Introduction to Research Design and Statistics

Between vs Within Subjects

Between-Subjects Designs

In behavioral and education research, subjects may be randomly sampled from some population and randomly assigned to one of two or more groups (control, treatment level 1, treatment level 2, etc.). A comparison of the groups tells us about the effects of the treatments. These treatment level effects represent differences between subjects.

In between-subjects designs, responses from a given subject appear in only one group.

The variability of scores within each group reflects individual differences and is accounted for by the chance elements in sampling. This sampling variability is thus due to chance.

The variability of means between groups reflects both individual (chance) differences and differences due to the treatment.

Consider the following experiment:

Sources of Variability

  • Variability within group one is due to sampling variability -- chance.
  • Variability within group two is due to sampling variability -- chance.
  • Variability between groups is due to a combination of sampling variability and treatment effect -- chance + treatment.

    Within-Subjects Designs

    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:

  • The same subject is observed in all treatment conditions.
  • The same subject is observed before and after a treatment.
  • Observations on subjects are not independent.
  • Subjects are matched on on one or more variables and then randomly assigned to treatments.

    Within-Subjects Example

    Subject IDPre-testPost-testFollow upmeans
    1Y11Y21Y31mean1
    2Y12Y22Y32mean2
    3Y13Y23Y33mean3
    ...Y1...Y2...Y3...mean...
    n-1Y1n-1Y2n-1Y3n-1meann-1
    nY1nY2nY3nmeann
    meansmean Y1mean Y2mean Y3

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    Phil Ender, 14Nov00