Everitt B.S. The Cambridge Dictionary of Statistics

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markedly according to the methodology used. [Statistical Methods in Spatial Epidemiology,

2nd edn, 2006, A. B. Lawson, Wiley, New York.]

Disease surveillance: A process that aims to use health and health-related data that precede

diagnosis and/or conﬁrmation to identify possible outbreaks of a disease, mobilize a rapid

response and therefore reduce morbidity and mortality. Such a process provides essential

information for control and response planning, helping to identify changes in incidence and

affected group, thereby providing valuable additional time for public health interventions.

[The Lancet, 1997, 349, 794–795.]

Dispersion: The amount by which a set of observations deviate from their mean. When the values of a

set of observations are close to their mean, the dispersion is less than when they are spread

out widely from the mean. See also variance. [MV1 Chapter 1.]

Dispersion parameter: See generalized linear models.

Dissimilaritycoefficient: A measure of the difference between two observations from (usually) a

set of

multivariate data

. For two observations with identical variable values the dissimilarity

is usually deﬁned as zero. See also metric inequality. [MV1 Chapter 1.]

Dissimi larity matrix: A

square matrix

in which the elements on the main diagonal are zero, and the

off-diagonal elements are

dissimilarity coefﬁcients

of each pair of stimuli or objects of

interest. Such matrices can either arise by calculations on the usual multivariate data matrix

X or directly from experiments in which human subjects make judgements about the stimuli.

The pattern or structure of this type of matrix is often investigated by applying some form of

multidimensional scaling

. [MV1 Chapter 4.]

lip cancer excedence probability

0.99 to 1

0.9 to 0.95

0.8 to 0.9

0.5 to 0.8

0.2 to 0.5

0.95 to 0.99

(66)

(46)

(31)

(33)

(10)

Fig. 55 Disease mapping illustrated by age-standardized mortality rates in part of Germany.

(Reproduced from

Biometrics

by permission of the International Biometric Society.)

139

Distance measure: See metric inequality.

Distance sampling: A method of sampling used in ecology for determining how many plants or

animals are in a given ﬁxed area. A set of randomly placed lines or points is established and

distances measured to those objects detected by travelling the line or surveying the points.

As a particular object is detected, its distance to the randomly chosen line or point is

measured and on completion n objects have been detected and their associated distances

recorded. Under certain assumptions unbiased estimates of density can be made from these

distance data. See also line-intersect sampling.[Canadian Field-Naturalist, 1996, 110,

642–8.]

Distributeddatabase: A

database

that consists of a number of component parts which are situated

at geographically separate locations. [Principles of Distributed Database Systems, 2nd

edition, 1999, M.T. Ozsu, P. Valdunez, Prentice Hall.]

Distribution free methods: Statistical techniques of estimation and inference that are based on a

function of the sample observations, the probability distribution of which does not depend on a

complete speciﬁcation of the probability distribution of the population from which the sample

was drawn. Consequently the techniques are valid under relatively general assumptions about

the underlying population. Often such methods involve only the ranks of the observations

rather than the observations themselves. Examples are

Wilcoxon’s signed rank test

and

Friedman’s two way analysis of variance

. In many cases these tests are only marginally less

powerful than their analogues which assume a particular population distribution (usually a

normal distribution), even when that assumption is true. Also commonly known as

non-

parametric methods

although the terms are not completely synonymous. [SMR Chapter 9.]

D istr i buti o n funct i on: See probability distribution.

Divide-by-total models: Models for polytomous responses in which the probability of a particular

category of the response is typically modelled as a multinomial

logistic function

[Psychometrika, 1986, 51, 567–77.]

Di visive clusteri ng:

Cluster analysis

procedures that begin with all individuals in a single cluster,

which is then successively divided by maximizing some particular measure of the separation

of the two resulting clusters. Rarely used in practice. See also agglomerative hierarchical

clustering methods and K-means cluster analysis. [MV2 Chapter 10.]

Dixon, Wilfred J . (1 91 5^20 08): Born in Portland, Oregon, USA, Dixon received a B.A. in

mathematics from Oregon State College in 1938, an M.A. in mathematics from the

University of Wisconsin in 1939 and a Ph.D in mathematical statistics from Princeton in

1944 under the supervision of

Samuel S. Wilks

. During the Second World War he was an

operations analyst at Princeton University. After the war Dixon went to work at the

University of Oregon and then in 1955 moved to the University of California at Los

Angeles where he remained for the rest of his career. He made major contributions in several

areas of statistics including

nonparametric statistics

experimental design

and

robust statis-

tics

, but Dixon is probably most widely remembered for his pioneering efforts in the

development of statistical software which culminated in the 1960s with the release of the

Biomedical Computer Programs, later to become the

BMDP

Statistical Software. Dixon

died on September 20th 2008.

Dixontest: A test for

outliers

. When the sample size, n, is less than or equal to seven, the test statistic is

r ¼

ð1Þ

 y

ð2Þ

ð1Þ

 y

ðnÞ

140

where y

(1)

is the suspected outlier and is the smallest observation in the sample, y

(2)

is the

next smallest and y

(n)

the largest observation. For n

7, y

(3)

is used instead of y

(2)

and y

ðn1Þ

in place of y

(n)

. Critical values are available in some statistical tables. [Journal of Statistical

Computation and Simulation, 1997, 58,1–20.]

DMC: Abbreviation for data monitoring committees.

Doane’srule: A rule for calculating the number of classes to use when constructing a

histogram

and

given by

no: of classes ¼ log

n þ1 þ log

ð1 þ

ﬃﬃﬃﬃﬃﬃﬃﬃ

n=6

where n is the sample size and

γ is an estimate of

kurtosis

. See also Sturges’ rule.[The

American Statistician, 1977, 30, 181–183.]

Dodge, Harold (1893^1976): Born in the mill city of Lowell, Massachusetts, Dodge became one

of the most important ﬁgures in the introduction of quality control and the development and

introduction of

acceptance sampling

. He was the originator of the operating characteristic

curve. Dodge’s career was mainly spent at Bell Laboratories, and his contributions were

recognized with the Shewhart medal of the American Society for Quality Control in 1950

and an Honorary Fellowship of the Royal Statistical Society in 1975. He died on 10

December 1976 at Mountain Lakes, New Jersey.

Dodge’s continuous sampl ing plan: A procedure for monitoring continuous production

processes. [Annals of Mathematical Statistics, 1943, 14, 264–79.]

Doll, Sir Richard (191 2^20 05): Born in Hampton, England, Richard Doll studied medicine at St.

Thomas’s Hospital Medical School in London, graduating in 1937. From 1939 until 1945 he

served in the Royal Army Medical Corps and in 1946 started work at the Medical Research

Council. In 1951 Doll and

Bradford Hill

started a study that would eventually last for 50

years, asking all the doctors in Britain what they themselves smoked and then tracking them

down over the years to see what they died of. The early results conﬁrmed that smokers were

much more likely to die of lung cancer than non-smokers, and the 10-year results showed

that smoking killed far more people from other diseases than from lung cancer. The study has

arguably helped to save millions of lives. In 1969 Doll was appointed Regius Professor of

Medicine at Oxford and during the next ten years helped to develop one of the top medical

schools in the world. He retired from administrative work in 1983 but continued his

research, publishing the 50-year follow-up on the British Doctors’ Study when he was 91

years old, on the 50th anniversary of the ﬁrst publication from the study. Doll received many

honours during his distinguished career including an OBE in 1956, a knighthood in 1971,

becoming a Companion of Honour in 1996, the UN award for cancer research in 1962 and

the Royal Medal from the Royal Society in 1986. He also received honorary degrees from 13

universities. Doll died in Oxford on 24 July 2005, aged 92.

Doob ^ Meyer decompositi on: A theorem which shows that any

counting process

may be

uniquely decomposed as the sum of a

martingale

and a predictable, right-continous process

called the compensator, assuming certain mathematical conditions. [Modelling Survival

Data, 2001, T.M. Therneau and P.M. Grambsch, Springer, New York.]

D-optimal design: See criteria of optimality.

Doran estimator: An estimator of the

missing values

in a

time series

for which monthly observa-

tions are available in a later period but only quarterly observations in an earlier period.

[Journal of the American Statistical Association, 1974, 69, 546–554.]

141

Dorfman^ Berbaum ^ Metz method: An approach to analysing multireader

receiver operat-

ing characteristic curves

data, that applies an analysis of variance to pseudovalues of the

ROC parameters computed by

jackkniﬁng

cases separately for each reader–treatment

combination. See also Obuchowski and Rockette method.[Academic Radiology, 2005,

12, 1534–1541.]

Dorfmanscheme: An approach to investigations designed to identify a particular medical condition

in a large population, usually by means of a blood test, that may result in a considerable

saving in the number of tests carried out. Instead of testing each person separately, blood

samples from, say, k people are pooled and analysed together. If the test is negative, this one

test clears k people. If the test is positive then each of the k individual blood samples must be

tested separately, and in all k þ 1 tests are required for these k people. If the probability of a

positive test (p) is small, the scheme is likely to result in far fewer tests being necessary. For

example, if p ¼ 0:01, it can be shown that the value of k that minimizes the expected number

of tests per person is 11, and that the expected number of tests is 0.2, resulting in 80% saving

in the number of tests compared with testing each individual separately. [Statistics in

Medicine, 1994, 22, 2337–2343.]

Dose-rangi ng t ria l: A

clinical trial

, usually undertaken at a late stage in the development of a drug,

to obtain information about the appropriate magnitude of initial and subsequent doses. Most

common is the

parallel-dose design

, in which one group of subjects in given a placebo, and

other groups different doses of the active treatment. [Controlled Clinical Trials, 1995, 16,

319–30.]

Dose^respo nse cu rve: A plot of the values of a response variable against corresponding values of

dose of drug received, or level of exposure endured, etc. See Fig. 56.[Hepatology, 2001, 33,

433–8.]

Dot plot: A more effective display than a number of other methods, for example,

pie charts

and

bar

charts

, for displaying quantitative data which are labelled. An example of such a plot

showing standardized mortality rates (SMR) for lung cancer for a number of occupational

groups is given in Fig. 57.

Double-blind: See blinding.

Double-centred matrices: Matrices of numerical elements from which both row and column

means have been subtracted. Such matrices occur in some forms of

multidimensional

scaling

Doubl e-count su rveys: Surveys in which two observers search the sampled area for the species of

interest. The presence of the two observers permits the calculation of a survey-speciﬁc

correction for visibility bias. [The Survey Kit, 1995, A. Fink, ed., Sage, London.]

Double-d ummy techn ique: A technique used in

clinical trials

when it is possible to make an

acceptable placebo for an active treatment but not to make two active treatments identical. In

this instance, the patients can be asked to take two sets of tablets throughout the trial: one

representing treatment A (active or placebo) and one treatment B (active or placebo).

Particularly useful in a

crossover trial

. [SMR Chapter 15.]

Double-exponential distribution: Synonym for Laplace distribution.

Doubl e-masked: Synonym for double-blind.

Double reciprocal plot: Synonym for Lineweaver–Burke plot.

142

Dose

Response

0.0 0.2 0.4 0.6 0.8 1.0

0.75 0.80 0.85 0.90 0.95

Fig. 56 A hypothetical dose–

response curve.

Fig. 57 A dot plot giving standardized mortality rates for lung cancer for several occupational groups.

143

Double sampling: A procedure in which initially a sample of subjects is selected for obtaining

auxillary information only, and then a second sample is selected in which the variable of

interest is observed in addition to the auxillary information. The second sample is often

selected as a subsample of the ﬁrst. The purpose of this type of sampling is to obtain better

estimators by using the relationship between the auxillary variables and the variable of

interest. See also two-phase sampling. [KA2 Chapter 24.]

Doubly censored data: Data involving

survival times

in which the time of the originating event

and the failure event may both be

censored observations

. Such data can arise when the

originating event is not directly observable but is detected via periodic

screening studies

[Statistics in Medicine, 1992, 11, 1569–78.]

Doubly mult iva r iate data: A term sometimes used for the data collected in those

longitudinal

studies

in which more than a single response variable is recorded for each subject on each

occasion. For example, in a

clinical trial

, weight and blood pressure may be recorded for

each patient on each planned visit.

Doubly ordered conti ngency tables:

Contingency tables

in which both the row and column

categories follow a natural order. An example might be, drug toxicity ranging from mild to

severe, against drug dose grouped into a number of classes. A further example from a more

esoteric area is shown.

Cross-classiﬁcation of whiskey for age and grade

Grade

Years/maturity 12 3

742 0

522 2

100 4

Downton, Frank (1925^1984): Downton studied mathematics at Imperial College London and

after a succession of university teaching posts became Professor of Statistics at the

University of Birmingham in 1970. Contributed to

reliability theory

and

queueing theory

Downton died on 9 July 1984.

Dragstedt^Behrensestimator: An estimator of the

median effective dose

bioassay

. See also

Reed–Muench estimator.[Probit Analysis 3rd ed., 1971, D.J. Finney, Cambridge

Unversity Press, Cambridge.]

Draughtsman’splot: Synonym for scatterplot matrix.

Drift: A term used for the progressive change in assay results throughout an assay run.

Drift parameter: See Brownian motion.

Dropout: A subject who withdraws from a study for whatever reason, noncompliance, adverse side

effects, moving away from the district, etc. In many cases the reason may not be known. The

fate of subjects who drop out of an investigation must be determined whenever possible

since the dropout mechanism may have implications for how data from the study should be

analysed. See also attrition, missing values and Diggle–Kenward model for dropouts.

[Applied Statistics, 1994, 43,49–94.]

Drug stability studies: Studies conducted in the pharmaceutical industry to measure the degrada-

tion of a new drug product or an old drug formulated or packaged in a new way. The main

study objective is to estimate a drug’s shelf life, deﬁned as the time point where the 95%

lower conﬁdence limit for the regression line crosses the lowest acceptable limit for drug

144

content according to the

Guidelines for Stability Testing

.[Journal of Pharmaceutical and

Biomedical Analysis, 2005, 38, 653–663.]

Dual scali ng: Synonym for correspondence analysis.

Dual system estimates: Estimates which are based on a census and a post-enumeration survey,

which try to overcome the problems that arise from the former in trying, but typically failing,

to count everyone.

Dummy variables: The variables resulting from recoding categorical variables with more than two

categories into a series of binary variables. Marital status, for example, if originally labelled

1 for married, 2 for single and 3 for divorced, widowed or separated, could be redeﬁned in

terms of two variables as follows

Variable 1: 1 if single, 0 otherwise;

Variable 2: 1 if divorced, widowed or separated, 0 otherwise;

For a married person both new variables would be zero. In general a categorical variable

with k categories would be recoded in terms of k  1 dummy variables. Such recoding is

used before

polychotomous variables

are used as explanatory variables in a regression

analysis to avoid the unreasonable assumption that the original numerical codes for the

categories, i.e. the values 1; 2; ...; k, correspond to an

interval scale

. This procedure is often

known as dummy coding [ARA Chapter 8.]

Duncan’s test: A modiﬁed form of the

Newman–Keuls multiple comparison test

. [SMR Chapter 9.]

Dunnett’s test: A

multiple comparison test

intended for comparing each of a number of treatments

with a single control. [Biostatistics: A Methodology for the Health Sciences, 2nd edn, 2004,

G. Van Belle, L.D. Fisher P. J. Heagerty and T. S. Lumley, Wiley, New York.]

Dunn’s test: A

multiple comparison test

based on the

Bonferroni correction

.[Biostatistics:

A Methodology for the Health Sciences, 2nd edn, 2004, G. Van Belle, L. D. Fisher P. J.

Heagerty and T. S. Lumley, Wiley, New York.]

Duration dependence: The extent to which the

hazard function

of the event of interest in a

survival analysis is rising or falling over time. An important point is that duration depend-

ence may be ‘spurious’ due to unobserved heterogeneity or

frailty

.[Review of Economic

Studies, 1982, 49, 403–409.]

Duration time: The time that elapses before an

epidemic

ceases. [Biometrika, 1975, 62, 477–482.]

Durbin^Watson test: A test that the residuals from a linear regression or

multiple regression

are

independent. The test statistic is

D ¼

i¼2

ðr

 r

i1

i¼1

where r

¼ y



and y

and

are, respectively, the observed and predicted values of the

response variable for individual i. D becomes smaller as the

serial correlations

increase.

Upper and lower critical values, D

and D

have been tabulated for different values of q (the

number of explanatory variables) and n. If the observed value of d lies between these limits

then the test is inconclusive. [TMS Chapter 3.]

D utch book: A gamble that gives rise to certain loss, no matter what actually occurs. Used as a

rhetorical device in

subjective probability

and

Bayesian statistics

.[Betting on Theories,

1992, P. Maher, Cambridge University Press, New York.]

145

Dvoretzky-Kiefer-Wolfowitz inequality: A prediction of how close an empirically deter-

mined distribution function will be to the assumed population distribution form which the

empirical samples are taken. [Annals of Mathematical Statistics, 1956, 27, 642–669.]

Dynamic allocationindices: Indices that give a priority for each project in a situation where it is

necessary to optimize in a sequential manner the allocation of effort between a number of

competing projects. The indices may change as more effort is allocated. [Multiarmed Bandit

Allocation, 1989, J.C. Gittins, Wiley, Chichester.]

Dyn a mic graph i cs: Computer graphics for the exploration of

multivariate data

which allow the

observations to be rotated and viewed from all directions. Particular sets of observations can

be highlighted. Often useful for discovering structure or pattern, for example, the presence of

clusters. See also brushing scatterplots.[Dynamic Graphics for Statistics, 1987, W.S.

Cleveland and M.E. McGill, Wadsworth, Belmont, California.]

Dynamic panel data model: A term used in

econometrics

when an

autoregressive model

speciﬁed for the response variable in a

panel study

Dyn a mic popul a t ion: A population that gains and looses members. See also ﬁxed population.

Dynamic population modelling: The application and analysis of population models that have

changing vital rates. [Dynamic Population Models, 2006, R. Schoen, Springer, New York.]

146

E: Abbreviation for expected value.

Early detection program: Synonymous with screening studies.

EAST: A computer package for the design and analysis of group sequential

clinical trials

. See also

PEST. [CYTEL Software Corporation, 675 Massachusetts Avenue, Cambridge, MA 02139,

USA.]

Eberha rdt’s statistic: A statistic, A, for assessing whether a large number of small items within

a region are distributed completely randomly within the region. The statistic is based on

the

Euclidean distance

from each of m randomly selected sampling locations to the

nearest item and is given explicitly by

A ¼ m

i¼1

j¼1

[Biometrika, 1979, 66,73–79.]

EBM: Abbreviation for evidence-based medicine.

ECM algorithm: An extension of the

EM algorithm

that typically converges more slowly than

EM in terms of i terations but can be faster in total computer time. The basic i dea of the

algorithm is to replace the M-step of each EM iteration with a sequence of S >1condi-

tional or constrained maximization or CM-steps, each of which maximizes the expected

complete-data

log-likelihood

found in the previous E-step subject to constraints on the

parameter of interest, θ, where the collection of all constraints is such that the maxi-

mization is over the full parameter space of θ. Because the CM maximizations are over

smaller dimensional spaces, often they are simpler, faster and more reliable than the

corresponding full maximization called for in the M-step of the EM algorithm. See also

ECME algorithm.[Statistics in Medicine, 1995, 14,747–68.]

ECME algorithm: The Expectation/Conditional Maximization Either algorithm which is a general-

ization of the

ECM algorithm

obtained by replacing some CM-steps of ECM which

maximize the constrained expected complete-data

log-likelihood

, with steps that maximize

the correspondingly constrained actual

likelihood

. The algorithm can have substantially

faster convergence rate than either the

EM algorithm

or ECM measured using either the

number of iterations or actual computer time. There are two reasons for this improvement.

First, in some of ECME’s maximization steps the actual likelihood is being conditionally

maximized, rather than a current approximation to it as with EM and ECM. Secondly,

ECME allows faster converging numerical methods to be used on only those constrained

maximizations where they are most efﬁcacious. [Biometrika, 1997, 84, 269–81.]

Eco log i ca l fa ll a cy: A term used when aggregated data (for example, aggregated over different

regions) are analysed and the results assumed to apply to relationships at the individual

level. In most cases analyses based on aggregated level means give conclusions very different

147

from those that would be obtained from an analysis of unit level data. An example from the

literature is a correlation coefﬁcient of 0.11 between illiteracy and being foreign born

calculated from person level data, compared with a value of −0.53 between percentage illiterate

and percentage foreign born at the State level. [Statistics in Medicine, 1992, 11,1209–24.]

Ecological statistics: Procedures for studying the dynamics of natural communities and their

relation to environmental variables.

Econometrics: The area of economics concerned with developing and applying quantitative or

statistical methods to the study and elucidation of economic principles.

EDA: Abbreviation for exploratory data analysis.

ED50: Abbreviation for median effective dose.

Edgeworth, Francis Y sidro ( 1845^1926): Born in Edgeworthstown, Longford, Ireland,

Edgeworth entered Trinity College, Dublin in 1862 and in 1867 went to Oxford University

where he obtained a ﬁrstinclassics.HewascalledtotheBarin1877.Afterleaving

Oxford and while studying law, Edgeworth undertook a programme of self study in

mathematics and in 1880 obtained a position as lecturer in logic at Kin gs College,

London later becoming Tooke Professor of Political Economy. In 1891 he was elected

Drummond Professor of Political Economy at Oxford and a Fellow of All Souls, where

he remained for the rest of his life. In 1883 Edgeworth began publication of a sequence

of articles devoted exclusively to probability and statistics in which he attempted to

adapt the statistical methods of the theory of errors to the quantiﬁcation of uncertainty in

the social, particularly the economic sciences. In 1885 he read a paper to th e Cambridge

Philosophical Society which presented, through an extensive series of examples, an

exposition and interpretation of signiﬁcance tests for the comparison of means.

EdgeworthdiedinLondonon13February1926.

Edg e w orth’sformoftheTypeAseries: An expression for representing a probability distri-

bution, f (x), in terms of

Chebyshev–Hermite polynomials

, H

, given explicitly by

f ðxÞ¼αðxÞ 1 þ

120

þ 10κ

720



where κ

are the

cumulants

of f (x) and

αðxÞ¼

ﬃﬃﬃﬃﬃﬃ



Essentially equivalent to the

Gram–Charlier Type A series

. [KA1 Chapter 6.]

Effect: Generally used for the change in a response variable produced by a change in one or more

explanatory or factor variables.

Effect cod i ng: See contrast.

Effectivesamplesize: The sample size after dropouts, deaths and other speciﬁed exclusions from

the original sample. [Survey Sampling, 1995, L. Kish, Wiley, New York.]

Effect size: Most commonly the difference between the control group and experimental group

population means of a response variable divided by the assumed common population

standard deviation. Estimated by the difference of the sample means in the two groups

divided by a pooled estimate of the assumed common standard deviation. Often used in

meta-analysis

. See also counternull-value.[Psychological Methods, 2003, 8, 434–447.]

148