# Ruling out Chance as an Explanation (2 of 5)

Or, it could be that, by chance, more pleasant things happened to the experimental group than to the control group over the 12 weeks of the experiment. The way this problem is approached statistically is to calculate how often one would get a difference as large or larger than the one obtained in the experiment if the experimental treatment really had no effect (and thus the differences were due to chance). If a difference as large or larger than the one obtained in the experiment could be expected to occur by chance relatively frequently, say, one out of every four times, then chance would remain a viable explanation of the effect. If such a difference would only occur by chance very rarely, then chance would not be a viable explanation.

Returning to the study on the effectiveness of the antidepressant, recall that the experimental group differed from the control group by 6 - 4 = 2 units on the depression scale. For the sake of argument, assume that if there were no true difference between means, the sampling distribution of the difference between means would be as shown on the next page.