5.1 UNDERSTANDING RANDOM SELECTION

There are approximately 2000 school psychologists in Australia. A researcher has developed a new diagnostic tool to identify conduct disorder in children and wants to study ways to train school psychologists to administer the tool. How can she recruit a random sample of 30 school psychologists to participate in her study?

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She could use an online random numbers generator to randomly select a sample of 30 school psychologists for this study from among the target population of 2000 Australian school psychologists. Let’s try it. (You can search for “random numbers generator” on the Internet to find one.) To do so, she would tell the random numbers generator to produce one set of 30 numbers between 0001 and 2000. She would specify that she wants unique numbers, because no school psychologist can be in the study more than once. She can ask the program to sort the numbers, if she wishes, to more easily identify the participants who will comprise her sample. When we generated a set of 30 random numbers, we got the following:

Of course, each time we generate a list of random numbers, the list is different. Notice that the typical list of randomly generated numbers does not necessarily appear random. For example, in this list only 7 out of the 30 numbers are over 1000. There are also several cases in which numbers are close in value (e.g., 920 and 924).

5.2 USING RANDOM ASSIGNMENT

Imagine that the researcher described in How It Works 5.1 has developed two training modules. One is implemented in a classroom setting and requires that school psychologists travel to participate in in-person training. The other is a more cost-effective Web-based training module. She will administer a test to participants after they have received the training to determine how much they learned. How can she randomly assign half of the participants to classroom training and half to Web-based training?

In this case, the independent variable is type of training with two levels: classroom training and Web-based training. The dependent variable is amount of learning as determined by a test. This study is an experiment because participants are randomly assigned to conditions. To determine the condition to which each participant will be assigned, she could use a random numbers generator to produce one set of 30 numbers between 0 and 1. Those assigned to group 0 would receive in-person training and those assigned to group 1 would receive Web-based training. She would not want the numbers to be unique because she wants more than one of each type. She would not want the numbers to be sorted because the order of the numbers matters.

When we used an online random numbers generator, we got the following set of 30 numbers:

Based on these random numbers, the first two participants would be in group 1, and would receive Web-based training. The next four would be in group 0, and receive ­in-person training. And so on. This set contains 13 ones and 17 zeros. If we wanted exactly 15 in each group, we could stop assigning people to the 0 condition when we reached 15 zeros. Everyone else would then be assigned to the 1 condition.

5.3 CALCULATING PROBABILITY

Let’s say that a university provides every student with a laptop computer, but students complain that their computers “always” crash when they are on the Internet and have at least three other applications open. One student thought this was an exaggeration and decided to calculate the probability that the campus computers would crash under these circumstances. How could he do this?

He could start by randomly selecting 100 different students to participate in his study. On the 100 students’ computers, he could open three applications, go online, and record whether each computer crashed.

In this case, the trials would be the 100 instances (one trial on each of the 100 different laptops) in which the student opened three programs and then went online. The outcome would be whether or not the computer crashed. A success in this case would be a computer that crashed, and let’s say that happened 55 times. (You might not consider a crashed computer a success, but in probability theory, a success refers to the outcome for which we want to determine the probability.) He could then take the number of successes (55) and divide by the number of trials:

55/100 = 0.55

So the probability of a computer crashing when three programs are open and the student goes online is 0.55. Of course, to determine the true expected relative-frequency probability, he’d have to conduct many, many more trials.