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Optimal two treatment repeated measurement designs for three periods

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  • Miltiadis Chalikias
  • Stratis Kounias

Abstract

Repeated Measurement Designs, with two treatments, n (experimental) units and p periods are examined, the two treatments are denoted A and B. The model with independent observations within and between treatment sequences is used. Optimal designs are derived for: (i) the difference of direct treatment effects and the difference of residual effects, (ii) the difference of direct treatment effects, and (iii) the difference of residual effects. We prove that for three periods when n is odd the optimal design in the three cases (i), (ii), and (iii) is determined by taking the sequences BAA and ABB in numbers differing by one. If n is even, the optimal design in cases (i), (ii), and (iii) is again the same, by taking the sequences ABB and BAA in equal numbers. In case (i), for n even or odd, in the optimal design there is no correlation between the two estimated parameters. For n even, case (i) was solved by Cheng and Wu in 1980. The above imply that with two treatments in practice are preferable to use three periods instead of two.

Suggested Citation

  • Miltiadis Chalikias & Stratis Kounias, 2017. "Optimal two treatment repeated measurement designs for three periods," Communications in Statistics - Theory and Methods, Taylor & Francis Journals, vol. 46(1), pages 200-209, January.
    • Handle: RePEc:taf:lstaxx:v:46:y:2017:i:1:p:200-209
    DOI: 10.1080/03610926.2014.988264
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    Cited by:

    1. Miltiadis S. Chalikias, 2023. "Optimal Designs for Direct Effects: The Case of Two Treatments and Five Periods," Mathematics, MDPI, vol. 11(24), pages 1-12, December.
    2. Miltiadis S. Chalikias, 2019. "Optimal Designs for Carry Over Effects the Case of Two Treatment and Four Periods," Mathematics, MDPI, vol. 7(12), pages 1-10, December.
    3. Miltiadis S. Chalikias, 2019. "Optimal Repeated Measurements for Two Treatment Designs with Dependent Observations: The Case of Compound Symmetry," Mathematics, MDPI, vol. 7(4), pages 1-6, April.

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