Elementary Statistics (1+1)

3.1.9 Probability sampling methods

Simple Random Sampling

Simple random sampling refers to that sampling technique in which each and every unit of the population has an equal opportunity of being selected in the sample. In simple random sampling inclusion of items in the sample is simply a matter of chance—personal bias of the investigator does not influence the selection. It should be noted that the word ‘random’ does not mean ‘haphazard’ or ‘hit-or-miss’- it rather means that the selection process is such that the chance only determines which items shall be included in the sample. As pointed out by Chou, when a sample of size n is drawn from a population with N elements the sample is ‘simple random sample’ if any of the following is true. And, if any one of the following is true, so are the other two.

1. All n items of the sample are selected independently of one another and all N items in the population have the same chance of being included in the sample. By independent of selection we mean that the selection of particular item in one draw has no influence on the probabilities of selection in any other draw.

2. At each selection, all remaining items in the population have the same chance of being drawn. If sampling is made with replacement, i.e., when each unit drawn from the population is returned prior to drawing the next unit, each item has a probability of 1/N of being drawn at each selection. If sampling is without replacement, i.e., when each unit drawn from the population is not returned prior to drawing the next unit, the probability of selection of each item remaining in the population at the first draw is 1/N, at the second draw 1/(N-1), at the third draw is 1/(N-2), and so on. It should be noted that sampling with replacements has very limited and special use in statistics—we are mostly concerned with sampling without replacement.

3. All the possible samples of a given size n are equally likely to be selected.

To ensure randomness of selection one may adopt either the Lottery Method or use table of random numbers.