permutation approach for adjusted durbin rank test used in balanced incomplete block designs for tied data

Permutation approach for adjusted Durbin rank test used in balanced incomplete block designs for tied data

Durbin's rank test is widely used for testing treatment effects in Balanced Incomplete Block Designs (BIBDs) which have wide applications in sensory analysis. This test is failed for BIBDs when ties data occur. An adjusted version of Durbin rank test for this kind of data is given to solve this problem. Chi-square approximation, which is commonly used for this test, is not adequate for small BI...

Splitting balanced incomplete block designs

Robustness of Nested Balanced Incomplete Block Designs Against Missing Data

Robustness aspects of nested balanced incomplete block designs against missing data have been investigated using connectedness and efficiency criteria. Sufficient condition for robustness of a design has been obtained for the loss of any m observations, using connectedness criterion. Designs robust against the loss of any m observations belonging to one sub-block, loss of any two observations b...

Remarks on Balanced Incomplete Block Designs

Proof. Assume the hypothesis and the falsity of either conclusion. Construct matrix A of 2x + 2 rows and 4x+4 columns, with entries + 1 and — 1. The first column contains exclusively +1, and the second column — 1. Set up one-to-one correspondences between rows of A and elements of D ; between columns other than the first two of A and blocks of D. Enter +1 if the element is contained in the bloc...

Finding Balanced Incomplete Block Designs with Metaheuristics

This paper deals with the generation of balanced incomplete block designs (BIBD), a hard constrained combinatorial problem with multiple applications. This problem is here formulated as a combinatorial optimization problem (COP) whose solutions are binary matrices. Two different neighborhood structures are defined, based on bit-flipping and position-swapping. These are used within three metaheu...

Beautifully Ordered Balanced Incomplete Block Designs

Beautifully Ordered Balanced Incomplete Block Designs, BOBIBD(v, k, λ, k1, λ1), are defined and the proof is given to show that necessary conditions are sufficient for the existence of BOBIBD with block size k=3 and k1=2 and for k=4 and k1=2 except possibly for eleven exceptions. Existence of BOBIBDs with block size k=4 and k1=3 is demonstrated for all but one infinite family and the non-existe...