PhD Statistics Help - Comparing Two or more kinds of treatment with the control group (no treatment)

Using more than two groups in an experiment also allows researchers to determine whether each treatment is more or less effective than no treatment (the control group).To illustrate this, imagine that we are interested in the effects of aerobic exercises on anxiety. We hypothesize that the more aerobic activity one engages in, the more anxiety will be reduced. We use a control group that does not engage in 50 minutes per day of aerobic activity- a simple two-group design. Assume, however, that when using the design, we find that both those in the control group and those in the experimental group have high levels of anxiety at the end of the study-not what we expected to find. How can design with more than two groups provide more information? Suppose we add another group to the study-a moderate aerobic activity group (25 minutes per day)- and get the following results:

Control Group                                    High anxiety 

Moderate Aerobic activity                  Low anxiety

High aerobic activity                          High anxiety  

Based on these data, we have a V-shaped function. Up to a certain point, aerobic activity reduces anxiety. However, when the aerobic activity exceeds at a certain level, anxiety increases again. If we had conducted the original study with only two groups, we would have missed this relationship and erroneous concluded but there was no relationship between aerobic activity and anxiety. Using a design with multiple groups allows us to see more of the relationship between the variables. It also shows the other two groups comparisons control compared to moderate aerobic activity and moderate aerobic activity compared to aerobic activity.  

Comparing only the control to the high aerobic activity group would have led us to conclude that aerobic activity does not affect anxiety. Comparing only the control and the moderate aerobic activity group and high aerobic activity group would have led to the conclusion that increasing aerobic activity increases anxiety.

Being able to assess the relationship between the variables means that we can determine the type of relationship that exists. In the preceding example, the variables produced a V-shape function. Other variables may be related in a straight linear manner or in an alternative curvilinear manner (for example, a J-shaped or S-shaped function).In summary, adding levels to the independent variable allows us to determine more accurately the type of relationship that exists between the variables. 

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