Graziano & Raulin
Research Methods (9th edition)
Assignment of Participants
to Conditions
The random assignment of participants to conditions is the single best way to protect internal validity and therefore is critical in any experiment. The assignment can be done with a Table of Random Numbers, such as the table that appears in Appendix B, or with a Random Number Generator Program. We have included instructions on how to use a Random Number Generator Program in another section (Instructions for the Random Number Table Use).
Types of Random Assignment
We distinguish between free random assignment and matched random assignment. In free random assignment, all participants are assigned to the groups without regard to the assignments of other participants (i.e., the assignment of one participant has no effect on the assignment of other participants). In matched random assignment, participants are matched in sets prior to the beginning of the study. The set size is equal to the number of groups. Members of the sets are randomly assigned to each of the groups so that there is one member in each group from each set. This distinction is described in Chapter 9 in more detail.
We also distinguish between complete random assignment to conditions or assignment to conditions in blocks. When we carry out complete random assignment, each participant is assigned to a group, and no effort is made to restrict the number of participants assigned to each group. In assignment to conditions in blocks, a group of participants (usually equal in size to the number of conditions, but sometimes to a multiple of the number of conditions) is assigned so that there is an equal number of participants in each condition. For example, if we had four conditions, we would assign the first four participants so that there was one participants in each condition BEFORE we went on to assign the next four participants. Assigning participants in blocks assures that there will be approximately the same number of participants in each condition. If we are doing matched random assignment, we MUST assign participants in blocks.
Using the Random Number Table
To use the Random Number Table in Appendix B to assign subjects to groups, you must first randomly identify a starting place in the table. Note that the lines of the table are numbered from 1 to 200. You can select a number from 1 to 200 as a starting point, perhaps by closing your eyes and randomly pointing to a part of the random number table itself.
Once you have selected a starting point, the procedure will vary slightly depending on whether you are assigning participants in blocks or not. Let's assume that you are to assign 20 participants to 5 conditions and you intend to use a complete random assignment. You would then move from your starting point and list, in the order that they appear, all numbers between 1 and 5 until you have a total of 20 numbers. Then the first participant will be assigned to the condition indicated by the first random number, the second to the condition indicated by the second random number, and so on until all 20 participants have been assigned.
In contrast, if you are assigning participants in blocks, you would do the same thing except that you would list numbers that do not repeat numbers in the block until the block is full and then you would go on to the next block. To illustrate this process, we have produced a few lines of random numbers below.
23 12550 73742 11100 02040 12860 74697 96644 89439 28707 25815 24 63606 49329 16505 34484 40219 52563 43651 77082 07207 31790 25 61196 90446 26457 47774 51924 33729 65394 59593 42582 60527 26 15474 45266 95270 79953 59367 83848 82396 10118 33211 59466 27 94557 28573 67897 54387 54622 44431 91190 42592 92927 45973
If we wanted to assign 20 participants to 5 conditions with a complete free assignment procedure, the order of our assignment if we start on line 00023 would be 1, 2, 5, 5, 3, 4, 2, 1, 1, 1, 2, 4, 1, 2, 4, 4, 4, 4, 3, 2. We ignore any number other than 1 through 5.
Note that in this case we have 5 participants in Group 1, 5 in Group 2, 2 in Group 3, 6 in Group 4, and 2 in Group 5, which is probably not what we were hoping for. When you have relatively few participants to be assigned it it best NOT to use complete random assignment because your groups may well be uneven like this.
If we were to assign participants in blocks, we would make sure that each group received one participant before we started the next block. Again, if we started from line 00023, our order of assignment in blocks would be 1, 2, 5, 3, 4; 1, 2, 4, 3, 5; 1; 5; 3, 4, 2; 1, 5, 3, 4, 2; 1, 5, 2, 3, 4. Of course, when assigning in blocks, the groups are guaranteed to be very close to the same size if not exactly the same size.
As mentioned above, matched random assignment is essentially assignment in blocks, where the participants in the block have been matched on appropriate variables before the assignment process takes place.
Using the Random Number Generator Program
The procedures for using the random number generator program to assign subjects to groups is spelled out elsewhere on this site. We will not duplicate those instructions here.