In a between-subjects design, a subject is observed in one and only one treatment combination. This is true for both completely randomized and completely randomized factorial designs. Often it is desirable and sometimes it is possible to observe one subject in more than one treatment condition. Designs with repeated observations on the same subject are called within-subjects designs.
Within-subjects designs are also appropriate for pretest-posttest type designs. With this design, subjects are observed prior to any treatment, then they receive a treatment, and finally they are observed at posttest. It is possible to extend this design to include a retention test at a later time. Designs of this type may also be called repeated-measures designs.
Within-subjects can also be used in certain situations that involve dependent observations. For example research involving husbands and wives, studies involving twins or regular siblings, or research using subjects matched on one or more variables.
In summary, within-subjects designs can be found in the following situations: