Elementary Statistics (1+1)

3.1.9.2 Table of random Numbers

The lottery method discussed above becomes quite cumbersome as the size of population increases. An alternative method of random selection is that of using the table of random numbers.

The random numbers are generally obtained by some mechanism which, when repeated a large number of times, ensured approximately equal frequencies for the number from 0 to 9 and also proper frequencies for various combinations of numbers (such as 00,01,…………..99; 000, 001,………….999; etc) that could be expected in a random sequence of the digits 0 to 9.

Several standard table of random numbers are available, among which the following may be specially mentioned, as they have been tested extensively for randomness:

1. Tippett’s (1927) random number tables consisting of 41,600 random digits grouped into 10,400 sets of four –digit random numbers:

2. Fisher and Yates (1938) table of random numbers with 15,000 random digits arranged into 1,500 sets of ten-digit random numbers:

3. Kendall and Babington Smith (1939) table of random numbers consisting of 1,00,000 random digits grouped into 25,000 sets of four-digit random numbers:

4. Rand Corporation (1955) table of random numbers consisting of 1,00,000 random digits grouped into 20,000 sets of five-digit random numbers; and

5. C.R. Rao, Mitra and Mathai (1966) table of random numbers

Trippett’s table of random numbers is most popularly used in practice. We give below the first forty sets from Tippett’s table as an illustration of the general appearance of random numbers:

2952	6641	3992	9792	7969	5911	3170	5624
4167	9524	1545	1396	7203	5356	1300	2693
2670	7483	3408	2762	3563	1089	6913	7691
0560	5246	1112	6107	6008	8125	4233	8776
2754	9143	1405	9025	7002	6111	8816	6446

It is important that the starting point in the table of random numbers be selected in some random fashion so that every units has an equal chance of being selected.

One may question, and quite rightly, as to how it is ensured that these digits are random. It may be pointed out that the digits in the table were chosen haphazardly but the real guarantee of their randomness lies in practical tests. Tippett’s numbers have been subjected to numerous tests and used in many purposes. An example to illustrate how Tippett’s table of random numbers may be used is given below. Suppose we have to select 20 items out of 6,000. The procedure is to number all the 6,000 items from 1 to 6,000. A page from Tippett’s table may then be consulted and the first twenty numbers up to 6,000 are noted down. Items bearing those numbers will be included in the sample. Making use of the portion of the table the required numbers are noted as:

2952	3992	5911	3170	5624	4167
1545	1396	5356	1300	2693	2370
3408	2762	3563	1089	0560	5246
1112	4233

The items which bear the above numbers constitute the sample.

If the size of universe is less than 1,000 the procedure will be different, as Tippett’s numbers are available only in four figures. Thus, for example, if it is desired to take a sample of 10 items out of 400, all items from 1 to 400 should be numbered as 0001 to 0400. We may now select 10 numbers from the table which are up to 0400.

If the size of universe is less than 100, the table is used as follows: Suppose ten numbers from 0 to 80 are required. We start anywhere in the table and write down the numbers in pairs. The table can be read horizontally, vertically,diagonally or in any methodical way. Starting with the first and reading horizontally first we obtain 29, 52, 66, 41, 39,92,97,79,69,59,11,31, 70, 56, 24, 70,56, 24,41, 67 and so on. Ignoring the numbers greater than 80, we obtain for our purpose ten random numbers, namely, 29, 52, 66,41, 39, 73, 69, 59, 11 and 31.

Fishers and Yates tables consist of 15,000 numbers. These have been arranged in two digits in 300 blocks, each block consisting of 5 rows and 5 columns. Kendall and Smith also constructed random numbers (10,000 in all) by using a randomizing machine. However, this method of random selection cannot be followed in case of articles like ghee, oil, petrol, wheat, etc.

Merits. 1. Since the selection of items to the sample depends entirely on chance there is no possibility of personal bias affecting the results.

2.Compared to judgment sampling a random sample represent the universe in a better way. As the size of the sample increases, it become increasingly representative of the population.

3. The analyst can easily assess the accuracy of the estimate because sampling errors follow the principles of chance. The theory of random sampling is further developed than that of any other type of sampling which enables the analyst to provide the most reliable information at the least cost.

Limitations. 1. The use of simple random sampling necessitates a completely catalogued universe from which draw the sample. But it is often difficult for the investigator to have up-to-date list of all the items of the population to be sampled. This restricts the use of this method in economic and business data where very often we have to employ restricted random sampling designs.

2. The size of the sample required to ensure statistical reliability is usually larger under random sampling than non-probability sampling.

3. From the point of view of field survey it has been claimed that cases selected by random sampling tend to be too widely dispersed geographically and that the time and cost of collecting data become too large.

4. Random sampling may produce the most non-random-looking results. For example, thirteen cards from a well-shuffled pack of playing cards may consist of one suit. But the probability of this type of occurrence is very, very low.