Final answer:
A posttest only nonequivalent groups design is used when it is not possible to randomly assign participants to groups and there is no control over the composition of the groups.
Step-by-step explanation:
A posttest only nonequivalent groups design is used when it is not possible to randomly assign participants to groups and there is no control over the composition of the groups. This design is often used in situations where it is ethically or practically impossible to have a control group that is identical to the test group except for one variable.
In this design, the control group and test group may have many differences between them, which can make it difficult to determine the true effect of the independent variable. However, by comparing the posttest scores of the two groups, some information can still be gained about the effectiveness of the treatment.