| Abstract: | Block designs with nested rows and columns were introduced in Srivastava (1978
Srivastava , J. N. ( 1978 ). Statistical design of agricultural experiments . J. Ind. Soc. Agric. Statist. 30 : 1 – 10 . Google Scholar]) and more specifically defined in Singh and Dey (1979
Singh , M. ,
Dey , A. ( 1979 ). Block designs with nested rows and columns . Biometrika 66 ( 2 ): 321 – 326 .Crossref], Web of Science ®] , Google Scholar]). We present properties of some partially balanced block designs with nested rows and columns. The designs are considered for near-factorial experiments, when there are a levels of experimental factor A and b levels of experimental factor B and there is one control treatment added. In this article we extend the theory of block designs with nested rows and columns described by \L acka and Koz?owska (2009
?acka , A. ,
Koz?owska , M. ( 2009 ). Planning of factorial experiments in a block design with nested rows and columns for environmental research . Environmetrics 20 ( 6 ): 730 – 742 .Crossref], Web of Science ®] , Google Scholar]) and Koz?owska et al. (2011
Koz?owska , M. ,
?acka , A. ,
Krawczyk , R. ,
Koz?owski , R. J. ( 2011 ). Some block designs with nested rows and columns for research on pesticide dose limitation . Environmetrics 22 ( 6 ): 781 – 788 .Crossref], Web of Science ®] , Google Scholar]). We carry out our consideration by the derived mixed linear model resulting from randomization of blocks, rows and columns. For this model of observations, some properties of estimation of treatment contrasts are discussed. We calculate the efficiency factors of estimation of treatment contrasts. We formulate theorems for some partially balanced block designs with nested rows and columns. Plant protection experiment on limitation of food acceptability for T. urticae is given to show how the obtained results can be applied. |
