In probability sampling, each element of the population has a known non-zero chance of being selected for the sample. Among the probability sampling methods, **simple random sampling** is simplest as its name indicate and it underlies many of the more complex methods.

In a simple random sample of a given size, all such subsets of the frame are given an equal probability. Each element of the frame thus has an equal probability of selection: the frame is not subdivided or partitioned. Furthermore, any given pair of elements has the same chance of selection as any other such pair (and similarly for triples, and so on). This minimises bias and simplifies analysis of results. In particular, the variance between individual results within the sample is a good indicator of variance in the overall population, which makes it relatively easy to estimate the accuracy of results.

However, simple random sampling can be vulnerable to sampling error because the randomness of the selection may result in a sample that doesn’t reflect the makeup of the population. For instance, a simple random sample of ten people from a given country will on average produce five men and five women, but any given trial is likely to overrepresent one sex and underrepresent the other. Systematic and stratified techniques, discussed below, attempt to overcome this problem by using information about the population to choose a more representative sample.

Simple random sampling may also be cumbersome and tedious when sampling from an unusually large target population. In some cases, investigators are interested in research questions specific to subgroups of the population. For example, researchers might be interested in examining whether cognitive ability as a predictor of job performance is equally applicable across racial groups. SRS cannot accommodate the needs of researchers in this situation because it does not provide subsamples of the population. Stratified sampling, which is discussed below, addresses this weakness of SRS.

The following is a description of one of the ways a **simple random sample** can be selected, namely, the **lottery method**. **Lottery method** is very simple and easy to follow where the population is not too large.

Suppose twenty employees are to be chosen from a thousand employees of a factory for a study of job satisfaction. The name of each employee is written on a piece of paper of uniform size. The pieces of paper are thoroughly mixed before and after being placed on a large bowl. Then twenty pieces are drawn out without looking at the name. The sample so selected would be a simple random sample. Here each employee in the factory has twenty chances of being selected. It should be understood that random sampling is a highly scientific, equal probability selection procedure, and it is not the haphazard sampling method of meeting whoever crosses your way, though the dictionary may define the word random as haphazard. The haphazard man in the street interview does not require any sample frame or scientific selection procedure and it is a non-probability method of sampling called convenience sampling or accidental sampling and described later in this lesson. The lottery method may also be adopted using tokens numbering 0 to 9 in a container, picking them up one after other after. For picking the twenty employees first, the names of the thousand employees should be alphabetically arranged and serially numbered, using the tokens we have to get three digit random numbers. Suppose we pick 3 first, 0 next, and 8 next. The employees bearing the number 308 gets selected for the sample. If 000 is the next number, person bearing the number 1000 gets selected, ie. 001 is selected the employee whose name if first in the list is selected and so on, till twenty persons selected.

The lottery procedure, however, is tedious. So random number tables are for selecting a simple random sample. For this we should take a book of numbers, choose a page in it at random, and start from a line or column page at random. Suppose the numbers we get read

3125 |
1496 |
4905 |
9967 |
5414 |

5750 |
9867 |
4099 |
2082 |
7884 |

8144 |
5454 |
6703 |
3074 |
6836 |

Then, the twenty employees bearing the following numbers respectively are chosen from the sample frame:

312 | 514 | 964 | 905 | 996 | 754 | 145 | 750 | 986 | 740 |

992 | 82 | 788 | 481 | 445 | 454 | 670 | 330 | 746 | 836 |

If the same number appears again, it is dropped and the next number taken. How these numbers are got? From the first random number 312 is taken. The left out number is 5. This is prefixed to the first two numbers of the next random number, 1496 and we get 514. Then with the left out 96, first digit of the next random number 4905, ie., 4 is suffixed. And we get 964 and so on.