Write short notes on Simple Random Sampling

In statistics, a Simple Random Sample is a group of subjects (a sample) chosen from a larger group (a population). Each subject from the population is chosen randomly and entirely by chance, such that each subject has the same probability of being chosen at any stage during the sampling process. This process and technique is known as Simple Random Sampling, and should not be confused with Random Sampling.

In small populations such sampling is typically done "without replacement", i.e., one deliberately avoids choosing any member of the population more than once. An unbiased random selection of subjects is important so that in the long run, the sample represents the population. However, this does not guarantee that a particular sample is a perfect representation of the population. Simple random sampling merely allows one to draw externally valid conclusions about the entire population based on the sample. Although simple random sampling can be conducted with replacement instead, this is less common and would normally be described more fully as simple random sampling with replacement.

Conceptually, simple random sampling is the simplest of the probability sampling techniques. It requires a complete sampling frame, which may not be available or feasible to construct for large populations. Even if a complete frame is available, more efficient approaches may be possible if other useful information is available about the units in the population.

Advantages are that it is free of classification error, and it requires minimum advance knowledge of the population. It best suits situations where not much information is available about the population and data collection can be efficiently conducted on randomly distributed items. If these conditions are not true, stratified sampling or cluster sampling may be a better choice.

Simple Random Sampling:

Simple Random Sampling selects samples by methods that allow each possible sample to have an equal probability of being picked and each item in the entire population to have an equal chance of being included in the sample.

Suppose we have a population of four students in a seminar and we want samples of two students at a time for interviewing purposes. The table below illustrates all of the possible combinations of samples of two students in a population size of four, the probability of each sample being picked, and the probability that each student will be in a sample.