Abstract.
Draper and Guttman (1997) shows that for basic 2k−p designs, p≥0, k − p replicates of blocks designs of size two are needed to estimate all the usual (estimable) effects. In this work, we provide an algebraic formal proof for the two-level blocks designs results and present results applicable to the general case; that is, for the case of s k factorial (p=0) or s k−p fractional factorial (p >0) designs in s b blocks, where 0<b<k− p, at least replicates are needed to clear up all possible effects. Through the theoretical development presented in this work, it can provide a clearer view on why those results would hold. We will also discuss the estimation equations given in Draper and Guttman (1997).
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Research supported in part by the National Science Council of Taiwan, R.O.C., Grant No. NSC 89-2118-M110-010.
Acknowledgement. The authors would like to thank the referee for very helpful comments.
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Huang, MN., Wong, KF. sk−p Fractional factorial designs in sb blocks. Metrika 56, 163–170 (2002). https://doi.org/10.1007/s001840100170
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DOI: https://doi.org/10.1007/s001840100170