### Dr Janet Godolphin

## Academic and research departments

Department of Mathematics, Centre for Mathematical and Computational Biology.### Biography

I graduated with a BSc degree in Mathematics from Royal Holloway, University of London and gained a PhD in Statistics also from Royal Holloway. In 2003 I joined the Department of Mathematics at the University of Surrey. I spent a period of time seconded to the Office of the Dean of Students and am currently a Senior Lecturer in the Department of Mathematics.

### Research

### Research interests

My research interests are in the methodology of the statistical design and analysis of experiments. Experimental design is the process of determining the most appropriate use of resources, under a given set of circumstances, to obtain information to answer a set of experimental questions. My work combines theory and computation to solve problems typical in real experiments in engineering, agriculture and the pharmaceutical and manufacturing industries.

Current specific interests include:

- Planning an experiment which is robust against breakdown in the event of various patterns of observation loss, for a variety of design types;
- Construction of full and fractional factorial designs with single or double confounding, that is, with one or two forms of blocking, where main effects and selected interactions are required;
- Use of graph theory to obtain conditions on design properties and to inform and aid in design construction.

### My teaching

In 2018/19 I delivered the following modules and will be teaching the same modules in semester 1 of the 2019/20 academic year:

- MAT2002: General Linear Modules;
- MAT3021: Experimental Design.

### My publications

### Highlights

Godolphin JD (2018) Construction of Row-Column Factorial Designs, Journal of the Royal Statistical Society: Series B Wiley

Godolphin Janet (2017) Designs with Blocks of Size Two and Applications to Microarray Experiments, Annals of Statistics 46 (6A) pp. 2775-2805Institute of Mathematical Statistics (IMS)

Godolphin JD (2015) A Link between the E-value and the Robustness of Block Designs, Journal of the American Statistical Association Taylor and Francis

### Publications

experimental situations where observation loss is common, it is im-

portant for a design to be robust against breakdown. For designs

with one treatment factor and a single blocking factor, with blocks

of size two, conditions for connectivity and robustness are obtained

using combinatorial arguments and results from graph theory. Lower

bounds are given for the breakdown number in terms of design pa-

rameters. For designs with equal or near equal treatment replication,

the concepts of treatment and block partitions, and of linking blocks,

are used to obtain information on the number of blocks required to

guarantee various levels of robustness. The results provide guidance

for construction of designs with good robustness properties.

Robustness conditions are also established for row column designs

in which one of the blocking factors involves blocks of size two. Such

designs are particularly relevant for microarray experiments, where

the high risk of observation loss makes robustness important. Dis-

connectivity in row column designs can be classified as three types.

Techniques are given to assess design robustness according to each

type, leading to lower bounds for the breakdown number. Guidance

is given for robust design construction.

Cyclic designs and interwoven loop designs are shown to have good

robustness properties.

Balanced Incomplete Block Designs with two associate classes (PBIBD(2)s). New results

are obtained which add to the body of knowledge on PBIBD(2)s. In particular, using

an approach based on the E-value of a design, all PBIBD(2)s with triangular and Latin

square association schemes are established as having optimal block breakdown number.

Furthermore, for group divisible designs not covered by existing results in the literature,

a sufficient condition for optimal block breakdown number establishes that all members of

some design sub-classes have this property.

are investigated. The minimum number of replicates for estimation of all main effects

and two-factor interactions is established and a construction method is developed based

on replicate generators. Complete design classes are given in the minimum number of

replicates for p d 15. Designs in full replicates are used as root designs to obtain designs in

fractional 2p?r replicates, again to estimate main effects and two-factor interactions, and

designs are recommended for p = 4; . . . ; 15. Guidance is given on design construction when

only a subset of the interactions are of interest.

n factorials in row-column designs to estimate main effects

and two factor interactions is investigated. Single replicate constructions are given

which enable estimation of all main effects and maximise the number of estimable two factor

interactions. Constructions and guidance are given for multi-replicate designs in single

arrays and in multiple arrays. Consideration is given to constructions for 2

n?t

fractional

factorials.

design to be robust against breakdown. For incomplete block designs, with one treatment

factor and a single blocking factor, conditions for connectivity and robustness

are developed using the concepts of treatment and block partitions, and of linking

blocks. Lower bounds are given for the block breakdown number in terms of parameters

of the design and its support. The results provide guidance for construction of

designs with good robustness properties.