a_value

Returns the trace of the variance-covariance matrix of the
 estimators of the \(v_1 v_2\) elementary test-versus-control contrasts
 \(\tau_i - \tau_j\) (\(i\) a test treatment, \(j\) a control treatment),
 that is, the sum of their variances. When the information matrix is completely
 symmetric within the test set and within the control set (which holds for the
 A-optimal members of the catalogue) the value is computed in closed form from
 the canonical quantities \(f_1, f_2, f_4, f_5\) (the average diagonal and
 off-diagonal entries of the test-test and control-control sub-matrices of
 \(C\)). This reproduces the values reported in the design catalogues of
 Vinayaka et al. (2026); see also Hedayat and Majumdar (1984) and Stufken
 (1988).

Construction and evaluation of nested partially balanced bipartite block (NPBBB) designs for comparing a set of test treatments with a set of control treatments under a nested (blocks within blocks) structure. Six systematic construction methods are provided: composing partially balanced bipartite block designs with nested balanced incomplete block designs; augmenting nested partially balanced incomplete block designs with controls; merging rows of group-divisible nested designs; direct construction from group-divisible schemes; and expansion of partially balanced incomplete block designs (Vinayaka et al. 2026: In press). The A-efficiencies of the block and sub-block classifications are computed against the A-optimal completely symmetric reference design, following the test-versus-control optimality framework of Gupta and Parsad (1996) <doi:10.1080/03610929608831743> and Vinayaka et al. (2024) <doi:10.1080/03610926.2023.2251623>. These designs are particularly suited to agricultural, animal husbandry, industrial, and clinical trials involving multiple standard checks under nested experimental conditions, such as multi-environment trials where field heterogeneity (blocks) and within-field variation (sub-blocks) must be controlled simultaneously.

Vinayaka 

NPBBBdesigns

Construction and a-Efficiency of Nested Partially Balanced
Bipartite Block Designs

Rajender Parsad

B.N. Mandal

L.N. Vinaykumar

Gopalareddy Krishnappa

a_value function

<dl><dt>design</dt>
<dd>A matrix (or data frame) whose rows are the blocks or sub-blocks
and whose entries are the treatment labels. Test treatments must be labelled
<code>1, ..., v1</code> and control treatments <code>v1 + 1, ..., v1 + v2</code>.</dd>
<dt>v1</dt>
<dd>Number of test treatments.</dd>
<dt>v2</dt>
<dd>Number of control treatments.</dd></dl>

Arguments

A-Value of an NPBBB Design for Test-Versus-Control Contrasts — a_value

<dl>

<dt>design</dt>
<dd>A matrix (or data frame) whose rows are the blocks or sub-blocks
and whose entries are the treatment labels. Test treatments must be labelled
<code>1, ..., v1</code> and control treatments <code>v1 + 1, ..., v1 + v2</code>.</dd>


<dt>v1</dt>
<dd>Number of test treatments.</dd>


<dt>v2</dt>
<dd>Number of control treatments.</dd>

</dl>

a_value: A-Value of an NPBBB Design for Test-Versus-Control Contrasts

Description

Usage

Value

Arguments

References

Examples