## 4.2 Random assignment and experimental variation

Group comparisons are at the heart of many interesting questions addressed by psychologists, physicians, scientists, teachers, and engineers. Questions about group differences are often studied through scientific experiments.

### 4.2.1 Comparing study designs

When considering a scientific experiment to examine group differences, the design of the study plays a very important role. To help understand this, think about a researcher who is studying the efficacy of a new cold medication. Let’s say that the researcher has 100 people (each with a cold) who volunteer to be a part of her study. Let’s consider how she might design her study.

**Design 1:**She gives the cold medicine to all 100 volunteers.**Design 2:**She gives the cold medicine to the first 50 volunteers (treatment group) and a placebo to the other 50 volunteers (control group). (A*placebo*is a treatment that looks like the experimental treatment, but which has no medical value)**Design 3:**She randomly picks 50 of the volunteers to whom she gives the cold medicine (treatment group), and she gives a placebo to the other 50 volunteers (control group).

All three designs have been used, and are still used, in research studies. There are pros and cons to each of the designs, and all are useful depending on what you want to know.

In Design 1, it is hard to judge the efficacy of the medication. For example, what if 60 of the volunteers had no cold symptoms after four days? Did the medication work? You might be thinking, “what would have happened if they hadn’t received any medication?” That is a great question. In this design, we don’t know.

Design 2 gives the researcher a comparison group. She can compare the number of volunteers in each group who have no cold symptoms after four days. This is a better design than Design 1 for examining efficacy. But, what if she found that after four days, 35 of the volunteers who got the medication had no symptoms, while only 25 of the volunteers who didn’t receive medication had no symptoms. Is this enough evidence for her to say the cold medication is effective? Probably not. Maybe most of the volunteers in the treatment group were already in later stages of their colds. Maybe they had more robust immune systems to begin with (e.g., due to differing exercise or nutrition habits) than the control group. You can imagine many such reasons that the treatment group would show quicker improvement than the control group. The point is that because the groups were chosen based on particular criteria (in this case, whether they registered early or late), there may be *systematic* differences between the groups.

Design 3 has the same comparison group advantage as Design 2. The big difference, however, is that the volunteers were put into the groups at random. By assigning participants at random, the researcher makes it so that the groups are not systematically different. In fact, because there is regularity in randomness, we can say that the research “equalizes” the groups. What this means is that the groups have, *on average*, the SAME nutritional habits, the SAME exercise habits, and the SAME everything-else. That means that the only *systematic* thing that is different between the two groups is that the treatment group got the cold medication and the control group didn’t. At the same time, the researcher has introduced a new form of variability into the world: *experimental variation*.

### 4.2.2 Experimental Variation

Let’s say our hypothetical researcher used a strong design in which she randomly assigned her volunteers to treatment and control groups. After four days she found that the treatment group had 70% volunteers with no symptoms, and the control group had 54% of volunteers with no symptoms. Could she conclude that the cold medication is effective since more volunteers had no symptoms in the treatment group?

Actually no. And, the reason is because of *experimental variation.* Remember, the groups were randomly assigned. This means that the groups might be different *due to random chance.* Consider the situation where the treatment has absolutely NO EFFECT. In other words, it does nothing. Under that assumption, the treatment and the control groups should improve at about the same rate. Under the assumption of no treatment effect, differences between the treatment and control group are not a function of the cold medication. They are solely a function of random chance. Perhaps, just by chance, the treatment group has more people who would have naturally recovered than the control group.

Similar to the studies we looked at in Unit 2, we have to figure out how much chance variation is expected before we can say whether the difference of 16 percentage points in the recovery rate is actually an improvement. We can use Monte Carlo simulation to determine the expected variation due to random chance in the assignment to groups.

One key difference between this type of study and those in Unit 2 is that the chance variation arises from the assignment to groups in these studies, whereas in Unit 2, the chance variation arose because of sampling from a larger population. When the chance variation is due to the assignment of participants to groups, it is referred to as *experimental variation* (sometimes *randomization variation*).

⏯ You can learn more about experimental variation by watching this video

##### Key points

- Random assignment helps to “equalize” the compassion groups, because it ensures that there is no systematic reason why the groups should be different
- Random assignment introduces
*experimental variation*: an observed difference could be due to random chance in the assignment of participants to groups - We use Monte Carlo simulation to determine the expected amount of experimental variation, if the treatment has no effect.

##### Vocab

When the chance variation is due to the assignment of participants to groups, it is referred to as **experimental variation** (sometimes *randomization variation*)