Probability Sampling - Simple Random Sampling

The objective of a sample survey is to make an inference about the population from information contained in a sample and to obtain a specified amount of information about a population parameter at minimum cost.

Types of Surveys
1. Cross-sectional Surveys
• surveys a specific population at a given point in time
• will have one or more of the design components example: stratification (stratified random sampling), clustering with multistage sampling (cluster random sampling)

2. Longitudinal Surveys
• surveys a specific population repeatedly over a period of time, example: panel, rotating samples

Two factors affect the quantity of information contained in the sample and hence affect the precision of our inference making-procedure. The first is the size of the sample selected from the population. The second is the amount of variation in the data; variation can frequently be controlled by the method of selecting the sample. The procedure for selecting the sample is called the sample survey design.

Type of probability sampling:
1. Simple random sampling
2. Stratified Random Sampling
3. Systematic Random Sampling
4. Cluster Random Sampling

1. Simple Random Sampling
The basic design of sampling technique is sampling random design. The procedure of simple random sampling: if a sample of size n drawn from a population of size N in such a way that every possible sample of size n has the same chance of being selected. To draw a simple random sample from the population of interest is not as trivial as it may first appear. A simple random sample is obtained by choosing elementary units in search a way that each unit in the population has an equal chance of being selected. A simple random sample is free from sampling bias. However, using a random number table to choose the elementary units can be cumbersome. If the sample is to be collected by a person untrained in statistics, then instructions may be misinterpreted and selections may be made improperly. Instead of using a least of random numbers, data collection can be simplified by selecting say every 10th or 100th unit after the first unit has been chosen randomly as discussed below. such a procedure is called systematic random sampling.

Simple random sampling is the basic sampling technique where we select a group of subjects (a sample) for study from a larger group (a population). Each individual is chosen entirely by chance and each member of the population has an equal chance of being included in the sample. Every possible sample of a given size has the same chance of selection.
(Definition taken from Valerie J. Easton and John H. McColl's Statistics Glossary v1.1)

In simple random sampling, each sampling unit has equal and known probability of being selected.

How can we draw a sample from population in simple random sampling methods ? We might use our own judgment to “randomly” select the sample. This technique called haphazard sampling. Another technique called representative sampling, involves choosing a sample that we consider to be typical or representative of the population. Both haphazard and representative sampling are subject to investigator bias and they lead to estimates who properties cannot be evaluated.

This design does not attempt to reduce the effect of variation on the error of estimation. A simple random sample of size n occurs if each sample of n elements from population has the same chance of being selected. Random number tables are quite useful in determining the elements that are to be included in a simple random sample.

Scheme of Simple Random Sampling

*. Blue circle show us selected sample


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