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Conflicts between optimality criteria for block designs with low replication

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If you have a question about this talk, please contact Richard Samworth.

In designing experiments, we usually seek to make variances of estimators small. For incomplete-block designs, various ways of measuring multi-dimensional variance give the A-, D-, and E-optimality criteria, which I shall explain. If there exists a balanced incomplete-block design for the given parameters, then it is optimal on all these criteria. It is therefore natural to use the proxy criteria of (almost) equal replication and (almost) equal concurrences when choosing a block design.

However, work over the last decade for block size 2 has shown that when the number of blocks is near the lower limit for estimability of all treatment contrasts then the D-criterion favours very different designs from the A- and E-criteria. In fact, the A- and E-optimal designs are far from equi-replicate and are amongst the worst on the D-criterion.

I shall report on current work which extends these results to all block sizes. Thus the problem is not blocks of size 2; it is low replication.

This talk is part of the Statistics series.

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