Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Decomposition tables for experiments I. A chain of randomizations   One aspect of evaluating the design for an experiment is the discovery of the
relationships between subspaces of the data space. Initially we establish the
notation and methods for evaluating an experiment with a single randomization.
Starting with two structures, or orthogonal decompositions of the data space,
we describe how to combine them to form the overall decomposition for a
single-randomization experiment that is ``structure balanced.'' The
relationships between the two structures are characterized using efficiency
factors. The decomposition is encapsulated in a decomposition table. Then, for
experiments that involve multiple randomizations forming a chain, we take
several structures that pairwise are structure balanced and combine them to
establish the form of the orthogonal decomposition for the experiment. In
particular, it is proven that the properties of the design for such an
experiment are derived in a straightforward manner from those of the individual
designs. We show how to formulate an extended decomposition table giving the
sources of variation, their relationships and their degrees of freedom, so that
competing designs can be evaluated.

1
The categories of this paper are: cs
29
The categories of this paper are: funct-an
33
The categories of this paper are: plasm-ph
27
The categories of this paper are: comp-gas
7
The categories of this paper are: hep-th
9
The categories of this paper are: nlin
20
The categories of this paper are: acc-phys
17
The categories of this paper are: q-fin
13
The categories of this paper are: quant-ph
14
The categories of this paper are: math-ph
37
The categories of this paper are: supr-con
36
The categories of this paper are: cmp-lg
3
The categories of this paper are: physics
23
The categories of this paper are: solv-int
28
The categories of this paper are: alg-geom
22
The categories of this paper are: chao-dyn