Simple Random Sampling is a basic probabilistic sampling technique.

Requirements:

The population must be small.

It should be possible to list every member of the population (each member must be known).

Each member of the population must have the same probability of selection.

The sampling may be undertaken with or without replacement. What does “replacement” mean?

Assume one has to choose 2 balls from a bag containing 4 balls. The probability of selecting any one ball is 2/4 (or 1/2) before the sampling procedure.

I put my hand in the bag and pick one ball. The total number of balls in the bag is now 3. Therefore, the probability of selecting any one ball from the bag is 1/3 (instead of the initial 1/2).

Suppose I replaced the (selected) ball in the bag, the total number of balls in the bag would be 4. The probability of selecting any one ball from the bag will therefore be 2/4 (or 1/2), the same probability as before the procedure.

The first procedure, wherein I selected a ball, but did not put it back in the bag before selecting another ball, is termed “sampling without replacement“. It makes a small difference to the probability of selection in the sample. However, most often, simple random sampling is performed without replacement. The investigator merely assumes that the probability does not change by doing so, especially when drawing samples from relatively large populations. [In statistics, a sample size greater than 30 (or 40) would qualify as a large sample.] Regardless of the number of samples drawn from the population, each member can be selected only once.

The second procedure, wherein I replaced the ball into the bag after each selection, is an example of “sampling with replacement“. This method is employed when performing what is called “bootstrapping” (often with the aid of a computer). If multiple samples are drawn, members of the population may be selected more than once in any sample.

Summary:

Simple Random Sampling is a probabilistic sampling technique.

It is appropriate when the population is small, and every member can be listed.

Every member of the population has the same probability of selection.

If a member can be selected more than once in any sample drawn from a population, it is termed sampling with replacement.

If a member can be selected only once, it is termed sampling without replacement.