A Note on Balanced Designs

V. R. Rao

doi:10.1214/aoms/1177706729

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Home > Journals > Ann. Math. Statist. > Volume 29 > Issue 1 > Article

March, 1958 A Note on Balanced Designs

V. R. Rao

Ann. Math. Statist. 29(1): 290-294 (March, 1958). DOI: 10.1214/aoms/1177706729

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Abstract

It is proved that a necessary and sufficient condition for a general design to be balanced is that the matrix of the adjusted normal equations for the estimates of treatment effects has $v - 1$ equal latent roots other than zero.