Answer to Question 1
(a) Training of researchers typically involves group designs, the dominant approach in psychology, so researchers are often untrained in the potential utility of single-case research.
(b) Much single-case research is qualitative in nature. Most researchers are more comfortable with quantitative research.
(c) Researchers often have qualms about low levels of internal and external validity because of their lack of understanding of single-case designs.
(d) Researchers tend to believe that single-case designs are inherently more subjective than group designs, even though this isn't always the case.
Answer to Question 2
Measured variables are associated with quasi-experiments and ex post facto studies. Manipulated variables are associated with true experiments. If you want to make statements about causation, you need true experiments with manipulated variables that lend themselves to random assignment of participants to groups. Thus, it is important to know what kind of variable you are working with.
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The family described in Example Case 4