The key concept of a "Randomized" experimental design is to have the experimenter assign various treatments to the experimental units is a random fashion. Thus, the treatments are "spread" over the experimental units without grouping them or considering some special characteristic of the experimental units. Randomized experiments tend to be free from biases and confounding effects. However, they are not always practical.

In a laboratory setting, an experimenter may wish to investigate the effect that three different drugs have on cultures of bacteria. The cultures, all coming from the same source, are grown in different, isolated, and numbered Petri dishes. The dishes are stored 24 to a tray. The trays are stacked 8 trays to a rack. For a randomized experimental design the experimenter would take each dish in turn and randomly assign and administer a treatment drug to that Petri dish, which would then be returned to its spot on the tray and the tray, once completed, would be returned to its spot on the rack. We can see that by using this approach even if there were some difference in Petri dishes and even if there were some effect caused by the location of a dish on a tray and even if there were some effect caused by the location of a tray on a rack, the randomizing of the assigned drugs should cause all such differences to balance out over all the treatments.

You might notice that the approach described here could mean that there is an inequality of the number of Petri dishes receiving each of the different drugs. Assuming a large number of dishes the expectation is that such a difference in the number of dishes in each group would be minor. However, in many cases, experimenters will get around this inequality. For example, an experimenter with 900 dishes could start with a list of 900 numbers made up of 300 1's, 300 2's, and 300 3's. The experimenter could then randomly shuffle the list. At that point the experimenter has a list of 900 randomly arranged 1's, 2's, and 3's. Then, using that list the experimenter would assign treatments 1, 2, or 3 to the successive Petri dishes. This would result in a randomized design but one with an equal number of Petri dishes in each treatment.

As a second example, let us say that an experimenter wanted to look at the possible benefit of using four different approaches to teaching a topic in a statistics class (perhaps comparing the use of a simple calculator, an advanced calculator, Excel on a computer, and a statistical program on a computer) This comparison is to be done on the 412 students taking the statistics course this term. A randomized design for this would be to assign one of the four treatments to the students in a random fashion. Doing so will tend to "cancel out" the effects of the different backgrounds that the students present at the start of the experiment. Again, as above, the experimenter could start with a list of all of the 412 students and just randomly assign a treatment to each student. Alternatively, the experimenter could start with the list of the students and then randomly shuffle that list. After such a shuffle, the first 103 students could be assigned to the "simple calculator" treatment, the next 103 students could be assigned to the "advanced calculator" treatment, and so on. Either way we would have randomized the assignment of treatment to student.

This second example demonstrates the impractical side of a randomized design in some cases. Students take the statistics course in groups, that is, they are in a section of the course. It would be impractical to break apart sections of the course into smaller units that we would then teach, isolated from the other groups, their assigned approach. Unlike the Petri dishes of the first example, we do not have the luxury of assigning students to take their place in a specified "tray" in a "specified" rack. If we keep students in their course sections then we might assign, in some random fashion, different treatments to different sections. However, this would not be an example of a completely "Randomized" design. On the other hand, since we have many sections of the statistics course, we might shit our focus from the student as the experimental unit to the section of the course as the experimental unit. In that case assigning in a random fashion one of the four treatments to the sections would be a completely randomized design. Our elation at seeing this needs to be tempered by a number of facts.

1. Although there are many sections, there are not that many. Thus, our number of experimental units is relatively small, namely 15. This in turn means that we have just a few experimental units in each treatment.
2. We should have no expectation that the sections attract similar students. After all, day students may be different from evening students; face to face students may be different from on-line students; two-day a week students may be different from three-day a week studetnts, etc.
3. We should have no expectation that the different treatments will be presented in the same way. After allo, there are many different instructors and they each bring a different teaching style to the section or sections that they teach.