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What does the term "repeated measures" mean in the context of ANOVA?

I understand the distinction between within-subjects test and between-subjects test, but am not familiar with the term "repeated" in the following context: "ANOVA: Repeated Measures - between factors" and "ANOVA: Repeated Measures - within factors" (in G-Power 3).

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    $\begingroup$ I am not sure if this question is duplicated. The link provided did not answer my above question. I am confused with the word "repeated", hence the reason I am posing this question. I tend to confuse "within" with "repeated". Any clarification would be useful. Thanks $\endgroup$ – user39531 Feb 27 '14 at 23:15
  • $\begingroup$ @whuber I agree with user39531, this is not a duplicate. However user39531, could you make your question clearer ? You have already been more precise in your comment. $\endgroup$ – Stéphane Laurent Feb 27 '14 at 23:39
  • $\begingroup$ Thank you @Stéphane. It sounds like the question asks to distinguish "between factors" and "within factors," which indeed is no duplicate. $\endgroup$ – whuber Feb 28 '14 at 0:31
  • $\begingroup$ I re-state my question: What does "Repeated" mean in the context of ANOVA? I totally understand the distinction between within-subjects test and in-between subjects test, but not familiar with the wording "repeated" in the following:- "ANOVA:Repeated Measures - between factors" and "ANOVA: Repeated Measures - within factors." $\endgroup$ – user39531 Feb 28 '14 at 2:23
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    $\begingroup$ Dear user39531, you asked 21 questions on this site and got for 16 at least one answer. But your vote count shows only ONE up vote and nothing else. Moreover, no answer has ever been accepted by you. Accepted answers and up votes are, however, sort of the daily meal for people offering their time in order to help people which only contribute by questions - people like you. Please appreciate answers with votes, accept them and make us smile. $\endgroup$ – random_guy Jan 10 '15 at 19:08
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Repeated measures means exactly the same thing as within subjects: it means that the same subjects were measured in several different conditions. In ANOVA terminology, these conditions form a repeated measures factor, or equivalently a within subjects factor. See wikipedia.

What I guess confused you is that in a repeated measures experiment one can still have between-subjects factors! For example, you can measure all subjects in several conditions (within-subject factor), but have several distinct groups of subjects (e.g. patients/controls, or males/females) -- this will be your between-subject factor.

I made a quick google search, and e.g. here all of that seems to be explained pretty clear, with a nice example.

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    $\begingroup$ You could argue that it's possible to have repeated measures without having within subjects. E.g. if your subjects were idential twins, you might put one in condition A and one in condition B. It would be repeated measures, but not WS. (But it's pretty unusual.) $\endgroup$ – Jeremy Miles Feb 28 '14 at 21:01
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    $\begingroup$ @JeremyMiles: Good point. Basically it is a full analogy to the paired t-test (which is actually a simplest case of repeated measures ANOVA). $\endgroup$ – amoeba says Reinstate Monica Feb 28 '14 at 23:06
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It seems to me that there are two types of repeated measures ANOVA. The first deals with repeats such as within subject measurements where there can be some dependency between the before and after measurements or the twins comparison mentioned by Jeremy Miles in his comment on amoeba's answer. That type of repeated measures ANOVA is analogous to a paired t-test. Graphpad Prism uses what seems to me to be a 2-way ANOVA for such circumstances and calls is a repeated measures ANOVA.

The second type of repeated measures are where measurements are made repeatedly over time within a subject and there can be expected to be serial correlations such that the time 1 measurement is closely related to time 2 and less closely related to time 3. That results in the variance of the difference between time 1 and time 2 being less than the variance of the difference between time 1 and time 3 but similar to the variance of the difference between time 2 and time 3. That type of condition is usually described as a violation of the assumption of 'sphericity' (whatever that might be!). This type of repeated measures is often dealt with by a 'Greenhouse-Geisser' correction.

The stats guide at Graphpad is a pretty good place to begin: http://www.graphpad.com/guides/prism/6/statistics/index.htm?stat_sphericity_and_compound_symmet.htm

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I think there is a distinction between the "ANOVA: Repeated Measures - between factors" and "ANOVA: Repeated Measures - within factors" as pointed out by Michael Lew. To clear the doubt, just imagine two hypothetical experiments in which the effect of the application of two brands of cosmetics on each arm of a patient is studied. In the first one two brands are applied simultaneously so that the patient receives either "A" or "B" brand on each of his arms. But in the second experiment, the first brand is applied, the measurements were taken, then the second brand is applied.

For the first experiment, the environmental conditions that both the tested brands receive are the same. But in the second case (first brand followed by the second one), it is different.

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