Selection of Simple Random Sampling
Simple random sampling is the purest form of probability sampling and it is commonly used in the field of research. There are two ways of performing simple random sampling, i.e. Simple Random Sampling With Replacement (SRSWR) and Simple Random Sampling Without Replacement (SRSWOR). Simple Random Sampling can be done by any of the following methods:
- Lottery Method
- Mechanical Randomization or Random Number Method
- Lottery Method: Lottery method is the method in which there are three steps. The first step involves the act of constructing the sampling frame, i.e. the list of units of the target population. The lists may be students’ list, member list etc. in alphabetical order and numbered accordingly. The second step involves the act of writing the numbers listed in sampling frame on small pieces of papers and placing the papers in a vessel or drum or jar. The third step is mixing the papers properly and taking out a piece of paper from the jar. This process is continued until the required number of respondents is reached.
- Mechanical Randomization or Random Number Method: In this method, a random number table is created, which is an arrangement of digits from 0 to 9, in either a linear or a rectangular pattern where each position is filled with one of those digits. The random number table is created in such a way that the numbers within 0 and 9 appear independently of each other. Some commonly used random number tables are:
- Tippett’s Random Number Table
- Fisher and Yates’ Table
- Kendall and Smith Table
- A million random numbers
In broad sense, random number tables are the tables containing the digits from 0 to 9, each having an equal probability of selection at each draw. In 1927, Tippett produced 41,600 digits (from 0 to 9) arranged in a set of 4 in several columns and spread over 26 pages. This was followed by two great pioneer statisticians, Sir R.A. Fisher and Frank Yates, who created a table containing 15,000 digits formed by listing 15th to 19th digits in some 20 figure logarithm tables. Kendall and Smith published tables with 100,000 digits in 1955. A table containing 1 million digits was published by Rand Corporation in 1955.
Advantages of Simple Random Sampling
- Since the sample units are selected in random manner, giving each unit an equal chance of getting selected, the element of subjectivity or personal bias gets completely removed. Hence, a simple random sample carries more chances of acting as a representative of the population.
- A statistician can calculate the efficiency of the estimate of the parameters by considering the sampling distribution of the statistics (estimate). For example, n.ȳ as an estimate of N.Ȳ becomes more efficient as sample size n increases.
Disadvantages of Simple Random Sampling
- The selection of simple random sample requires an up-to-date frame, i.e. a completely catalogued population from which samples are to be drawn. Frequently, it is virtually impossible to identify the units in the population before the sample is drawn and this restricts the use of simple random sampling technique.
- A simple random sample may result in the selection of the sample units which are widely spread geographically and in such a case, the cost of collecting the data may be high in terms of time and money.
- At times, a simple random sample might give most non-random looking results. For example, if a random sample of size 13 is drawn from a pack of cards, it is possible that one gets the cards of the same suit. However, the probability of such a result is extremely low.
- For a given precision, simple random sampling usually needs a larger sample size as compared to stratified random sampling.