SurfStat 500 Random Digits, which provides 100 5-digit sets of randomly generated numbers

The Research Randomizer, includes an online form for inputting instructions for designing a simple random sample; following the instructions you provide, the Randomizer will produce a set of random numbers; also includes a tutorial that walks you through the process of selecting a sample

Regardless of the method you select, any random table or randomizer is used in the same way. A table of random numbers consists of rows and columns of numbers, usually in sets of 5 numbers. Each number in each set is a computer generated random number. Consequently, any single number or any combination of numbers, such as the first 2 or last 3 or all 5, also comprises a random number. With this explanation of the numbers in a table of random numbers, we turn to using the table to select a sample.

1. Assign a number to each sample element in the sample frame. In our faculty case we would number the names on the sample frame from 1 to 500.

2. Select a start point in the table. In using a table of random numbers, the first step is to select a starting point in the table. Since all the numbers in the table are randomly generated, it doesn't matter where one starts, but it is important that the start point is selected randomly — entirely by chance. This can be done by simply closing your eyes and lightly touching a page of the table with a pencil. The number the pencil rests on is your start point.

To continue with the faculty example, we want numbers between 1 and 500 or, in terms of a table of random numbers, between 001 and 500. But numbers between 001 and 500 are not listed as such in tables of random numbers. The numbers generally are listed in sets of 5 digits. You can select three-digit numbers by reading the sets of five digits from either the left side or from the right side of the column. It doesn't matter which way is used since all numbers or any combination are random. Let's say we decide to read numbers from the right side of the column. Then, reading left, we would accept as our starting point, any three numbers between 001 and 500. Any number larger than 500 is ignored because it is beyond the size of the sample we are selecting. From the initial number our pencil rested on, we can move either up or down, it doesn't matter, until we come to a set of three numbers that are between 001 and 500.

When we prepared this example, our pencil came to rest on the set of numbers consisting of 85205. Since we decided to read from the right side of the column, then reading right to left we find the number 205. This was in the range we were using (001 to 500), so it became our starting point. The number 205 would also be the first number selected for our sample.

3. Select the remaining numbers needed to complete the sample. Continuing the faculty illustration, we need to select another 99 three-digit numbers. From our starting point, we decided to move down each column, looking for any set of 3 digit numbers between 001 and 500 (and always reading from the right side of the column to the left). As we moved down the column, the next number was 71899, which we skipped over because 899 was beyond the size of our population of 500. Going down further, we came to 96214. Since this was within our range, we recorded the number 214 as the second selection for our sample. Going down further, we found 47348 and noted sample element 348 as our third selection. We continued this process, going down the column and then moving to the top of the next column, to the right or left — it doesn't matter — and then going down each column until we had selected the remaining 99 numbers.

In the process of selecting numbers, a number that already has been selected is bound to reoccur. When this happens, ignore the second or any additional occurrences of that number.

The same procedure can be used with sampling frames of any size. If the sampling frame contained up to 9,999 elements, entire sets of 5 digits would be used. For sampling frames with numbers in excess of 9,999, combinations can be created by including numbers from a row opposite the one first selected.  

4. Record the numbers as they are identified. Each number is recorded as it is selected The list of 100 selected numbers constitute the sample for the study of faculty members. Using the numbers assigned to each faculty member, we would then identify the names of faculty members represented by these numbers and seek data from them.