﻿ Assigning Participants Using the Random Number Program

Graziano & Raulin
Research Methods (8th 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 F, or with a Random Number Generator Program. We have included a Random Number Generator Program on this Student Resource Website, which will handle most assignment tasks easily.

### 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 D 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 70 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 70 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

To use the Random Number Generator Program, you must first copy it from the Student Resource Website to your hard drive. The program is called randnum.exe, which you can download to your computer by clicking on the link. To start the program, click on the program name from the Windows explorer as shown on this screen, which will open a window giving you this program introductory screen. Select option 2 for random assignment of participants to groups or conditions, which will give you this screen. If you want complete random assignment, select option 1. We recommend this option ONLY if you are assigning a large number of participants to conditions or will be willing to tolerate unequal numbers of participants in each condition. If you select option 1, you will get this screen. The program will then ask you how many conditions in the study and then how many participants in the study, as shown in this screen. In our example, we asked to have 70 participants assigned to 5 conditions. Hitting return provides this output, which is also written to a file named rand-out.txt on the same subdirectory as the randnum.exe file resides. This is the reason that the randnum.exe program must be copied onto you hard drive (to allow the program to write its output to this file).

It is possible to have complete random assignment to conditions and still guarantee equal cell sizes by adding the constraint of equal cell sizes after the random numbers are selected. For example, if you want to assign 70 subjects to 5 conditions, you might tell the program that you want to assign 100 or 120 participants to 5 conditions and then you stop assigning participants to a given condition as soon as the condition is full--in this case with 14 participants (70/5).

If you want to to assign participants to conditions in blocks, you select option 2 on the program introductory screen and option 2 on the assign subjects to conditions screen. Again the program will ask for the number of participants and the number of conditions, as shown on this screen. In our example, we again ask to have 70 participants assigned to 5 conditions, only this time the assignment will be within blocks. Hitting return will produce this output, which again is written to the file rand-out.txt. Note that the output has rows of five conditions and that each row has each condition appearing only once.

Option 2 (assignment within blocks) can also be used for matched random assignment and for random assignment of orders when using a within-subjects design. In matched random assignment, the order of assignment on any row of the output determines which matched participants get assigned to which conditions. When using this procedure for selecting random orders of conditions, one should input the number of conditions as usual, but instead of inputting the number of participants, one should input a number equal to the number of conditions times the number of participants. For example, if you wanted to assign 14 participants in a within-subjects conditions to 14 random orders of 5 conditions, tell the program that you have 5 conditions and 70 subjects and you will get 14 lines, each representing a random order of conditions.