Simple random sampling is a simple and widely used method of sampling in which the samples with equal probability of being selected at each draw, are selected unit by unit. It is a technique of drawing a sample in such a way that each population unit has an equal and independent chance of being included in the sample. There are two ways of drawing a sample through simple random sampling:
- Simple random sampling with replacement: In this sampling, an item previously drawn is replaced before the next draw in which the same unit may be included more than once in the sample.
- Simple random sampling without replacement: In this method, an item previously drawn is not replaced before the next draw in which all units in the sample are distinct.
- Simple random sampling with replacement (SRSWR): A simple random sampling with replacement (SRSWR) of size n from a population of N units can be imagined as an act of drawing independent samples of size 1. A unit is randomly selected from the population to be the first sampled unit, with probability 1/N. Then, the sampled unit is replaced in the population, and a second unit is randomly selected with probability 1/N. This procedure is repeated until the sample has n units, which may include duplicates from the population. The number of possible sample having sample size n from the population size N is Nn. Hence, the probability of one sample = 1/Nn.
However, in finite population sampling, sampling the same person twice provides no additional information. We usually prefer to sample without replacement, so that the sample contains no duplicates.
- Simple random sampling without replacement (SRSWOR): A simple random sample without replacement (SRSWOR) of size n is selected so that every possible subset of n distinct units in the population has the same probability of being selected as the sample. One unit is randomly selected from the population to be first sampled unit with probability 1/N. The sampled unit is not replaced and the second unit is randomly selected with probability 1/(N-1). Similarly, the second sampled unit is not replaced and third unit is randomly selected with probability 1/(N-2) and so on until the sample has n units obtained from the population. There are NCn possible samples of size n from population size N and each is equally likely. So, the probability of selecting any individual sample of n units is 1/NCn.