RANDOM ASSIGNMENT

Random does not mean "any old way." You cannot assign subjects or objects to groups according to whatever strikes your fancy or let others make the assignment decisions for you. Randomness requires a very specific, systematic approach to minimize the chance of distortion of groups due to the inclusion of disproportionate numbers of particular types of individuals or products.

If you allowed teachers to select which of their students receive personal computers, for example, they might select well-behaved students to reward them for past efforts. These students may be more intelligent or more diligent than the students who do not get to use the special equipment. Any evaluation of the effect of personal computers would be tainted by the differences between the selected students and the population as a whole.

Or consider this example: An engineer is trying to study customers' perceptions of the effect of adjustable brakes in vehicles. The results would be very different if the sample was based only on individuals with a height of more than 5 feet 11 inches, rather than a random sample of drivers of different heights.

A good way to assign people, animals, or objects to groups is to use a table of random numbers. You cannot just make up a table of numbers that you think are random. You are likely to have certain number biases. Unlike experimenters, random number tables do not have birthdays, license plates, children, or any other reasons to prefer one number over another. In a properly constructed table of random numbers, every number from zero to nine has the same chance of appearing in any position in the table.

Table I.1 shows a small random number table. The table has the numbers grouped into fours, but the grouping is just for convenience. It has no other significance. To randomly assign subjects to groups, you start at an arbitrary place in the table and assign the digit at that place to the first subject or object. Each new subject gets a digit from successive places in the table. If you start at the fourth digit of the first vertical group in the fourth position in Table I.1, for example, and then proceed to the right, the first subject gets the number 7, the next subject the number 0, and the next subject the number 8. (These three digits have been printed in bold type.) Since everything is random, it really does not matter whether you read the table across or down. However, once you have selected a starting point, stay in sequence. Using the table in this systematic way prevents you from choosing "favorite" numbers as starting points or as the next numbers in the sequence. You can never be too careful when you are trying to be random.

Table I.1: A Limited Table of Random Numbers

8588	5171	0775	7818	8683	3168 ...
7185	8645	1537	3754	0201	2450 ...
1053	9728	3028	8725	4855	0218 ...
7517	0826	7257	5527	2668	8157 ...
3551	3316	3584	9439	0011	7365 ...
‹
7405	7764	6131	6204	8835	0345 ...

You use the numbers you assigned to the subjects to assign them to experimental groups. For example, if you have two groups, you can assign subjects with even numbers to one group and subjects with odd numbers to another group. This procedure should result in about the same number of subjects in the two groups. But if you want the groups to be exactly equal in size , you can assign two- or three-digit random numbers to each of the subjects. Then arrange the numbers in order, from smallest to largest. Subjects with numbers in the lower half go to one group, and subjects with numbers in the upper half go to the other. You can use all sorts of systems with a random number table to assign subjects to groups, even in very complicated experimental designs. It is customary nowadays to use a computer generator program to generate random numbers.

Does randomness really matter? Yes, it does. Unless you use a procedure that assigns your subjects randomly, the results of your study may be difficult or impossible to interpret. Many assignment schemes that appear random to the inexperienced investigator turn out to have hidden flaws. For example, on one occasion, researchers at a hospital compared two treatments for a particular disease. Patients who were admitted on even-numbered days received one treatment, and those admitted on odd-numbered days received the other. That assignment sounds random enough, but it failed. The number of patients admitted with the disease on even days gradually became larger than the number admitted on odd days. Why? What happened is that some of the physicians figured out the scheme and made it a point to admit their patients on days when the procedure they preferred was in use. A bias such as this makes it possible for the patients admitted on even and odd days to be quite different. You cannot rely on the results of a study that used nonrandom assignment.