**Speaker**: Rosemary Anne Bailey, University of St Andrews

**Date**: Thu, Nov 16, 2017

**Time**: 17:20 - 18:20

**Venue**: Middle Meeting Room

**Title**: Relations among partitions (II): Adjusting for one partition

**Abstract**:

Two partitions with $n$ and $m$ parts respectively define an $n \times m$ incidence matrix between the two partitions.

I will give a few examples to show the statistical background, to motivate the idea of projecting onto the orthogonal complement of the subspace defined by a partition, which is known as adjusting for that partition. From this point of view, the usual notion of balance (in incomplete block designs) is just a adjusted uniformity. I will say a little about balanced block designs.

Similarly, two partitions have adjusted orthogonality with respect to a third partition if adjusting for the third partition makes something defined by the first two really zero. Ordinary orthogonality can be recast in this light. Adjusted orthogonality can also be defined in terms of matrices, or, more combinatorially, by counting various things.

**Slides**:
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