Simple Random Samples from a Table of Random Digits

Of all statistical samples, the simple random sample is indeed the gold standard. This type of sample is characterized by two properties:

• Every individual in the population is equally likely to be chosen for the sample
• Every set of size n is equally likely of being chosen.

A simple random sample guards against bias and allows us to apply results from probability, such as the central limit theorem, to our sample.

Simple random samples are so necessary that we it is important to have a process to obtain such a sample. While computers will generate random numbers, these are actually pseudorandom. Good tables of random digits are the result of random physical processes. The following example goes through a detailed example. We can see how to construct a simple random sample with the use of a table of random digits.

Statement of Problem

Suppose that we have a population of 85 college students and want to form a simple random sample of size eleven to survey about some issues on campus. We begin by assigning numbers to each of our students. Since there are a total of 85 students, and 85 is a two digit number, every individual in the population is assigned a two digit number beginning 01, 02, 03, . . . 83, 84, 85.

Use of the Table

We will use a table of random numbers to determine which of the 85 students should be chosen in our sample. We blindly start at any place in our table and write the random digits in groups of two. Beginning at the fifth digit of the first line we have:

23 44 92 72 75 19 82 88 29 39 81 82 88

The first eleven numbers that are in the range from 01 to 85 are selected from the list. The numbers below that are in bold print correspond to this:

23 44 92 72 75 19 82 88 29 39 81 82 88

At this point there are a few things to note about this particular example of the process of selecting a simple random sample. The number 92 was omitted because this number is greater than the total number of students in our population. We omit the final two numbers in the list, 82 and 88. This is because we have already included these two numbers in our sample. We only have ten individuals in our sample. To obtain another subject it is necessary to continue to the next row of the table. This line begins:

29 39 81 82 86 04

The numbers 29, 39, 81 and 82 have already been included in our sample. So we see that the first two-digit number that fits in our range and does not repeat a number that has already been selected for the sample is 86.

Conclusion of the Problem

The final step is to contact students who have been identified with the following numbers:

23, 44, 72, 75, 19, 82, 88, 29, 39, 81, 86

A well-constructed survey can be administered to this group of students and the results tabulated.