Simple Random Sampling

Probability sampling is the only sampling technique available that will provide an objective measure of the precision of the ample estimate. The simplest possible probability sampling method is called simple random sampling. In probability sampling, every possible sample of a given size drawn from a specified universe has a known chance of being selected. In simple random sampling every possible sample has a known and equal chance of selection.

Simple random sampling is discussed in detail. Given below are the reasons:

1) It is the easiest probability sampling method to understand. It will serve as a vehicle for introducing some of the more complicated ideas involved in drawing inferences from samples.
2) It may serve as a good approximation to some of the more complex methods used in practice.

What is a simple random sample?

A simple random sample is a sample generated by a process that guarantees, in the long run, that every possible sample of a given size will be selected with known and equal probability.

Selection of a simple random is fully analogous to dealing a “hand” of playing cards from a well shuffled deck. If the process of thorough shuffling and dealing is repeated a very large number of times, then all possible “hands” of cards (i.e. samples of that number of cards from the universe of all cards) will occur with equal frequency. The probability of dealing a given hand (i.e. a given sample) is the same for all possible hands (i.e. all possible samples).

Selecting Universe items with Random Numbers:

In practice; individual universe items are selected one at a time, using a table of random numbers. This process is conceptually equivalent to shuffling and selecting cards as above. Table is a short table of random numbers.

The table consists of 400 digits arranged in 40 columns and 10 rows. There is no pattern to the occurrence of any particular digit. If, for example, the pattern of occurrence of the digit 7 in the first row is studied, it is found that this digit occurs in the columns 14, 28, 30, 31, and 37. If the 7s are traced throughout the remaining columns of the table, one finds no systematic pattern of their occurrence. The 7s occur ‘at random” in the table, and make up approximately 10 percent of the digits in the table.

Using a Table of Random Numbers:

To illustrate the use of a table of random numbers for sample selection, suppose it was desired to choose a simple random sample of 15 from a universe of 83 furniture stores. First assign numbers 01 to 83 to the universe items. Then, beginning at an arbitrary place in a table of random numbers, choose two digit random numbers between 01 and 83.

Suppose the starting place was the two digits in row 1, columns 20 and 21 (i.e. 41). Store 41 would be the first store selected. Moving horizontally, the next store chosen would be 51. Continuing the process, the sample would consist of stores with these numbers: 41, 51, 83, 38, 78, 77, 26, 53, 21, 49, 69, 01, 45, 43, and 07.

Note that two digit numbers exceeding the universe size (here N = 83) are ignored – for example, the number 87, which appears in columns 36 – 37. Also note that once a particular random number has chosen (e.g. 53) that number is ignored if it is encountered again.

If the universe is very large (for example, the hotel chain prospect list of 21,476 mentioned at the beginning), and extremely large table of random numbers would be required. To chose a simple random sample from that universe, one would number prospects from 00001 to 21476, and then select five digit random numbers in that range until the sample was identified.