PBIBD-package {PBIBD}

Partially Balanced Incomplete Block Designs

Description

The PBIB designs are important type of incomplete block designs having wide area of their applications for example in agricultural experiments, in plant breeding, in sample surveys etc. This package constructs various series of PBIB designs and assists in checking all the necessary conditions of PBIB designs and the association scheme on which these designs are based on. It also assists in calculating the efficiencies of PBIB designs with any number of associate classes. The package also constructs Youden-m square designs which are Row-Column designs for the two-way elimination of heterogeneity. The incomplete columns of these Youden-m square designs constitute PBIB designs. With the present functionality, the package will be of immense importance for the researchers as it will help them to construct PBIB designs, to check if their PBIB designs and association scheme satisfy various necessary conditions for the existence, to calculate the efficiencies of PBIB designs based on any association scheme and to construct Youden-m square designs for the two-way elimination of heterogeneity.

Details

The DESCRIPTION file:

Package:	PBIBD
Type:	Package
Title:	Partially Balanced Incomplete Block Designs
Version:	1.3
Date:	2017-12-20
Author:	Parneet Kaur <[e-mail]>, Kush Sharma <[e-mail]>, Davinder Kumar Garg <[e-mail]>
Maintainer:	Kush Sharma <[e-mail]>
Description:	The PBIB designs are important type of incomplete block designs having wide area of their applications for example in agricultural experiments, in plant breeding, in sample surveys etc. This package constructs various series of PBIB designs and assists in checking all the necessary conditions of PBIB designs and the association scheme on which these designs are based on. It also assists in calculating the efficiencies of PBIB designs with any number of associate classes. The package also constructs Youden-m square designs which are Row-Column designs for the two-way elimination of heterogeneity. The incomplete columns of these Youden-m square designs constitute PBIB designs. With the present functionality, the package will be of immense importance for the researchers as it will help them to construct PBIB designs, to check if their PBIB designs and association scheme satisfy various necessary conditions for the existence, to calculate the efficiencies of PBIB designs based on any association scheme and to construct Youden-m square designs for the two-way elimination of heterogeneity. R. C. Bose and K. R. Nair (1939) <http://www.jstor.org/stable/40383923>.
License:	GPL (>=2)

Index of help topics:

PBIBD-package           Partially Balanced Incomplete Block Designs
apbibd                  Calculates the efficiencies of PBIB designs
                        with any number of associate classes.
circulant               This function generates circulant matrix of
                        order n.
series1                 This function constructs five-associate class
                        PBIB designs.
series2                 This function constructs five-associate class
                        PBIB designs
series3                 This function constructs five-associate class
                        PBIB designs
series4                 This function constructs three-associate class
                        PBIB designs.
series5                 This function constructs three-associate class
                        PBIB designs.
series6                 This function constructs three-associate class
                        PBIB designs.
verify                  Verifies all the necessary conditions for the
                        existence of PBIB designs based on any
                        association scheme.
ym1                     The function constructs Youden-m square
                        designs. The function provides the parameters
                        of the PBIB design constituted when the
                        incomplete columns of this Youden-m square are
                        taken as blocks.
ym2                     The function constructs Youden-m square
                        designs. The function provides the parameters
                        of the PBIB design constituted when the
                        incomplete columns of this Youden-m square are
                        taken as blocks.
ym3                     The function constructs Youden-m square
                        designs. The function provides the parameters
                        of the PBIB design constituted when the
                        incomplete columns of this Youden-m square are
                        taken as blocks.

Note

This package is currently under intensive development and changes are to be expected in the near future.

Author(s)

Parneet Kaur <[e-mail]>

Kush Sharma <[e-mail]>

Davinder Kumar Garg <[e-mail]>

Maintainer: Kush Sharma <[e-mail]>

References

Dey, A. (1986). Theory of block designs.Wiley Eastern Limited, New Delhi

Garg, D.K., and Singh, G.P. (2015). General solution of normal equations in the intra-block analysis of PBIB designs with any (m>=2) number of associate classes. American Journal of Sustainable Cities and Society, 4(11), 196-202

Kaur, P. and Garg, D. K. (2016). Construction of some higher associate class PBIB designs using symmetrically repeated differences, Arya Bhatta Journal of Mathematics and Informatics, 8(2), 65-78.

Rao, C. R. (1947b). General methods of analysis for incomplete block designs, J. Amer. Statist. Assoc. 42, 541-561

Sharma, K. and Garg, D. K. (2017) Construction of Three associate PBIB designs using some sets of initial blocks. International Journal of Agricultural and Statistical Sciences (IJASS), 13(1): 55-60

Sharma, K. and Garg, D. K. (2017). m-associate PBIB designs using Youden-m Squares. Communications in Statistics-Theory and Methods, In press. DOI: 10.1080/03610926.2017.1324990