Donald Arthur Preece: A life in statistics, mathematics and music

Donald Arth ur P ree ce: A life in statistics, mathematics and m usic R. A. Bailey , Sc ho ol of Mathemati cs and Statistics, Universit y of St And r ews, St Andr ews, Fi fe KY16 9SS, Unit ed Kingdo m, and Scho ol o f Mat hemati cal Sciences (emeri ta) , Queen Ma ry Un i v er sity of London, Mile E n d Roa d, London E1 4NS, Unit ed King dom Donald Arth ur Preece died on 6 Ja nuary 2014, aged 74. He is surviv ed b y his b ro ther Robert. 1 Edin burg h and S t Andrew s Donald w as born in Edin burgh on 2 Octob er 1939 . His father, Isaac Arthur Preece, w as a lecturer (later the holder o f the ﬁrst c hair) in Brewing and In- dustrial F ermen tations at Heriot–W att College, whic h w as to b ecome Heriot– W att Univ ersity . His mother, Dorothy Maud, n ´ ee Banner, play ed violin (as a non- professional) in the Reid Symphon y Orche stra, whic h w a s conducted b y Donald T ov ey . F rom 1945 to 1958 Donald a ttended Georg e Heriot’s Sc ho ol in Edin burgh, where he w on medals in b oth Mathematics and F renc h in 195 6. He w alk ed to sc ho ol, and nev er forgot the day when the Clean Air Act came in to force: for the ﬁrst time, he could see the sea on his daily walk. He also learn t to pla y the cello, piano and orga n. He w as a cellist in the Na t io nal Y outh Orches tr a of G reat Brita in under the baton of Malcolm Arnold during 1957– 1958 and b ecame an Asso ciate of the Roy al College o f Organists in 1958. A t the end of sc ho o l he had to mak e a choice b et w een his tw o b elo ved sub jects—mathematics and m usic. He decided that he w o uld nev er b e quite go o d enough to mak e a decen t living as a p erforming m usician, and so studied 1 Mathematics at St Andrews Unive rsity from 1958 to 1 962, o btaining medals in b o th Pure Mathematics and Applied Mathematics. Ian Anderson star t ed his degree in Mathematics at St Andrews in 1960. He sta y ed in St Regulus Hall, the same r esidence as Donald, who oﬀered to b e his ‘senior man’ (men tor). Ian still has the Latin receipt that Donald gav e him for a p ound of raisins on Raisin Monday . Donald w as part of a cello quartet at St Andrews. He w as also a co- founder of the unive rsity Madrigal G r o up, whic h he directed from 1960 to 1962. Just as the tug betw een m usic and mathematics nev er left him, so to o his later life sho ws that he w as pulled b etw een statistics, sp eciﬁcally the design of agricultural experimen ts, and combinatorics, speciﬁcally deﬁning and constructing new ﬁnite com binator ia l ob jects. In reality , t hese tw o ﬁelds are not so far apart: f o r example, La t in squares o ccur in b oth. 2 Cam bridge and Roth amsted After graduating from St Andrews, he sp en t a y ear at St Catha r ine’s College, Cam bridge. He pla y ed in the univ ersity orc hestra and obtained Cam bridge Univ ersit y’s Diploma in Mathematical Statistics. One of his lecturers, Dav id Kendall, encouraged him to seek employ ment in the Statistics Department at Ro thamsted Exp erimen ta l Stat io n in Harp enden. After remark ably little formal pro cedure, he to ok up his ﬁrst job there, as a Scien tiﬁc Oﬃcer, in 1963. A t that time Rothamsted w as o ne of a b out fo r t y rese a r c h stations run b y the Agricultural Researc h Council (AR C): it sp ecialized in ag r icultural ﬁeld trials. Colleagues in the departmen t at the time included H. D esmond P atterson, John Gow er and Gavin Ross. He a lso got to kno w George Dyk e, who w o r ked in the Field Exp eriments Section. He k ept in to uc h with all of these un til the end (George Dyk e died in 2012, and Desmond Patterson in 2013). F rank Y ates was the head of the Statistics D epartmen t then. F or the rest of his life, Dona ld r ega led colleagues with stories of FY, a s he w as kno wn. He passed on FY’s m a xim of “one new idea per pap er”; rep o r t ed that FY claimed to read no pap ers written b y an y o ne other than R. A. Fisher or himself; and retold FY’s story that the “ob vious” idea for balanced incomplete-blo c k designs came to him while he w as in the bath. T o researc hers used t o a univ ersit y en vironmen t, it is almost unbeliev able that scien tists at Rot hamsted could not submit a pap er to a journal without ﬁrst giving copies to bo th the head of departmen t and the director of the 2 whole of Rothamsted, and obtaining written approv al from b oth. In the 1980s, I had to obtain such approv al from John Nelder and Sir Leslie F owden for pap ers on group theory or com binatorial intricacy as w ell as for those more directly connected with agricultural r esearch. According to Dona ld, FY w ould nev er appro ve of any pap er con taining matrices: he dislik ed them, and could not see the need for them. Ho w eve r, Jo hn Gow er rep orts a less extreme view: although FY himself knew nothing ab out matrices, John and Mic hael Healy used them extensiv ely without disapprov al. It was typic al for Rothamsted statisticians in the 1960s to publish pa- p ers in B iometrics , Biom e trika a nd Journal o f the R oyal Statistic al So ciety, Series B . In 1 966 Do nald published pap ers [1, 2, 4] in all three of these, as w ell as one [3] in T e chnometrics . In their diﬀeren t w a ys, all four of these pap ers were ab out a topic tha t w ould remain central t o Dona ld’s researc h: designs for exp erimen ts in rectangular lay outs, and the consequen t need to explore prop erties of relat io nships b et we en factors, suc h as ro ws, columns and v arious treatment factors. Rothamsted Manor House had b een the home of John Bennet La w es, who founded Rothamsted Exp erimental Station in 1843. It w as b ough t by the Law es Agricultural T rust in 1934, and later b ecame eﬀectiv ely a hall of residence for Rothamsted staﬀ and their scien tiﬁc visitors. Dona ld and others no w set up the Rothamsted Manor Recitals, whic h contin ue to this day . The m usicians at the earliest recitals w ere all Rothamsted scien tists, including Donald himself. T o matc h the am bience of the Great D ra wing Ro o m, where the recitals w ere held, Donald thought that male mem b ers o f t he audience should wear suits, but few obliged him. 3 Univ ersity of Ken t Donald was promoted to Senior Scien tiﬁc Oﬃcer in 19 68. How ev er, thing s at Rothamsted w ere changing. F rank Y ates retired in 19 6 8, and Desmond P atterson had mo v ed to the AR C’s Unit of Statistics (ARCU S) in Edin burgh in 1 967. Donald was already in touch with S. Cliﬀord P earce and Geoﬀ(rey) F reeman a t East Malling Researc h Station in Ken t, whic h w as also run by the AR C and conducted r esearch o n fruit trees. In 1969 Donald b ecame a Lecturer in Statistics in the Mathematical Institute o f the Univ ersit y of Ken t at Canterbury , whic h w as in easy reac h of East Malling. In 1972 this univ ersit y a w ar ded him a PhD in Sta tistics for published w orks, and also promoted him to Senior Lecturer. He was in terim head of Sta tistics fo r six mon ths in 197 3 . Donald lectured on a range of statistical topics, including ‘D esign and 3 analysis of experiments ’. One of his earliest undergraduate studen ts, Miriam Lewis, recalls that he enliv ened his teac hing by including ﬁeld trips to East Malling and Rothamsted. Of course, he did not give up mu sic. He w as conductor of the univ ersit y’s Madrigal So ciet y during 1977 –1978. A t Can terbury , Donald collabo rated with Cliﬀord P earce, publish ing a pap er [18] with him and J. R. Kerr in 197 3 on designs f o r three-dimensional exp eriments. This is the ﬁrst of four w ays of g eneralizing a rectangular lay out b y including a no ther factor. He a lso maintained con tacts with Ro t ha msted, publishing a pap er [16] with John Gow er in 19 72 in the Journal of Combi- natorial The ory, Series A . P erhaps this is when Donald b egan to mo ve tow ards com binat o rics. The British Com binatorial Conference (BCC ) b ega n in 1969, and is no w held ev ery t w o y ears. Attendanc e at the ﬁrst three w as b y in vitation only , but the 1973 conference, in Ab eryst wyth in July , w as o p en to all, and D o nald attended. He gav e a talk ab out his curren t researc h on a problem in v o lving four factors with sp eciﬁed relationships. The only concise w ay to describ e these relationships is to use ma t r ices. This ta lk struc k a c hord with Pete r Cameron, who ha d not met Donald b efore. On the conference outing, Pe ter delib erately sat next to Donald on the bus, and ask ed him for more infor- mation. There w ere problems of translation: Donald talk ed a b out factors on a set o f exp erimen tal units, but P eter thoug h t ab out the incide nce b e- t w een the lev els of eac h pair of factors, with no concept of an underlying set; D onald used lo wer-case letters for matrices whereas P eter thought that ev ery one used upp er- case letters. Ho we ver, they established that Do na ld’s problem w as related to something that P eter w as thinking ab out in g roup theory . After some more work on b oth sides, this led to a jo in t pa p er [22] in Utilitas Mathematic a in 19 7 5. Thirty y ears later, P eter published further w ork [O1 9 ] on this, and said in the corresp onding talk at the 2001 BCC that it w as only then that he really understo o d what Donald had b een sa ying o n the bus. 4 Australia F rom Septem b er 1974 to August 1975 D onald to ok sabbatical lea v e from the Univ ersit y of Ken t to w ork in Australia, ﬁrst in the Departmen t of Mathe- matical Statistics at the Univ ersit y of Sydney , then in the D ivision of Mathe- matics and Statistics of CSIRO (the Commonw ealth Scientiﬁc and Industrial Researc h Orga nisatio n) in Adelaide, South Australia , where R. A. Fisher had sp en t the la st ﬁv e ye a r s of his life and John Nelder had sp en t 1965–196 6 . Here 4 he w orked with W. Bruce Hall, who sp ecialized in cyclic designs, whic h are made b y dev eloping one or more initia l arra ys using the integers mo dulo n . Tw o pap ers [20, 21] in the A ustr alian Journal of Statistics follo we d. A t this time, statisticians in Adelaide were v ery receptiv e to the ideas b eing put forward b y Alan Ja mes and Graham Wilkinson [O4, O 7 ], using matrix algebra to explain the relatio nships b et wee n facto r s. O f course, this c himed with one of Donald’s ma jor interes t s, and he wrote a pap er [26] on non-ort ho gonal Graeco-Latin designs, whic h he presen ted at the F ourth Australian Conference on Comb ina t o rial Mathematics, whic h to ok place in Adelaide in August 1 975. Earlier, Cliﬀord P earce and his colleagues had deﬁned designs according to the pa ir wise relatio nships among the factors: a pair ma y b e orthogona l to each other; one ma y b e nested in the other; one ma y be balanced with resp ect t o the other; and so on [O3, O5]. No w Donald ma de it absolutely plain that if there are t hree or more factors whose relationships are neither orthogo nalit y no r nesting then the pairwise rela- tionships are not enough t o give t he prop erties of the whole design. Decades later, I appreciated the clarity of this insigh t [O18, O20]. Donald liv ed in St Mark’s college in Adelaide. He found that the noisy p ossums disturb ed his sleep, so he used wax ear-plugs. These melted in his ears, causing him considerable problems. John Gow er w as also based tempor arily at CSIRO in Adelaide. One w eek end, he and his family to ok D onald for a trip o n a housebo at o n the Murra y Riv er. They had a little dingh y to go b etw een the shore and the houseb oat. Donald decided to clean this up, but while doing so he threw a w ay the cork bung. F oun tains of w ater shot up, while John rushed to get his camera. 5 Edin burg h again Bac k in t he UK by the end of 1975, D o nald paid his usual Christmas visit to his mother in Edin burgh (his father had died in August 19 6 4). As usual on these visits, he called in on ARCUS in early Janu a ry to see Desmond P atterson. Here he found me, in the ﬁrst mon th of my Science Researc h Council p ost-do ctoral researc h fellows hip to w or k on problems of restricted randomization, oﬃcially under the supervision of Professor Da vid Finney but in practice under D esmond’s g uida nce. Donald p osed us a problem tha t he had b een t hinking ab out in Australia : if last y ear’s exp eriment on fruit trees used a Latin square, and t he same trees are to b e used for this y ear’s exp eriment, but there may b e some residual eﬀects of last y ear’s treatmen ts, ho w should this year’s exp erimen t b e designed and randomized? 5 Donald, Desmond and I met fo r sev eral hours eac h da y to w ork on this problem. Colleagues listened to us arguing ov er coﬀee in the common ro om, at lunc h in the staﬀ club, or ov er a b eer. W e obtained go o d results, whic h w ere published [33] in the Au str alian Journal of Statistics in 1978. Through- out the discussions , I w as in aw e of the o ther t wo: I could do the necessary p erm utatio n group theory , but I did not ev en know tha t the w ord bias had a precise tec hnical meaning. A t the end of Dona ld’s visit, I w as astonished when he presen ted us b oth with copies of a libretto he had written for an op eretta called When shal l we thr e e me et again? The reference to the Scottish play w as not lost on us. Desmond w as correctly cast as basso profundo, and Donald as tenor. The only mistak e was to p ortray me as soprano altissima: Do nald w as not to kno w tha t I w ould go on to sing second alto , or ev en ﬁrst tenor, with the Edinb urg h Univ ersit y Renaissance Singers. The text w a s a fairly close tak e-oﬀ of our actual discussions, gen tly p oking fun a t a ll three o f us, but most esp ecially at Do nald himself. 6 Rothamsted again In 1978 Donald returned to Rothamsted Exp erimen tal Station, this time as Principal Scien tiﬁc Oﬃcer and Biometrics Liaison Oﬃcer (Field Crops) of the Minis try of Overs eas Deve lo pment, later the Ov erseas Dev elopment Administration ( O D A). He headed a group of three t o four statisticians. His w ork included visits to the W est Indies, South America, T anzania, Sudan and Syria, and the British Council sp onsored a six-w eek visit to the Univ ersit y of Ife in Nigeria. Donald’s w ork for ODA did not prev en t him in teracting with other Rot- hamsted statisticians. He w as pa rticularly go o d at n urturing y ounger col- leagues without patro nizing them. F or example, he had already done some w ork himself on iden tiﬁcation key s: no w he encouraged Roger P a yne to get in v olved, and this led to a jo in t paper [41] read to the Ro y al Statistical So ciet y (RSS) in Marc h 1980. I joined the Statistics Departmen t at Rothamsted a t the start of 1981. I particularly remem b er t w o things that Donald taugh t me. One w as what he called “sniﬃng ov er data”: befo r e you ana lyse the data, cast y our ey e o ver it for anomalies, so that y ou can ask the scien tist to explain these while there is still a c hance that he migh t remem b er the reason. Why is that n umber double all the rest? Wh y did the last ten plots t o b e ha r ves ted pro duce suc h lo w yields? Do es that pattern of ﬁnal digits indicate that the data w ere recorded by v arious diﬀeren t p eople? See [42]. 6 The second thing that D onald taught me was ho w to read publishe rs’ pro ofs. He would ho ld the publishe r’s v ersion and read it out, in his im- maculate clear enunc ia t io n, while I listened a nd matched it to the original v ersion in front of me. Both of us would use rulers or cards or fore-ﬁngers to k eep our attention on one line of text a t a time. One o f the go o d things ab out ha ving statisticians in a group, as opp osed to b eing lo cated one p er other departmen t, is that y ou can pic k eac h others’ brains o ver relev an t t opics: a statistical problem in one area of application ma y already hav e been solv ed in another. Unfortunately , at this time in Rothamsted there was an unsp ok en rule that statisticians should not talk ab out statistics at coﬀee time or t ea time. Rumour had it that one y oung statistician had once displa ye d ignorance and that the then head of depart- men t, John Nelder, had put him do wn so sharply (probably in tending to denigrate t he ignorance rather than the p erson) that ev ery one decided to a void this dang er in f uture. Donald’s solution w as to in tro duce what he called “topic sessions”. Ev ery so often the coﬀee break w as turned into a teac hing session led by him on a single straightforw ard topic, suc h as missing data. These w ere alw ay s follo we d b y ha ndout s consisting of four sides of A4 pap er cov ered with t yp escript. One particularly am using topic w as ab out Bortk ewitsc h’s hor se-kick data. Donald show ed the original data, classiﬁed by Prussian corps. Deaths fro m horse-kic ks were not constan t across corps: those in the Catering corps suf- fered relativ ely few. With his t ypical insistence on precise language, Donald complained ab out those who said that the data w ere ab out Prussian oﬃ- cers ( Herr en ) when it was actually the fo ot-soldiers ( He er en ) that died, the oﬃcers being safely on horsebac k. In his usual generous w ay , he inv olved col- leagues Ga vin Ro ss and Simon Kirb y as co-authors of the ensuing pap er [74]. Donald and I often talk ed to each other ab out researc h during these y ears. He would sa y “I’v e though t of this new concept: should w e call it a genus or a sp e cies ?” I would r eply “It do esn’t matter. W e’re mathematicians. W e can call it an ything w e like so long as we giv e a clear deﬁnition of the meaning.” Donald disagreed on tw o coun ts. First, he t hough t t ha t a n y one should b e able to see the pattern in a collection of examples, so that there was no need for a formal deﬁnition. Secondly , he though t that the name should help the reader. More than that, it seemed that helpful terminology was crucial to his own abilit y t o think further ab out the sub ject. One day , he solve d a long-standing puzzle of his. He managed to arrang e a normal pack o f pla ying cards into a 4 × 13 rectangle in suc h a w ay that eac h suit o ccurred once in eac h column; eac h rank ( 1 –10, Jac k, Queen a nd King) o ccurred once in eac h row ; eac h ro w had four cards of o ne suit and three of eac h of the others; and each pair of ra nks o ccurred together in precisely 7 one column: see [50 ]. He glued the cards in this arrangemen t onto a card- b oard bac king, framed this, and hu ng it up in the departmen t, in the Fisher building. I suggested that he should call this arrangemen t, and its general- ization to k × v rectangles, a double Y ouden r e ctangle . F or once, Donald w as deligh ted with m y terminology: he claimed t hat this name enabled him t o think clearly ab out the structure, and w en t on to write sev eral pap ers on the sub ject. Many y ears later, when the Fisher building w as closed, G a vin Ross rescued the framed design and returned it to Donald. During his second p erio d at Rothamsted, D onald con tinue d to main tain con tact with Cliﬀord P earce and Geoﬀ F reeman, particularly o v er designs for rectangular lay outs. The latter, who had now mo ved to the ARC’s Na- tional V egetable Researc h Station at W ellsb ourne, in W arwic kshire, wrote t w o pap ers [O 8 , O9] ab o ut quasi-complete Latin squares, whic h ha v e the neigh b our- balance prop ert y that eac h unordered pair of letters o ccurs as neigh b ours t wice in ro ws and t wice in columns. This inspired me to take the w ork f ur t her in [O10], and this in turn seems to ha v e inspired m uc h of Donald’s combinatorial w ork after 20 0 0. In another generalization of rectangular lay outs, eac h plot is divided in to subplots. Semi-Latin squares are suitable designs for suc h lay o uts. D o nald and Geoﬀ F reeman a lso published a pap er [5 3 ] on these, whic h I and m y studen ts drew on for later work. Ho w eve r, during t his p erio d Donald’s pap ers w ere less ab out new ideas. He wrote a series of what w ere essen tially literature reviews [20, 31, 38, 48]. With his liking for pr ecise terminology , he w as upset that diﬀ erent statisticians could use w ords lik e ortho go nal or b alanc e d to mean diﬀeren t things. He compiled a bibliography of randomization, and kep t it up to date, but neve r published it. He did publish exp ository articles [40, 42, 44, 65, 69] in the Statistician ab out simple parts of statistics and ho w to teac h them, as w ell as some r a n ts [47, 51, 58 , 64, 71] ab out statistical practice in the design of real exp erimen ts and the subsequen t data analysis. These ma y hav e b een motiv ated by p o or practice that he f o und in exp erimen tal stations on his o ve rseas trips or b y the struggles of his junior colleagues. John Nelder had established t he statistical programming language Gen- stat at Rothamsted. Donald so on learnt ho w to use it, and published a series of notes [57, 67, 68, 73, 96, 100, 106, 116] in the Genstat Newsletter a b out his fav o urite designs. 8 7 East Malling In 1975 Cliﬀord P earce retired from East Malling and b ecame Professor of Biometry at the Univ ersit y of Ken t. He w as succeede d b y Ken Martin. In 19 8 5, Donald to ok his p osition as Head of the Sta tistics Department at East Malling Researc h Station. Because of the natural rectangular la youts, designing exp erimen ts on orc ha r ds was very congenial to him. He also had a n excellen t junior colleague in Mart in Ridout. He mo v ed bac k to Ken t, and the Univ ersit y of Ken t made him a n honorary Reader in Agricultural Bio metrics in 1987 . A t East Malling, D o nald b ecame in volv ed with the Lunc heon Club. Al- though this w as tec hnically op en to all staﬀ, its mem b ers w ere almost entirely retired. He organized sev eral m usical ev en ts there, using the grand piano in Bradb ourne House. He f requen tly dres sed up in sp ecial costumes, a nd ex- p ected other p erformers to do lik ewise. Ev en a s a h umb le page-turner, Mart in had to wear fancy dress. Sadly , things did not w ork out professionally for D onald at East Malling as w ell as he had hop ed. Cliﬀord P earce had earn t enormous resp ect from his scien tiﬁc colleagues during his decades there. Donald had exp ected to w alk in to his sho es, and w as tak en aback to disco v er that he would ha v e to earn resp ect himself afresh. Moreo v er, the en vironmen t had c hanged in the ten y ears since Cliﬀord had left. The emphasis on ﬁeld experimen ts w as reduced, and D onald had to ov ersee the closing of the Records Oﬃce, whic h had previously k ept details of all tria ls ev er conducted there. Giv en his frequen t use of the ar chiv es while at R othamsted, this m ust hav e upset him. There w as a series of changes in the AR C, whic h renamed itself the Agriculture and F o o d Researc h Council (AFRC) in 198 3 and b ecame part o f the new Biotec hnolog y a nd Biological Sciences Researc h Council in 199 4. The AFR C merged its previously sep a rate researc h stations into ten institutes, and re-organized p ersonnel, partly under the common misapprehension that there w as less need for statisticians now that all scien tists had computers on their desks. In 199 0 Donald to ok redundancy from what w as now called the Institute of Horticultural Researc h at East Malling, as did man y colleagues. Martin Ridout sta ye d un til 2000 b efore joining the Univ ersit y of Ken t. Later, Donald w as to sa y that sev eral other redundan t scien t ists of his o wn ag e simply did not kno w what to do with themselv es. He described it as “enforced retirement”, and said tha t he neve r w an ted to b e retired ag ain. 9 8 Univ ersity of Ken t again F ortunately , the Univ ersit y o f Ken t oﬀered him a p osition, ﬁrst as a part-time lecturer, then (fr om 1 994) as a half-time Professor of Statistics. He threw his energies in to teac hing again, esp ecially pro ject studen ts. He encouraged junior colleagues, advising them that when they ﬁnished writing a pap er they should put it into a draw er for a while rather than submitting it immediately . He supervised his ﬁrst and only PhD studen t, Chris Christoﬁ, who completed his thesis [O11] in 1 9 93, a nd wen t on to publish tw o pap ers [O14, O17] o n t he topic. Donald b egan new collab orations in com binato rics with his colleague Barry V owden, with lo cal retiree David Rees, and with Pete r Ow ens at the Univ ersit y o f Surrey , who retired in 1 993 but remained active . Most exciting w as an unforeseen new collab oration that dev elop ed. In [O6], Jo hn Nelder ha d b een concerned with the problem of computing the matrix pro duct X X ⊤ when only k of the v rows of X could b e he ld in memory at any one time. He sough t a linearly ordered collection of b blo c ks of k ro w-nu mbers suc h that (i) eac h pair o ccurs in at least one blo ck and that (ii) eac h blo c k diﬀers fr o m it s predecess or in just one elemen t. D onald’s ﬁrst ov ertly com binatorial publication [16] was a step to w ards solving this problem, with the extra condition that (iii) the new elemen t in eac h blo c k do es not pro duce a ny pairs that ha v e o ccurred b efore. Robin Constable w as a com binator ia l statistician at the Unive rsity of St Andrews, who had visited East Malling during his statistical training in Ab erdeen. He had met Donald at the Ab eryst wyth meeting in 1973, and sta y ed in to uc h. He sp ent the ﬁrst t hree mon ths of 1978 on sabbatical lea v e at the Univ ersit y of Kent. He w ork ed with Do nald, ﬁnding some errors in [1 6] and disco vering more designs satisfying (i) –(iii), but nothing was published. In 19 92 D onald was an in vited speaker at the Carb ondale Com binato r ia l Conference at Southern Illinois Univ ersit y (SIU) and the fo llo wing meeting of the American Mathematical So ciet y at Day ton, Ohio. A t a part y in W al W allis’s house in Carb ondale, he met Guo-Hui (G ran t) Zhang, who ask ed him what he would speak ab out in Da yton. Donald told him ab out the w ork with Robin Constable, and w as astonished to ﬁnd that G ran t and W al had tw o pap ers [O1 2 , O13] in press on the same sub ject, ha ving b een p osed essen tially the same pro blem b y an elec trical engineer. They had deﬁned tigh t (for condition (iii)) single-c hange (condition ( ii) ) co vering (conditio n (i)) designs. This led to an exciting collab oration inv olving three further p eople from SIU. The story is told in [110]. Not only was this collab oration exciting in its o wn right. Donald w ent on to write sev eral further pap ers, on v arious topics, with his new collab orato rs. 10 Ho w eve r, Donald did not break his links with a g ricultural statistics. He to ok part in the Genstat conference held at Can terbury in July 1993 , where he and John Nelder play ed piano duets at the concert that he organized. In 1996 John Morgan, in the USA, published a join t pap er [O15] and a handb o o k c hapter [O16] ab out nested designs: blo c ks are divided into sub- blo c ks, a nd the prop erties of the design in whole blo c ks and the design in sub-blo c ks are b oth imp ortan t. Alternativ ely , in the third generalization of rectangular la y o ut s, t he blo c ks may b e rectangles, and the prop erties of the design in blo cks , in rows and in columns are all imp o rtan t. This reminded Donald of w ork [6] tha t he had published in Bi o metrika in 1967, as w ell as a pro ject that he was then undertaking with Da vid Rees, so he con tacted John, and t w o join t pap ers [1 30, 133] f ollo wed . Donald b ecame a regular attender at the BCC, where he ga ve himself the task of org anizing the concert and pla ying the piano fo r an y one who needed accompanimen t. A t short notice, the promised ven ue for the 1999 BCC w as withdra wn. Donald stepp ed in to the breac h, and oﬀered to host the 1999 BCC at the Univ ersit y of Ken t, b eing jo int lo cal organizer with his colleague John Lamb. This oﬀ er was accepted, and so Donald b ecame a mem b er of the British Com binatorial Committee f o r tw o y ears. Unfortunately , John Lamb b ecame seriously ill in early 19 99, and D onald had to do the lion’s share o f running a v ery succes sful conference. 9 Learned so cie ties Throughout these w orking y ears, D o nald was activ e in the International Bio- metric So ciet y (IBS), t he RSS, and other learned so cieties. He joined the British Region of the IBS. He w as elected a F ello w of the RSS in D ecem b er 1963, an Ordinary Mem b er of the In ternational Statistical Institute in 1977, and a F ello w of the Institute of Statisticians in 1982. He joined the Institute of Com binator ics and it s Applications in 1995 . In the R SS, he encouraged colleagues to attend read pap ers and contribute to the dis cussion. He w as a mem b er of the General Applications Section Committee, 1 9 70–1971 ; of the Journals Committee, 1975–1 978; of Council, 1976–198 0; of the Lo cal Groups Co ordinating Committee, 1978–1982 , b eing c hairman 1978–198 0 ; of Programme Committee, 19 78–1979 and 1993 – 1996; of the Researc h Section Committee, 1983–1986 ; of the Editorial Committee, 1993–199 5; and the Editor ia l P olicy Board, 1 996. In the British Region of the IBS he was k een on the sessions fo r y oung biometricians, and ma y ev en ha v e b een instrumen tal in setting them up. As a PhD studen t, Stev en Gilmour talked in one of these sessions in the y ear 11 1989–199 0. After the talk, Donald told him ab out Hadamard mat rices of order 16, and p osed some questions ab o ut their use fo r non-regular factorial designs. He attended some of the in ternat io nal conferences (IBCs) of the IBS. He to ok his mother to the one in Constanza, R omania in August 1974, where he b o ok ed separate ro o ms in the names of Mr and Mrs Preece. The hotel was short of ro oms, and thought that they ought to share. At the IBC in Guaruja, Br a zil in August 1979, the OD A insisted that he use a c heap er hotel t han the standar d one on oﬀer: Donald rep orted that he found himself in what was essen tially a brothel for gay seamen. He w a s a member of the Editorial Advisory Committee of the IBS, 19 85–1989 ; and t he British Region Committee, 198 7–1990. He serv ed as a member o f the Ov erseas Committee of the Institute of Statisticians, 1982 – 1984; and as a mem b er of Council of the Institute of Com binatorics and its Applications, 199 9 –2002. He also underto ok a wide r ange of editoria l responsibility . He w as British Regional editor of S tatistic al The ory and Metho d Abstr acts from 1966 to 1 9 74. He w as an asso ciate editor of Biometrics from 19 79 to 1989, and Abstracts editor f o r the Biom etric B ul letin from 1 988 to 1991. He w as a mem b er of the editorial b o ards of the Journal of A gricultur al S c ienc e from 1988 to 1 9 94, and of Utilitas Mathematic a from 1 9 90 to 2000, then Mana g ing Editor from 2001 to 2005. Most imp ortantly , he w as j oin t editor of Applie d S tatistics fr o m 1993 to 1996, sharing the editorship ﬁrst with W o j t ek Krzanowsk i and then with Sue Lewis. W o j t ek had ov erlapp ed with him fo r a y ear at Rotha msted in 1968– 1969, where he had b eneﬁted from the help and resp ect tha t Donald alwa ys sho w ed to new comers. A published letter from the join t editors in 1994 reminded prospectiv e author s that it w as not enough for a new statistical metho d to be applicable in man y areas; t o b e suitable for publication in Applie d Statistics , a pap er m ust b e motiv ated b y a real application in a single ar ea. Altho ug h this letter had b een prompted by the large num b er of submitted pap ers con taining little evidence of an y practical application, it did seem a rather strange con trast to the dir ection o f Do na ld’s own researc h in terests at the t ime. When Sue Lewis replaced W o jt ek she b eneﬁted greatly from D onald’s kind advice and supp ort. He w as dev o ted to the journal, and ga v e a tremen- dous amount of his time to explaining to authors ho w their pap ers could b e impro v ed, or why t hey w ere b etter suited to other journals. In spite of this, Byron Morgan rep o rted that this w ork load did not seem to distress Donald at all. Donald strongly b eliev ed that the Summary at the start of eac h pap er should b e a statemen t of what the authors had found out, not merely of what they w ere inv estigating, and he campaig ned en th usiastically 12 for the summaries to match his view. Just as his mu sic had not b een abandoned, neither had his F renc h. He sp en t Jan ua r y 1973 as exc hang e professor at the Orsay campus o f the Uni- v ersit ´ e de P aris XI (Paris-Sud). It used to b e that F renc h and English w ere equally acceptable languag es to the IBS. In Septem b er 1982 the IBC w as held a t T oulo use, in F rance. Donald sp ok e on L a biom´ etrie: p as rites mais scienc e . In Septem b er 1991 he w as one of s eve ra l p eople giving half-da y sessions at the Europ ean Comm unity Adv anced Course in Statistics (D esign of Exp erimen ts) at S` e t e, in F rance. Sp eak ers had all b een ﬁrmly told that this w as an in ternational meeting and so they m ust sp eak in English. Ho w- ev er, Donald observ ed tha t most of the par ticipan ts w ere francophone, so he conducted his session in F renc h. Donald was a pianist and organist, and surely practised b efore giving p erformances. His lectures, whether in English or F renc h, also seemed lik e p olished p erformances. I was nev er sure whether he had learnt his script b y heart or had simply rehearsed giving the lecture. It is true that informal questions in the middle could sometimes throw him completely oﬀ track . 10 Queen Mary , Univ er sit y of London Donald’s mot her died in Septem b er 1997. That gav e him a certain amoun t of ﬁnancial indep endence, as w ell as p ersonal indep endence. He told Byron Morgan, who w as then head of the Institute of Mathematics and Statistics at the Univ ersit y of Ken t, that he w anted to resign his p osition on his 60th birthda y , in 1999, to give himself time to do the things that he really w a n ted to do. This was gra nted, a nd he w as made honorary Professor of Com bina- torial Mathematics. I had mov ed to the Univ ersit y of London in 1991, ﬁrst at Goldsmiths College, then at Queen Mary a nd W estﬁeld College, now called Queen Mary , Univ ersit y of London ( Q MUL). I had b een running w eekly seminars on De- sign of Experiments during that t ime, and Dona ld ha d attended those when his teac hing commitme nts allo wed. P eter Cameron ha d b een running the ﬂourishing Combinatorics Study G roup at QMUL sinc e 1986. I therefore p ersuaded QMUL to oﬀer D onald a professorial fello wship at QMUL from 2000. The salary w as derisory: the purp ose was m utual b eneﬁt to him and us fro m researc h in teraction. It seems appro priate to quote here part of the case that I made fo r his app ointme nt. “One of Preece’s strengths is as a collab o r a tor and inspire r. By asking awk ward questions, he goads other p eople into doing researc h. . . . He is also v ery go o d a t encouraging b oth PhD students and staﬀ to k eep 13 going on a piece of researc h that ha d a pp eared to b e stuc k, or to em bark on new pro j ects.” Donald accepted t he p osition at QMUL. He contin ued to live at his house near East Malling, and also maintained and used his mother’s old house in Edin burgh. He underto ok some teac hing a t the Univ ersit y of Ken t, especially the sup ervision of ﬁnal- y ear undergraduate pro jects. One of these led to a four-author pap er [16 9] in 201 1 . He also did a small a moun t of teac hing at QMUL: for example, eac h y ear he gav e t wo undergraduat e lecture s on the design of questionnaires. On the researc h f ron t, Dona ld really switc hed his base to QMUL, where he gradually mov ed himself from the Design of Exp erimen ts seminar to the Com binatorics Study Group, where he w as a regular sp eak er. He w ould talk ab out mathematics to any one who would listen, treating eve ryone as an equal. A t ypical reaction would b e “Donald has inv ented a new concept, giv en me sev entee n examples and a conjecture: no w m y jo b is to deﬁne the concept and pro ve the conjecture.” Just as at East Malling, Donald b ecame in v olve d in the QMUL Lunc heon Club. This surprised other QMUL staﬀ, b ecause, although the club is op en to all pa st and presen t staﬀ of all grades, most no n- retired staﬀ are either una w ar e that they may join it or b eliev e that they do not ha v e time to attend. Through the Luncheon Club he met p eople from sev eral diﬀerent departmen ts at QMUL. In particular, he made con tact with the p eople in c harge of the organ in the G reat Hall a nd w a s giv en p ermission to pla y it. What surprised p eople m uc h more was Dona ld’s decision to take up ro ck- clim bing. He j oined a club in Mile End P ark, and learn t to clim b on their clim bing w all. Thereafter, he w ould astound Byron Morgan with announce- men ts lik e “I shall tak e a small div ersion on m y w ay bac k from Edin burgh so that I can clim b up t he outside of suc h-and-suc h an industrial c himney .” Then he progr essed to abseiling down the outside of large buildings to ra ise money for c harity . He ev en star t ed to tak e up sky-diving, but had to stop all of this a ctivit y b ecause o f a detac hed retina. Nev ertheless, he neve r displa y ed an y sign of external frailt y , and he remained vigorous and upright. One strand of D onald’s researc h af t er 2 000 concerned neigh b our- balanced designs. He used the idea of a terr ac e that I had deﬁned while at Rothamsted. This is a ro w of diﬀeren t n umbers arra nged in a sp ecial w ay: what matters is whic h n um b er is next do or to whic h other num b er. This made me t hink of a terrace of houses: hence the name. Unfortunately , one of his ODA colleagues assumed that I meant designs suitable for use in experimen ts on terraces o n steep hillsides in Nepal. How ev er, b y 2000 D onald seemed happ y with the w ord, and pro duced a string of pap ers, some with my PhD student Matt Ollis, giving new constructions for terraces. T a lks and pap ers had attractive 14 titles like Dancing on R amsg ate sands . He also started a new fruitful collab oration on this with Ian Anderson of the Univ ersit y of G lasgo w. Ian and D onald had lost touch after St Andrews but met again at one of the BCCs. Ian w as approa ched b y his statistical colleague T om Aitc hison to construct a sc hedule for t r eatmen t of gro ups of patien ts whic h balanced consecutiv e pairs of treatmen ts in a particular w ay . Ian wrote a draft, and sen t it to Donald, asking if t he idea w as new. He replied that he thoug h t it w as, but suggested exp a nding it, and the result w as a joint pap er [137] on lo cally balanced ch a nge-o ver designs in Utilitas Mathematic a in 200 2 . This is y et another generalization of the r ectangula r la yout: patien ts are columns, p erio ds are row s, and the columns are clump ed in to groups. The balance on consecutiv e pairs of treatmen ts is akin to, but not the same as, the neigh b our-balance prop ert y of a quasi-complete Latin square. Th us b egan a study of terraces that lasted a decade and pro duced ov er a dozen jo int pap ers. The basic idea w as to construct terraces in the set o f in tegers mo dulo n by ﬁtting together sequenc es of p o we rs of certain integers in clev er w ays: they called these “p ow er sequences”. Do nald later suggested the most unlikely , but fruitful, strategy of using t he arithmetic mo dulo n to construct terraces for the in tegers mo dulo m where m = n + 1 o r n − 1 or n − 2. D onald could pro duce endless supplies of elegant examples, and it w as Ian’s ta sk to provide the n umber theory whic h formed their basis. Before this collab oration, Ian had w orked a lo t on whist tournaments . No w Do na ld realised that these formed examples of the nested designs that he also studied. When Donald learn t that Ian’s c hildren w ere m usically inclined, he sho w ed great interest, remem b ering the f a mily cham b er m usic sess ions of his c hild- ho o d. O n his Edinb urg h visits, he would go across to Glasgow to pla y cham- b er music with Ian’s c hildren. He passed on to them scores of v a r io us trios and quartets. Another long collab oration was with P eter Cameron. When the n um b er of treatmen ts is a prime p ow er, suc h as 4 or 13, there are often general con- structions that can b e made f r om a single star t ing array by using a primitiv e elemen t of t he ﬁnite ﬁeld o f that order. Things are more diﬃcult for com- p osite num b ers. In terminology from R. D. Carmichael [O1, O2], a prim itive lamb d a-r o ot mo dulo an in teger n is an elemen t of maximal order in the mu lt i- plicativ e group of units mo dulo n . No w the tric k w as to ﬁnd sev eral starting arra ys that could be expanded b y using a primitiv e lam b da- ro ot and then glued together. Donald w as an exp ert at ﬁnding suitable pieces to glue to- gether, while Pete r dev elop ed more general theory . T ogether they pro duced an ev er-growing series of lecture notes [176], to o long for a pap er, but to o 15 short for a b o ok. As Peter said, in these collab orations it w as as if Donald had climbed straigh t up the w all b y instinct, lea ving us to put in the pitons a nd mark the w a y so that others could follow . In 2004, Dona ld decided to arrang e a celebration for his 65 th birthday . It w a s held at QMUL in Nov ember. The forma l part consis ted of mus ic and mathematics, with Do nald con tributing to b o th. This w as fo llo we d b y a buﬀet supper and drinks, for mathematicians, mus icians and family . As part of the preparation for this ev ent, Donald managed to r e-establish contact with some family members whom he had not met for decades. Inte ra ction with them ga ve him m uc h pleasure in the following y ears. 11 Retiremen t In July 2008, Dona ld w as told that he w o uld hav e t o retire from QMUL. At that time, the oﬃcial retiremen t age was 65, whic h he had already pa ssed. He ask ed to defer retiremen t, and ev en expand his teaching, but this w a s not allo we d. Instead, he w as granted emeritus professorship in Septem b er 2008. The accompan ying letter stated that this w as “the last suc h title approv ed b y Prof essor Adrian Smith in his role as Principal of the college, whic h gav e great pleasure to b ot h AFMS and D AP .” Donald now had to v acate his oﬃce and mo v e to the ro om shared by emeritus staﬀ . Colle a gues we r e handed b o oks and reprin ts, some signed “D. A. Preece”, others signed “F. Y ates”. He con tin ued to come into QMUL t w o or three da ys p er w eek, but he b egan to hav e health problems a nd stays in hospital. He regaled colleagues with the details: w e did not mind; w e to ok the view that w e w ere his family and he needed to talk to someone. Sometimes he threatened t o die b efore the next wee k, but there w as alw ays a twink le in his ey e and so no one b eliev ed him. In Octob er 2009 he laid on another birthda y party at QMUL. A session on “Reminiscences and m usic” in the Octagon w as follo we d b y a buﬀet in the Senior Common R o om. He also mark ed his 70th birthda y with a special lecture on mathematics in literature at the Univ ersity of Ken t, follow ed by a piano recital. He rep eated the lecture at QMUL in 20 10, and turned the material into a pap er [172] published in 2012. In August 2010 Donald sen t an email en titled ‘triple Y ouden rectangles’ to six co-authors spread around the w o rld. It really shows his ongoing en thu- siasm and excitemen t ab out the mathematics, as w ell as his ty pical commen ts on health, so I quote it in full. Mirabile dictu, I seem to hav e found the tw o inﬁnite series 16 that I ha ve w an ted for suc h a long time. The ‘truc’ for forcing the construction to work in general (t he multiplication by 2 − 1 mo d k ) is so simple that I can only squirm in em barr a ssmen t that I didn’t sp ot it b efore. Ah, hindsigh t. . . ! The whole t hing will hav e to b e written up from scratc h, prob- ably with at least one of you helping me with pro ofs. In the mean time, I’v e merely revised the text that some o f y ou hav e seen befor e, and a .dvi cop y of it is attac hed. I fear that it mak es very hea vy reading, but I can see ho w to rewrite the thing in a wa y that will mak e for muc h easier understanding. T o ha ve ac hieve d this aft er so long is exc iting to the p oint that I b ecame worried ab out m y blo o d- pressure! How ev er, the readings tha t I to ok w ere ‘normal’, so it lo oks like I’ll surviv e this latest dev elopmen t. Awkw a r dly , this brings me to the end of the list of mathe- matical things that I said I wan t ed to see solve d “b efore I die”! But I’d b etter not sa y my Nunc Dimittis until I’v e written it up prop erly! (If I don’t surviv e that long, any of y ou should feel free to complete the task.) An y comments , thoughts, ideas on the w ork w ould of course b e very w elcome. My b est wishes to y o u all. Donald Preece Mir abile indeed, it was John Morgan who replied, ev en though it w as nearly a decade since they had la st w ork ed together. They started w ork on another joint pap er [177], this time on multi-la y ered Y ouden rectangles, ex- c hanging v ersions by email, and meeting during John’s 2011 visit to the UK. John w ould write a theorem or t w o ; Donald w ould resp ond that these w ere not quite co vering a ll that he thought should b e p ossible. With eac h itera- tion Donald w o uld explain more, un til ﬁnally John felt that he understo o d. Unfortunately , John b ecame b ogged dow n in univers ity administration, as so man y o f us do, and t he nearly-complete pap er w as unﬁnished at the time of Donald’s death. Only a few mon ths earlier he had sent an email including the w ords “I’d lik e it published in my lif etime, but if y ou eve r hear that I’m no longer around, do pro ceed with it without me.” In June 2011 Do nald ﬁnally gav e up all teac hing at the Univ ersit y of K ent. He comp osed an organ piece fo r t he mathematics graduation ceremonies held in Can terbury cathedral the follow ing mon th. It w as called A c ademi c fanfar e and verse , and was based on the studen t song b eginning “Gaudeamus ig itur, juv enes dum sum us”. 17 Donald then ga v e himself an inte resting new pro ject. He set himself the task of ﬁnding out ab out all of the pip e organs in the East End of London. He visited them; he pla ye d them; he talke d to vicars, organists and historians; he consulted arc hiv es. He put all of this know ledge in t o a b o ok en titled The Pip e-Or ga ns of L ondon ’s East End and its Pe ople ’ s Palac es , which he t yp eset himself in L A T E X: it w as publishe d b y QMUL in 2013. The b o ok [175] is selling w ell. It had a v ery nice review recen tly in the B ritish Journal of Or gan Studies , where he w as w armly we lcomed as a new author in the ﬁeld. Of course, one of the East End organs w as the Rutt organ in the G reat Hall of t he P eople’s P a lace a t QMUL, whic h had b egun its life bringing m usic to the lo cal p eople in the ﬁrst half of the tw en tieth cen tury . Do na ld w as afraid t hat this o r gan w ould b e destroy ed in the refurbishmen t of the Great Hall. He liaised with Philip Ogden, the Senior Advis er to Principal Simon Gask ell, previously Senior Vice-Princip a l with sp ecial resp onsibilit y for estate dev elopmen t and also acting Principal for the y ear 2008–2009. Through them, he p ersuaded QMUL to restore the organ. A concert w as held in the Great Hall in March 2013 to inaugurate the refurbished organ: Donald w as v ery pro ud not o nly to giv e a sp eec h at this but to hear the ﬁrst public p erformance of the piece Nostalgic interlude t ha t he ha d written esp ecially for this organ. The organist, Alan Wilson, told the audience that it featured “b eautiful undulating string sounds alongside solo ﬂutes”. Donald was one of the in vited sp eak ers at t he conference Co m binatorics, A lge b r a and Mor e held at QMUL in July 2 0 13 to celebrate P eter Cameron’s retiremen t. He w as on go o d form, liv ely and c heerful. His talk use d the tredoku puzzle fro m o ne of the daily newspap ers a nd turned it into a mathe- matical question. During another sp eak er’s later ta lk, whic h w a s admittedly rather opaque, I w as a m used to see that audience mem b ers who ha d giv en up attempting to follow it had instead started trying to w ork o n D onald’s question. Donald had a ches ty cough for most of 201 3. Although he complained ab out it, those of us who sa w him week ly did no t think that he w a s g etting an y w orse. In Nov ember he w as one of the inv it ed sp eak ers at the Old Co dge r’s combinatorics collo quium in Reading o rganized b y Anthon y Hilton. Some attenders rep o rted that he w as lo oking p o orly; Ian Anderson said that Donald said things lik e “ I do not think that I shall b e able to ﬁnish this piece of w ork, so some of y ou will hav e to do it.” Ho w ev er, he w as back on form in QMUL in D ecem b er, talking excitedly ab out more East End organs that he had disco v ered since ﬁnishing his b o ok, a nd passing on from Gavin Ross a jok ey v erse ab out R. A. Fisher written by his non-statistical colleagues at Rothamsted at Chris tmas 1919. His last comp osition w as an organ piece written fo r the QMUL gra duation ceremon y in Decem b er 20 13 in the Great 18 Hall. As usual, Donald sp ent the Christmas/New Y ear p erio d at t he house in Edin burgh. While t here, he w a s tak en to the W estern General Hospital with a viral infection. He started to resp ond to treatmen t, but then died of an apparen tly unrelated brain haemorrhage. When the news w as passed to p eople in t he Sc ho ol of Mathematical Sci- ences at Q MUL, the resp onses were remark ably similar. F rom PhD studen ts to professors emeriti, from statisticians and astronomers to pure and applied mathematicians, p eople said “Ho w can this b e? He was still doing so m uch. He w as m y friend.” W e are all s t unned, but I think that we are also all grateful that he nev er had the ‘retiremen t with nothing to do’ that he so dreaded. In John Morgan’s w ords: “Ho w health y and vital Donald alwa ys ap- p eared, and ho w m uc h energy he exuded, despite his ceaseless litany o f health complain ts. I will think of his demise a s a result of his brain b eing no longer able to con tain his endless mental energy .” Ac knowledge ments I should like to thank the follo wing for information and reminisce nces: Ian Anderson, Chris Brien, P eter Cameron, Bernard Carr, Robin Constable, Ric hard Cormac k, Stev en Gilmour, John Go w er, Mariana Iossifov a- Kelly , W o jtek Krzanows ki, John Lam b, Sue Lewis, Byron Morgan, John Morgan, Philip Ogden, Martin O wen, Rob ert Preece, Martin Ridout, G a vin Ross and Iwan Williams Publication s o f D. A. Preece [1] D. A. Preece: Some row and column designs for tw o sets o f treatments . Biometrics 22 ( 1 966), 1–25. [2] D. A. Preece: Classifying Y ouden rectangles. Journal of the R oyal Sta- tistic al So ciety, Series B 28 (19 66), 118– 130. [3] D. A. Preece: On Addelman’s 2 17 − 9 resolution V plan. T e chnom etrics 8 (1966), 7 05–707. [4] D. A. Preece: Some balanced incomplete blo c k designs for t wo sets of treatmen ts. Biometrika 53 (1966 ) 497–50 6. [5] D. A. Pree ce: Cyclic generation of Robinson’s bala nced incomplete blo c k designs. Biome trics 23 (1967), 574– 5 78. [6] D. A. Preece: Nested balanced incomplete blo ck designs. Biometrika 54 (1967), 4 79–486. 19 [7] D. A. Preece: Incomplete blo c k designs with v = 2 k . Sa n khy¯ a, Series A 29 (196 7), 305–3 1 6. [8] D. A. Preece: Balanced 6 × 6 designs for nine treatmen ts. Sankhy¯ a, Series B 30 (1968 ), 443–446. [9] D. A. Preece: Discussion o n ‘On the future of statistics—a second lo ok’ (b y M. G. Kendall). Journal of the R oyal Statistic al So ciety, Series A 131 (1968), 1 98–199. [10] D. A. Preece: Balanced incomplete blo c k designs with sets of iden tical blo c ks. T e chnom etrics 11 (1969), 613 – 615. [11] J. B. F ree & D. A. Preece: The eﬀect of t he size of a honeybee colon y on its fora ging activit y . Ins e cts So ciaux 16 ( 1 969), 73– 78. [12] D. A. Preece: Near-cyclic represen tations for some resolution VI frac- tional factorial plans. Annals o f Mathematic al Statistics 40 (1969 ) , 1840–184 3. [13] D. A. Preece: D iscussion on ‘Problems in the bibliogra ph y of statistics’ (b y H. O. Lancaster) and ‘On coping with new informat io n in proba bil- it y and statistics’ (b y J. Gani). Journal of the R oyal S tatistic al So ciety, Series A 133 (19 70), 452– 4 53. [14] D. A. Preece: Iterat ive pro cedures for missing v alues in exp erimen ts. T e chnome trics 13 (1 971), 743 –753. [15] D. A. Preece: Some new balanced ro w-and-column des ig ns fo r t wo non-in teracting sets of treatmen ts. Biometrics 27 (197 1), 426–4 30. [16] J. C. G o we r & D. A. Preece: Generating successiv e incomplete blo c ks with eac h pair o f elemen ts in at least one blo ck . Journal of Combina- torial The ory, S e ri e s A 12 (1 972), 81–97. [17] D. A. Preece: Non-additivity in t w o-wa y classiﬁcations with missing v alues. Bi o m etrics 28 (197 2 ), 574–57 7. [18] D. A. Preece, S. C. P earce & J. R. Kerr: Orthogonal designs for three- dimensional exp erimen ts. B iometrika 60 (1973) , 349–358 . [19] D. A. Preece & J. C. Gow er: An iterativ e computer pro cedure for mixed-up v alues in exp eriments . Applie d Statistics 23 (1974), 73–7 4 . [20] D. A. Preece: Bibliography of designs for exp erimen ts in three dimen- sions. Aust r alian Journa l of Statistics 17 (1975), 51–55. [21] D. A. Preece & W. B. Hall: Balanced designs fo r row-and-column exp eriments with t wo non-interacting sets of treatmen ts, one set not b eing a pplied to all the ro ws. Austr alia n Journal of Statistics 17 (19 7 5), 186–191. 20 [22] D. A. Preece & P . J. Cameron: Some new fully-balanced Graeco-Latin Y ouden ‘squares’. Utilitas Mathematic a 8 (1975), 1 9 3–204. [23] D. A. Preece: Some designs ba sed on 11 × 5 Y ouden ‘squares’. Utilitas Mathematic a 9 (1976), 139–146 . [24] D. A. Preece: Iden tiﬁcation k eys and diagnostic tables. Mathem atic al Scientist 1 (1976), 43–6 5 . [25] D. A. Preece: D esigns for exp erimen ts in three dimensions. Mathemat- ic al Scien tist , Supplemen t 1 (1976), 38 –40. [26] D. A. Preece: Non-orthogonal G raeco-Latin designs. In Combi n ato- rial Mathema tics I V: Pr o c e e dings of the F ourth Austr alian Confer- enc e on Combinatorial Mathematics, A delaide (eds. L. R. A. Casse & W. D. W allis), L ecture Notes in Mathematics, 56 0 , Springer-V erla g : Berlin, 1976, pp. 7–26. [27] D. A. Preece: A second domain of bala nced 6 × 6 designs for nine equally-replicated treatments . Sankhy¯ a, Series B 38 (1976) , 1 92–194. [28] D. A. Preece: Discussion on ‘A reform ulatio n of linear mo dels’ (b y J. A. Nelder). Journal of the R oyal Statistic al So ciety, Series A 140 (1977), 69–70 . [29] R. W. Pa yne & D. A. Preece: Incorp orating che cks against observ er error in to iden tiﬁcation k eys. New Phytolo gist 79 (1977), 203 – 209. [30] D. A. Preece: Discussion on ‘Maximum lik eliho o d fr o m incomplete data via the EM alg o rithm’ (by A. P . Dempster, N. M. La ird & D. B. Rubin). Journal of the R oyal Statistic al So ciety, Series B 39 (19 77), 28. [31] D. A. Preece: O r thogonality and designs: a terminological m uddle. Utilitas Mathematic a 12 (1 977), 201 –223. [32] D. A. Preece: Discus sion on ‘R udimen ts of n umeracy’ (b y A. S. C. Ehrenb erg ) and ‘Statistics and decisions: the imp ortance of comm u- nication a nd the p o wer of graphical presen tation’ (by B. H. Mahon). Journal of the R oyal S tatistic al So ciety, Series A 140 (1977), 308 –310. [33] D. A. Preece, R. A. Bailey & H. D. P atterson: A randomization prob- lem in fo rming designs with superimp osed tr eatmen ts. Au str alian Jour- nal of Statistics 20 (1978), 111 –125. [34] D. A. Preece: Discussion on ‘Nearest neigh b our mo dels in the ana lysis of ﬁeld exp eriments ’ (by M. S. Bartlett). Journal of the R oyal Statistic al So cie ty, Series B 40 (1 978), 163 . 21 [35] R. A. Bailey , D. A. Preece & P . J. Zemro ch: T ota lly symmetric La tin squares and cubes. Utilitas Mathematic a 14 (1978), 161–170. [36] D. A. Preece: Discussion on ‘The analysis of un balanced cross- classiﬁcations’ (b y M. Aitkin). Journal of the R o yal Statistic al So ciety, Series A 141 (19 78), 215. [37] E. V. Mark ov a & D. A. Preece: Latinskie kub y i svy azann y e s nimi plan y . Zavo dskaya L ab or atoriya 44 (1978 ), 123 1 –1237. T ranslated in to English as: Latin cub es and related designs. Ind ustrial L ab or atory 44 (1978), 1392– 1 399. [38] D. A. Preece: Supplemen tary bibliography of designs for experiments in three dimensions. Austr alian Journal of Statistics 21 (19 79), 170– 172. [39] D. A. Preece: Discussion on ‘Public opinion p olls’. Journal of the R oyal Statistic al So ciety, Series A 142 (1979), 462. [40] D. A. Preece: Cov aria nce analysis, factorial exp erimen ts and marginal- it y . Statistician 29 (1980 ) , 97–122. [41] R. W. P ayne & D. A. Preece : Identiﬁc a t io n k eys and diagnostic tables: a review (with discuss ion). Journal of the R oyal Statistic al So ciety, Series A 143 (19 80), 253– 2 92. [42] D. A. Preece : Distributions of ﬁnal digits in data. Statistician 30 (1981), 31–60 . [43] D. A. Preece: Discussion on ‘A review of statistical ideas relev ant to in tercropping researc h’ (b y R. Mead & J. Riley). Journal of the R oyal Statistic al So ciety, Series A 144 (1981), 498– 4 99. [44] D. A. Preece: t is for t r ouble (and textbo oks): a critique of some examples of the paired-samples t -test. Statistician 31 (1982), 1 69–195. [45] D. A. Preece: Discussion o n ‘R egr ession diagno stics, transformations and constructed v ariables’ (by A. C. Atkin son). Journal o f the R oyal Statistic al So ciety, Series B 44 (19 82), 25. [46] D. A. Preece, R. W ebster & J. A. Catt: Discussion on ‘The statistical analysis of comp ositional data’ (b y J. Aitc hison). Journal of the R oyal Statistic al So ciety, Series B 44 (19 82), 171. [47] D. A. Preece: The design and analysis of exp eriments — What has gone wrong? Utilitas Mathematic a 21A (1982 ) , 201–244 . [48] D. A. Preece: Balance and designs: Another terminological tangle. Utilitas Mathematic a 21C (1 982), 85– 186. 22 [49] D. A. Preece: Discussion on ‘The analysis of library data’ (by Q. L . Bur- rell & V. R. Cane). Journal of the R oyal Statistic al So ciety, Series A 145 (1982), 6 9. [50] D. A. Preece: Some partly cyclic 13 × 4 Y ouden ‘squares’ and a balanced arrangemen t for a pac k of cards. Utilitas Mathematic a 22 ( 1 982), 255– 263. [51] D. A. Preece: The statistical education required b efore computer pro- grams can rightly b e use d fo r ana lysing agricultura l exp erimen ts. In Computing for National Development , Heydon and Son: London, 1982, pp. 38–51. [The published v ersion include s editorial c hang es not ap- pro ve d by the author.] [52] D. A. Preece: Discuss ion on ‘Nearest neigh b our (NN) a nalysis of ﬁeld exp eriments’ (b y G. N. Wilkinson, S. R. Ec kert, T. W. Hanco c k and O. Ma y o). Journal of the R oyal Statistic al So ciety, Series B 45 (1983), 202. [53] D. A. Preece & G. H. F reeman: Semi-Latin squares and related designs. Journal of the R oyal Statistic al So ciety, Series B 45 (19 83), 267– 277. [54] D. A. Preece: Latin squares, Latin cub es, Latin rectangles, etc. In En- cyclop e dia of Statistic a l Scienc es , V olume 4 (eds. S. Kotz & N. L. John- son), Wiley: New Y ork, 198 3, pp. 504–5 1 0. [55] D. A. Preece: The design and analysis o f experiments — what is it ab out? In Pr o c e e dings of the First International Conf e r enc e on T e ach- ing Statistics , V olume I I, T eac hing Statistics T rust, 1983, pp. 575–590 . [56] D. A. Preece: Criss-cross designs (corresp ondence). Bi o metrics 39 (1983), 1115– 1 116. [57] D. A. Preece: Genstat analysis of v ariance and the distan t clien t. Gen- stat Newsletter 13 (March 1 984), 35– 38. [58] D. A. Preece: Biometry in the Third W orld: Science not ritual. Bio- metrics 40 (1984), 519–523 . [59] D. A. Preece: Discussion o n ‘Selection of subsets of regression v a riables’ (b y A. J. Miller). Journal of the R oyal Statistic al So ciety, Series A 147 (1984), 419. [60] D. A. Pree ce: Discussion on ‘Some asp ects of the spline smo othing approac h to non- parametric regression curv e ﬁtting’ (by B. W. Silv er- man). Journal of the R oyal Statistic al So ciety, Series B 47 (1985 ) , 42. [61] G. J. S. Ross & D. A. Pree ce: The negativ e binomial distribution. Statistician 34 (1985 ), 323–33 5. 23 [62] D. A. Preece: Discussion on ‘Pro jections of studen t n um b ers in higher education’. Journal of the R oyal S tatistic al So ciety, Series A 148 (1985), 199. [63] D. A. Preece : Discuss ion on ‘The initial examination o f data’ (b y C. Chatﬁeld). Journal of the R oyal Statistic al So c iety, Se rie s A 148 (1985), 234–2 3 5. [64] D. A. Preece: Some general principles of crop rotatio n experiments. Exp erim e n tal A gricultur e 22 , (1986), 1 87–198. [65] D. A. Preece: Illustrativ e examples: illustrative of what? Statistician 35 (1986), 3 3–44. [66] D. A. Preece: D iscussion on ‘The eﬀec ts of seat b elt legislation on British road casualties: a case study in structural time series mo delling’ (b y A. C. Harve y & J. Durbin). Journal of the R oyal Statistic al So ciety, Series A 149 (19 86), 224. [67] D. A. Preece: The use of pseudo-facto r s when treatments w ere sup er- imp osed in an orchard exp erimen t. Genstat Newsletter 17 (June 1986), 46–48. [68] D. A. Preece: The use of pseudo-factors for a balanced 6 × 6 row- and-column design for nine treatmen ts. Genstat Newsle tter 19 (Marc h 1987), 48–51. [69] D. A. Preece: The language of size, quan tity a nd comparison. Statisti- cian 36 (19 8 7), 45–54. [70] D. A. Preece: Discussion on ‘Graphical perception: the visual de- co ding of quan titative info rmation on graphical displa ys o f data’ (b y W. S. Clev eland & R. McGill). Journal of the R oyal Statistic al So ciety, Series A 150 (19 87), 215. [71] D. A. Preece: G o o d statistical pra ctice. Statistician 36 (1987), 397– 408. [72] D. A. Preece: Discussion on ‘Sy mmetry mo dels and hypotheses for structured data la youts ’ (b y A. P . Dawid). Journal of the R oyal Sta- tistic al So ciety, Series B 50 (19 88), 28. [73] D. A. Preece: Genstat analyses for complex ba lanced designs with non- in teracting factors. Genstat Newsletter 21 (March 1988), 33–4 5 . [74] D. A. Preece, G . J. S. R o ss & S. P . J. Kirb y: Bortk ewitsc h’s horse-kic ks and the generalised linear mo del. Statistician 37 (1988), 313–318. 24 [75] D. A. Preec e: Discussion on ‘Some asp ects of elections—to ﬁll one seat or ma ny’ (b y I. D. Hill). Journal of the R oyal Statistic al So c iety, Series A 151 (19 88), 270. [76] G. W. F. Sew ell, D . A. Preece & R. F. Elsey: Apple replan t disease: the inﬂuenc e of soil phosphorus and other factors on the growth re- sp onses of apple seedlings to soil f umigation with chloropicrin. Annals of Applie d Biolo gy 113 (1988), 605 – 615. [77] D. A. Preece: Semi-Latin squares. In Encyclop e d i a of Statistic a l Sci - enc es , V olume 8 ( eds. S. K o tz & N. L. Johnson), Wiley: New Y ork, 1988, pp. 359 –361. [78] D. A. Preece: Letter: O for some n um b ers! R oyal Statistic al So ciety News and Notes 15( 3) (Nov em b er 1 988), 2. [79] D. A. Preece: F actoria l exp erimen tation in second-order Latin cub es. Journal of Applie d Statistics 16 (1989), 19–24. [80] D. A. Preece: Dev elopmen ts in exp erimen tal design in a gricultural and horticultural researc h. Kwan titatieve Metho den 32 (1989), 65–73. [81] D. A. Preece: Letter: F or t he greater go o d . . . . R o yal Statistic al So ciety News and Notes 16( 6) (F ebruar y 1 9 90), 2. [82] D. A. Preece: Confounding: confusion m uc h confounded? R oyal Sta- tistic al So ciety News and Notes 16(8) (April 19 9 0), 8–9. [83] D. A. Preece: Fift y y ears of Y ouden squares: a review. Bul letin of the Institute of Mathematics and its Applic ations 26 (1990), 65–75 . [84] D. A. Preece: Discussion on ‘Record link age: statistical mo dels for matc hing computer records’ (by J. B. Copas & F. J. Hilton). Journal of the R oyal S tatistic al So ciety, Series A 153 (1990), 3 1 7. [85] D. A. Preece: R. A. Fisher a nd exp erimen tal design: a review. B iomet- rics 46 (1990), 925–935. [86] D. A. Preece: Do uble Y ouden rectangles of size 6 × 11. Mathematic al Scientist 16 (1991), 41–4 5 . [87] D. A. Preece: D iscussion on ‘Strata for ra ndo mized exp eriments ’ (b y R. A. Bailey ). Journal of the R oyal Statistic al So ci e ty, Series B 53 (1991), 67–68 . [88] D. A. Preece: La t in squares as exp erimen tal designs. Chapter 10 in L atin Squar es: New Developments in the The ory and Applic ations (eds. J. D´ enes & A. D. Keedw ell), ( A nnals of D iscr e te Mathematics 46 ), North-Holland: Amsterdam, 1991, pp. 317–342. 25 [89] D. A. Preece: En umeration of some 7 × 15 Y ouden squares and con- struction o f some 7 × 15 double Y ouden rectangles. Utilitas Mathematic a 41 (1992), 5 1–62. [90] D. A. Preece: Discus sion on ‘The future for honours degree courses in Mathematics’ (b y P . M. Neumann) and ‘Statistics degree courses’ (by H. P . Wynn). Journal of the R oyal Statistic al So ciety, Series A 155 (1992), 214–2 1 5. [91] D. A. Preece : A set o f double Y ouden rectangles o f size 8 × 15. Ars Combinatoria 36 (199 3), 215–219. [92] D. A. Preece: Discussion on ‘Info r ma t iv e drop out in longitudinal data analysis’ (by P . Digg le & M. G. Kenw ard). Applie d Statistics 43 (1994), 86. [93] D. A. Preece: Double Y ouden rectangles—an up date with examples of size 5 × 11. D iscr ete Mathematics 125 (1994), 30 9–317. [94] D. A. Pree ce, P . W. Brading , C. Lam & M. Cot ´ e: Balanced 6 × 6 designs f o r 4 equally replicated treatmen ts. Di s cr ete Mathematics 125 (1994), 319–3 2 7. [95] D. A. Preece: Letter: SD vs. SE. RSS News 21(8) (April 1994 ), 4. [96] D. A. Preece: D ouble a nd triple Y ouden rectangles and Genstat ANO V A. Genstat Newsletter 30 (Ma y 199 4), 48–52 . [97] D. A. Preece: T riple Y ouden rectangles—a new class of fully ba la nced com binatorial arrangemen ts. Ars Combinatoria 37 (1994), 175–1 8 2. [98] D. A. Preece: Balanced Ouc hterlon y neigh b our designs and quasi Rees neigh b our designs. Journal of Combinatorial Mathematics and Combi- natorial Computing 15 (1 994), 197 –219. [99] D. A. Preece: D iscussion on ‘Deconstructing statistical questions’ (b y D. J. Hand). Journal of the R oyal Statistic al So ciety, Series A 157 (1994), 342–3 4 3. [100] E. D . G ardiner & D. A. Preece: Eﬃcie ncy factors for some bal- anced hyper-G r a eco-Latin sup erimp ositions of Y ouden squ a res. Gen- stat Newsletter 31 (Nov em b er 1994), 24–29 . [101] D. A. Preece: Discussion on ‘Inferenc e in forensic iden tiﬁcation’ (b y D. J. Balding & P . Donnelly). Journal of the R oyal Statistic al So ciety, Series A 158 (19 95), 45. [102] D. A. Preece: Ho w man y 7 × 7 Latin squares can b e partitioned in to Y ouden squares? D iscr ete Mathematics 138 (1995), 34 3–352. 26 [103] D. A. Preece & B. J. V owden: Graeco-Latin squares with em b edded balanced superimp ositions of Y ouden squares. D iscr e te Mathematics 138 (1995), 3 53–363. [104] D. A. Preece: Discussion on ‘The 1 991 census of p o pulation in Eng- land and W ales’ (b y E. J. Thompson). Journal of the R oyal Statistic al So cie ty, Series A 158 (1995), 237. [105] R. A. Bailey , D . A. Preece & C. A. Ro wley: Randomisation fo r a balanced superimp osition of one Y ouden square on another. Journal of the R oyal Statistic al So ciety, Series B 57 (19 95), 459– 469. [106] D. A. Preece & G. J. S. Ross: Fitting the negativ e binomial distribu- tion. Genstat Newsle tter 32 (Ma y 1995), 20– 30. [107] D. A. Preece, R. L. Constable, G. Zha ng, J. L. Y ucas, W. D. W al- lis, J. P . McSorley & N. C. K. Phillips: Tight single-c hange cov ering designs. Utilitas Mathematic a 47 (19 9 5), 55–84 . [108] R. L. Constable, D . A. Preece, N. Phillips, T. D. Porter & W. D. W allis: Single c hange neigh b or designs. Austr alasian Journal of Co mbinatorics 11 (1995), 2 47–255. [109] D. A. Preece, B. J. V owden, R. Hughes Jones, C. A. Ro dger & C. J. V owden: Choreographing designs. Mathematic al Sc ientist 20 (1995), 15–32 . [110] D. A. Preece: Tight single-c hange co ve ring designs — the inside story . Bul letin of the In stitute of Combinatorics and its Applic ations 13 (1995), 51–55 . [111] P . J. Ow ens & D . A. Preece : Complete sets of pairwise orthogonal Latin squares of order 9. Journal of Combinatorial Mathem a tics and Combinatorial Computing 18 (1 995), 83– 96. [112] P . J. O w ens & D. A. Preece : Some new non-cyclic Latin squares that ha v e cyclic and Y ouden prop erties. Ars Com binatoria 44 (1996), 137– 148. [113] D. A. Preece: Multi-factor balanced blo ck designs with complete ad- justed orthogonality for all pair s of treatmen t factors. Aust r alian Jour- nal of Statistics 38 (1996), 223 –230. [114] D. A. Preece: Y ouden squares . Section IV.55 in CRC Handb o ok of Combinatorial D esigns (eds. C. J. Colb ourn & J. H. Dinitz), CRC Press: Bo ca Ra ton, 1996, pp. 511–51 4 . 27 [115] D. A. Pree ce: Discussion o n ‘Hierarc hical generalized linear mo dels’ (b y Y. Lee & J. A. Nelder). Journal of the R o yal Statistic al So ciety, Series B 58 (1996 ), 669. [116] D. A. Preece & G . J. S. R oss: Using G enstat to ﬁt contin uous actuarial distributions. Genstat Newsl e tter 33 (Ma y 1997) , 5–1 9 . [117] P . J. Ow ens & D. A. Preece: Aspects o f complete sets of 9 × 9 pairwise orthogonal Latin squares. Discr ete Mathematics 167/168 (1 9 97), 519– 525. [118] D. A. Preece: Some 6 × 11 Y ouden squares and some 6 × 11 double Y ouden rectangles. Discr ete Mathematics 167/168 (19 97), 527– 541. [119] D. A. Preece & N. C. K. Phillips: A new ty p e of F reeman–Y o uden rectangle. Journal o f Combinatorial Mathematics and Combinatorial Computing 25 (1997), 65–78. [120] D. A. Preece: Discussion on ‘Statistics and mathematics—trouble at the interface’ (b y P . Spren t), ‘Br eaking misconceptions—statistics and its relationship to mathematics’ (by D. J. Hand), ‘Mathematics: go v- erness or handmaiden’ (b y S. Senn) and ‘Statistics and mathematics— the appropriate use of mathematics within statistics’ (by R. A. Bailey). Statistician 47 (1998 ), 274. [121] D. A. Preece: Letter to the editor: P atien ts’ names. The T i mes , Mon- da y 19 Octob er 1998, p. 21. [122] D. A. Preece: Commen t : D esign of questionnaires. RSS News 26(4) (Decem b er 1998), 11. [123] D. A. Preece: Commen t: Iden tifying by name and num b er. RSS News 26(6) (F ebruary 1999), 1–2. [124] B. J. V ow den & D. A. Preece: Some new inﬁnite series o f F reeman– Y ouden rectangles. A rs Combinatoria 51 (1999), 49–6 3. [125] D. A. Preece, B. J. V ow den & N. C. K. Phillips: D ouble Y ouden rect- angles of sizes p × (2 p + 1 ) and ( p + 1) × (2 p + 1). Ars C ombinatoria 51 (1999), 1 61–171. [126] N. C. K. Phillips & D. A. Preece: Tigh t single-ch a nge cov ering designs with v = 12, k = 4. Discr ete Mathematics 197/198 (1999), 65 7–670. [127] D. A. Preece & B. J. V o wden: Some series o f cyclic balanced hy p er- Graeco-Latin sup erimp ositions of three Y ouden squares. Discr ete Math- ematics 197/198 (1999), 671–68 2 . 28 [128] D. H. R ees & D. A. Preece: P erfect Graeco-Latin balanced incomplete blo c k designs (p ergolas). Dis c r ete Mathematics 197/198 (1999 ), 691– 712. [129] D. A. Preece: Discussion on ‘Bay esian ana lysis of agricultural ﬁeld ex- p erimen ts’ (by J. Besag & D . Higdon). Journal of the R oyal Statistic al So cie ty, Series B 61 (1 999), 718 –720. [130] D. A. Pree ce, D. H. Rees & J. P . Morgan: D oubly nested balanced incomplete blo c k designs. Congr essus Numer antium 137 ( 1 999), 5–18. [131] D. A. Preece: Discussion o n ‘In v ariance and factorial mo dels’ ( by P . McCullagh). Journal of the R oyal Statistic al So ciety, Series B 62 (2000), 243–2 4 4. [132] D. A. Preece: Discussion on ‘Consensus and contro v ersy in phar ma- ceutical statistics’ (b y S. Senn). Statistician 49 (2000), 164– 165. [133] J. P . Morgan, D . A. Preece & D. H. Rees: Nested ba la nced incomplete blo c k designs. Discr ete Mathematics 231 (2 0 01), 351– 389. [134] D. A. Preece: Ty p es of factor in experimen ts. Journal of Statistic al Planning and I nfer en c e (sp ecial issue o n design com binatorics in honor of S. S. Shrik ande) 95 (2001), 269 –282. [135] D. A. Preece, B. J. V ow den & N. C. K. Phillips: D ouble Y ouden rect- angles of size ( p + 1) × ( p 2 + p + 1). Utilitas Mathematic a , 59 (20 0 1), 139–154. [136] D. A. Preece & N. C. K. Phillips: Eule r at the b ow ling green. Utilitas Mathematic a 61 (2002), 129–165 . [137] I. Anderson & D. A. Preece: Locally balanced c ha ng e- o ve r de signs. Utilitas Mathematic a 62 (2 002), 33– 59. [138] N. C. K. Phillips, D. A. Preece & D. H. Rees: Do uble Y ouden rectangles for the four biplanes with k = 9. Journal of Com binatorial Mathematics and Combinatorial Computing 44 (2 003), 169 –176. [139] I. Anderson & D. A. Preece: P o wer-se quence terraces f o r Z n where n is an o dd prime p ow er. Discr ete Mathematics 261 (2003), 31–58. [140] R. A. Bailey , M. A. Ollis & D . A. Preece: Round-dance neigh b our designs from terra ces. Discr ete Mathematics 266 (2003), 69 – 86. [141] M. A. O llis & D . A. Preece: Sectionable terraces and the (generalised) Ob erw olfa ch problem. D iscr ete Mathematics 266 (2003), 39 9 –416. 29 [142] N. C. K. Phillips & D. A. Preece: Finding double Y ouden rectangles. In Designs 2002: F urther Computational and Co nstructive D esign The o ry (ed. W. D . W allis), Klu w er: Amsterdam, 2003, pp. 301–315 . [143] I. Anderson & D. A. Preece : Some narcissistic half-and- half p o w er- sequence Z p terraces with segmen ts o f diﬀeren t lengths. Congr essus Numer antium 163 (2003), 5–26. [144] I. Anderson & D. A. Preece: Narciss istic half-and-half p o wer-se quence terraces for Z n with n = pq t . Discr ete Mathem atics 279 (2004), 33–60. [145] I. Anderson & D. A. Preece : Some p o we r- sequence terraces for Z pq with as few segmen ts as p ossible. Discr ete Mathematics 293 ( 2 005), 29–59. [146] N. C. K. Phillips, D. A. Preece & W. D. W allis: The sev en classes of 5 × 6 triple arra ys. D iscr e te Mathematics 293 (2005), 21 3–218. [147] D. A. Preece, W. D. W allis & J. L. Y ucas: P aley triple arra ys, Aus- tr alasian Journal of C ombinatorics 33 (2005), 237– 246. [148] I. Anderson & D. A. Preece: Logarithmic terraces. Bul letin of the In- stitute of Combinatorics and its Applic ations 46 (2 0 06), 49–6 0. [149] A. E. Brouw er, P . J. Cameron, W. H. Haemers & D. A. Preece: Self- dual, not self p olar. Di s cr ete Mathematics 306 (2006), 305 1 –3053. [150] D. A. Preece: Discussion on ‘Multiple randomizations’ (b y C. J. Brien & R. A. Bailey). Journal of the R oyal Statistic al So ciety, Series B 68 (2006), 601–6 0 2. [151] I. Anderson & D. A. Preece: Tw o sp ecial terraces for Z 121 . Bul letin of the Institute of Combinatorics and its Appli c ations 49 (2007), 93–98 . [152] P . Dob cs´ anyi, D. A. Preece & L. H. Soic her: On balanced incomplete- blo c k designs with rep eated blo ck s. Eur op e an Journal of Combinatorics 28 (2007), 1 955–1970 . [153] I. Ande r son & D. A. Preece : Some Z n − 1 terraces from Z n p ow er- sequence s, n b eing an o dd prime p ow er. Pr o c e e dings of the Edinbur gh Mathematic al So ciety (2) 50 (2007), 527–549. [154] D. A. Preece & C. J. Colb o ur n: Y ouden squares a nd generalised Y ouden designs. Section VI.65 in Handb o ok of Combinatorial Design s , 2nd edi- tion (eds. C. J. Colb o urn & J. H. Dinitz), Chapman and Hall/CRC : Bo ca Rato n, 2007, pp. 668–674. [155] I. Anderson & D. A. Preece: Some d a c ap o directed p ow er-sequence Z n +1 terraces with n an o dd prime p o we r. Di s cr ete Mathematics 308 (2008), 192–2 0 6. 30 [156] I. Anderson & D . A. Preece: A general approac h to constructing p o we r- sequence terraces for Z n . Disc r ete Mathematics 308 (2008), 631–64 4. [157] D. A. Preece: Daisy c hains—a fruitful com binatorial concept. A us- tr alasian Journal of C ombinatorics 41 (2008), 297– 316. [158] D. A. Preece: Discussion on ‘Exit p olling in a cold climate: the BBC– ITV exp erience in Britain in 2005’ (b y J. Curtice & D. Firt h). Journal of the R oyal S tatistic al So ciety, Series A 171 (2008), 5 3 6. [159] I. Ande r son & D. A. Preece : Some Z n +2 terraces from Z n p ow er- sequence s, n b eing an o dd prime. Discr ete Mathematics 308 (20 08), 4086–410 7. [160] D. A. Preece: Discussion on ‘Research prioritizatio n based on ex- p ected v a lues of partia l p erfect inf o rmation: a case-study on interv en- tions to increase upta ke of breast cancer screening’ (b y N. J. W elton, A. E. Ades, D. M. Caldw ell & T. J. P eters). Journal of the R oyal Sta- tistic al So ciety, Series A 171 (2008), 836–8 37. [161] D. A. Preece: Some mutually orthogonal p ow er-sequence terraces. B ul- letin of the Institute of C o mbinatorics and its Applic ations 54 (2008), 11–32. [162] D. A. Preece: Zigzag and foxtrot terraces for Z n . Austr ala s i a n Journal of Combinatorics 42 (2008), 261– 2 78. [163] D. A. Preece: Half-cycle s a nd c haplets. Austr al a sian Journal of Com- binatorics 43 (20 09), 253– 280. [164] D. A. Preece: Daisy c hains with three generators. Austr a l a sian Journal of Combinatorics 45 (2009), 157– 1 74. [165] I. Anderson & D. A. Preece: Com binatorially fruitful prop erties of 3 · 2 − 1 and 3 · 2 − 2 mo dulo p . D i s cr ete Mathematics 310 ( 2 010), 3 12– 324. [166] I. Ande r son & D. A. Preece : Some Z n − 2 terraces from Z n p ow er- sequence s, n b eing an o dd prime p o we r. Glasgow Mathem a tic al Journal 52 (2010), 6 5–85. [167] I. Anderson & D. A. Preece: Some narcissistic p o w er-sequence Z n +1 terraces with n an o dd prime p o w er. A rs Combin atoria 97A (2010), 33–57. [168] D. A. Preece & E. R. V aughan: Da isy c hains with four generators. A ustr alasian Journal of Comb i n atorics 49 (201 1), 77–93 . 31 [169] A. Ahmed, M. I. Azimli, I. Anderson & D. A. Preece: Rotational ter- races from rectangular arrays. Bul letin o f the Institute of C o mbinatorics and its Applic ations 63 (2011), 4–12. [170] P . J. Cameron & D. A. Preece: Three-factor decomp ositions of U n with the three generato r s in arithmetic progression. http://arxi v.org/abs/1111.3507 [171] P . Spren t, E. E. Bassett & D. A. Preece: Obituary: Stanley Cliﬀord P earce, 1914–201 2. Journal of the R oyal Statistic al So ciety, Series A 175 (2012), 8 15–817. [172] D. A. Preece: Mathematics in literature. Journal o f Humanistic Math- ematics 2 (20 1 2), 36–57 . [173] D. Preece & G. Clarke: Obituar y: Georg e V aughan Dyk e, No ve mber 10th, 1921– Marc h 29th, 2012. Journal of the R oyal Statistic al So ci e ty, Series A 175 (20 12), 1069 . [174] D. A. Preece & I. Anderson: O bt a ining all or half of U n as h x i × h x + 1 i . Inte ge rs 12 (2012), pap er A52 (42pp.). [175] D. A. Preece: The Pip e-Or gans of L ondon ’s East En d an d its Pe ople’s Palac es , Queen Mary , Univ ersity of L ondon, 20 1 3. [176] P . J. Cameron and D. A. Preece: Primitiv e lam b da-ro ot s. http://came roncounts.files.wordpress.com/2014/01/plr1.pdf Also GAP co de, http://came roncounts.wordpress.com/lecture-notes/gap-code-for-plrs-2/ [177] J. P . Morgan & D. A. Preece: Tw o inﬁnite series of multi-la y ered Y ouden rectangles. In preparation. Other refere nces [O1] R. D. Carmic hael: Note on a new num b er theory function. Bul le tin of the Americ an Mathema tic al So ciety 16 (1909–10 ), 232 –238. [O2] R. D. Carmic hael: Generalizations of Euler’s φ -function, with applica- tions t o Ab elian groups. Quarterly Journal of Mathematics 44 (1 913), 94–104. [O3] T. N. Hoblyn, S. C. Pe a rce & G. H. F reeman: Some considerations in the design of successiv e exp eriments in fruit plan tations. Biome trics 10 (1954), 5 03–515. 32 [O4] A. T. James: The relationship algebra of an exp erimental design. An- nals of Mathematic al Statistics 28 (1 9 57), 993– 1002. [O5] S. C. P earce: Th e use and classiﬁc a t io n of non-orthogonal designs . Journal of the R oyal S tatistic al So c iety, Series A 126 (1963), 353– 377. [O6] J. A. Nelder: The eﬃcien t formation of a tria ngular array with re- stricted storag e f or data. Applie d Statistics 18 (1969), 20 3–206. [O7] A. T. James and G. N. Wilkinson: F a ctorization of the residual op- erator and canonical decomp o sition o f nonorthogonal factors in the analysis of v ariance. Bio metrika 58 (1971), 2 79–294. [O8] G. H. F reeman: Complete La t in squares and related experimen ta l de- signs. Journal of the R oyal Statistic al So ciety, Series B 41 (1979), 253–262. [O9] G. H. F reeman: F urther results on quasi-complete Latin squares. Jour- nal of the R oyal Statistic al So ciety Series B 43 (1981), 314– 320. [O10] R. A. Bailey: Quasi-complete Latin squares: construction and ran- domization. Jo urna l o f the R oyal Statistic al So ciety, Series B 46 (1984), 323–3 3 4. [O11] C. Christoﬁ: On the structure, en umeration and classiﬁcation of Y ouden squares and DYRs. PhD t hesis, Univ ersit y of Kent at Can- terbury , 199 3 . [O12] W. D . W allis, J. L. Y ucas & G.-H. Zha ng : Single c hange cov ering designs. Desig ns, Co des and Crypto gr aphy 3 (1 993), 9–1 9. [O13] G.-H. Zhang: Some new b ounds on sin g le- c hange cov ering designs. SIAM Journal of Discr ete Mathematics 7 (1 994), 166 –171. [O14] C. Christoﬁ: En umerating 4 × 5 and 5 × 6 double Y ouden r ectangles. Discr ete Mathematics 125 (19 94), 129– 135. [O15] J. P . Morgan & N. Uddin: Optimal blo c ked main eﬀects plans with nested rows and columns and related designs. Annals of Statistics 24 (1996), 1185– 1 208. [O16] J. P . Morgan: Nested designs. In Handb o ok o f Statistics, V olume 13, Design and Analysis of Exp erimen ts (eds. S. Ghosh & C. R. Rao), North-Holland: Amsterdam, 1996, pp. 939–976. [O17] C. Christoﬁ: On the num b er of 6 × 7 double Y ouden rectangles. Ars Combinatoria 47 (199 7), 223–241. 33 [O18] R. A. Bailey: Resolv ed designs view ed as sets of partitions. In Combinatorial D esigns and their Applic ations (eds. F. C. Holroyd , K. A. S. Quinn, C. Rowley & B. S. W ebb), Chapman & Ha ll/CR C Press Researc h Not es in Mathematics 403, CRC Press LLC: Bo ca Ra- ton, 1999, pp. 17–47. [O19] P . J. Cameron: Multi-letter Y ouden rectangles fro m quadratic forms. Discr ete Mathematics 266 (20 03), 143– 151. [O20] R. A. Bailey & P . J. Cameron: What is a design? How should we classify them? De signs, Co des and Crypto gr a phy 44 (2 007), 223 –238. 34

Donald Arthur Preece: A life in statistics, mathematics and music

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