling
• Example: Selecting every 100th listing in a telephone book after the first randomly selected listing.
• This method has the properties of a simple random sample, especially if the list of the population elements is a random ordering.
• Advantage: The sample usually will be easier to identify than it would be if simple random sampling were used.


Source:
-. Richard L. Scheaffer, William Mendenhall, Lyman Ott; Elementary Survey Sampling, 4-th, PWS-Kent Publishing Company, 1990, Boston
-. Mugo Fridah W, Sampling in Research
-. SamplingBigSlides.pdf

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