Characterizing experimental designs by properties of the standard quadratic forms of observations

Volume 34 / 2007

Czesław St/epniak Applicationes Mathematicae 34 (2007), 39-45 MSC: Primary 05B06, 62K10; Secondary 51E05, 15A27. DOI: 10.4064/am34-1-4


For any orthogonal multi-way classification, the sums of squares appearing in the analysis of variance may be expressed by the standard quadratic forms involving only squares of the marginal and total sums of observations. In this case the forms are independent and nonnegative definite. We characterize all two-way classifications preserving these properties for some and for all of the standard quadratic forms.


  • Czesław St/epniakInstitute of Mathematics
    University of Rzeszów
    Al. Rejtana 16A
    35-959 Rzeszów, Poland
    Statistics and Econometrics Unit
    Maria Curie-Sk/lodowska University
    Pl. Marii Curie-Sk/lodowskiej 5
    20-031 Lublin, Poland

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