Everitt B.S. The Cambridge Dictionary of Statistics

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accuracy of imputation is improved by ﬁrst forming two or more imputation classes using

control variables observed in all sample units, and then applying the procedure separately

within each imputation class for each item with missing values. [Statistics in Medicine,

1997, 16,5–19.]

Hotelling, Harold (1895^1973): Born in Fulda, Minnesota, Hotelling ﬁrst studied journalism at

the University of Washington but eventually turned to mathematics gaining a Ph.D. in

1924 for his dissertation in the ﬁeld of topology. Hotelling worked ﬁrst at Stanford

University before, in 1931, being appointed Professor of Economics at Columbia

University. His major contributions to statistical theory were in multivariate analysis and

probably his most important paper was ‘The generalization of Student’s ratio’ now known

as Hotelling’s T

. He also played a major role in the development of

principal components

analysis

and of

canonical correlations

. Elected to the National Academy of Sciences in

1972 and in 1973 to a membership of The Academia Nazionale dei Lincei in Rome.

Hotelling died on 26 December 1973 in Chapel Hill, North Carolina.

Hotelling ^ Lawley trace: See multivariate analysis of variance.

Hotelling’sT

test: A generalization of

Student’s t-test

for

multivariate data

. Can be used to test

either whether the population mean vector of a set of q variables is the null vector or whether

the mean vectors of two populations are equal. In the latter case the relevant test statistic

is calculated as







1







þ n

where n

and n

are sample sizes,



and



are sample mean vectors, and S is a weighted

average of th e separa te samp le

variance– c ovarian ce matrices

. Under the hypothesis that

the population mean vectors are the same,

þ n

 q  1

ðn

þ n

 2Þq

has an

F-distribution

with q and (n

+ n

− q − 1) degrees of freedom. See also Mahalanobis

.[Principles of Multivariate Analysis, 2nd edition, 2000, W. J. Krzanowski, Oxford

Science Publications, Oxford.]

H ot hand h ypothesis: Synonymous with streaky hypothesis .

H ouseho ld interview surveys: Surveys in which the primary

sampling units

are typically

geographic areas such as counties or cities. For each such unit sampled, there are

additional levels of subsampling involving successively smaller geographic areas, for

example, census districts, neighbourhoods within census districts and households within

neighbourhoods. Individuals within sampled households may also be subsampled. The

main purpose of the multistage cluster sampling is to lessen the number of areas to

which interviewers must travel. [ Nonresponse in Household Interview Surveys, 1998,

R. M. Groves, M. P. Couper, Jossey Bass.]

Hsu,Pao-Lu(1910^1970): Born in Beijing, China, Hsu ﬁrst studied chemistry at what was later

to become Beijing University, but transferred to the Department of Mathematics in Qin

Huo University in 1930. In 1938 he received a Ph.D. degree from University College,

London. Hsu worked in a number of areas of probability theory and mathematical

statistics particularly on the distribution of sample variances from nonnormal popula-

tions. In 1956 he was made Director of the ﬁrst research institute for probability and

statistics to be established in China. Hsu died on 18 December 1970 in Beijing.

209

Huberized estimator: Synonym for sandwich estimator.

Huber’scondition:A necessary and sufﬁcient design condition for the estimates from using

least squares estimation

in linear models to have an asymptotic normal distribution provided

the error terms are independently and identically distributed with ﬁnite variance. Given

explicitly by

lim

n!1

max

1in

¼ 0

where h

are the diagonal elements of the

hat matrix

.[Robust Statistics, 2003, P. J. Huber,

Wiley, New York.]

Human capital model: A model for evaluating the economic implication of disease in terms of the

economic loss of a person succumbing to morbidity or mortality at some speciﬁed age.

Often such a model has two components, the direct cost of disease, for example, medical

management and treatment, and the indirect cost of disease, namely the loss of economic

productivity due to a person being removed from the labour force. [Berichte über

Landwirtschaft, 1996, 74, 165–85.]

Human height growth curves: The growth of human height is, in general, remarkably regular,

apart from the pubertal growth spurt. A satisfactory longitudinal

growth curve

is extremely

useful as it enables long series of measurements to be replaced by a few parameters, and

might permit early detection and treatment of growth abnormalities. Several such curves have

been proposed, of which perhaps the most successful is the following ﬁve-parameter curve

X ¼ A 

2ðA BÞ

exp½Cðt  EÞ þ exp½Dðt  EÞ

where t = time (prenatal age measured from the day of birth), X = height reached at

age t, A = adult height, B = height reached by child at age E, C =aﬁrst time-scale factor in

units of inverse time, D = a second time-scale factor in units of inverse time, E = approximate

time at which the pubertal growth spurt occurs. [Biometrics, 1988, 44, 995–1003.]

Hurdle model: A model for count data that postulates two processes, one generating the zeros in

the data and one generating the positive values. A binomial model governs the binary

outcome of whether the count variable has a zero or a positive value. If the value is

positive the ‘hurdle is crossed’ and the

conditional distribution

of the positive values is

a suitable

zero-truncated probability distribution

.[Regression Analysis of Count Data,

1998, C. A. Cameron and P. K. Trivedi, Cambridge University Press, Cambridge.]

Huynh ^ Feldt correction: A correction term applied in the analysis of data from

longitudinal

studies

by simple

analysis of variance

procedures, to ensure that the within subject

F-tests

are approximately valid even if the assumption of

sphericity

is invalid. See also

Greenhouse–Geisser correction and Mauchly test. [MV2 Chapter 13.]

Hybrid log-normal distr ibution: The distribution of a random variable, X, when Y = log (ρ X)+

ρ X , ρ > 0 is normally distributed with mean μ and variance σ

.Asρ increases the shape of

the distribution changes from log-normal to normal. For ﬁxed ρ the distribution is of log-

normal type for small values of X but for large X it is of normal shape. The distribution has

been used as a model for worker’s periods of exposure to radiation. [Japanese Journal of

Applied Statistics, 1986, 15,1–14.]

Hyperbolic distributions: Probability distributions, f (x), for which the graph of log f (x)isa

hyperbola. [Statistical Distributions in Scientiﬁc Work, Volume 4, 1981, edited by C. Taillie,

G. P. Patil and B. Baldessari, Reidel, Dordrecht.]

210

Hyperexponential distribution: A term sometimes used for a mixture of two

exponential

distributions

with different means, λ

and λ

, and mixing proportion p, i.e. the probability

distribution given by

f ðxÞ¼pl

l

þð1  pÞl

l

Hypergeometric distribution: A probability distribution associated with

sampling without

replacement

from a population of ﬁnite size. If the population consists of r elements of

one kind and N - r of another, then the probability of ﬁnding x elements of the ﬁrst kind

when a random sample of size n is drawn is given by

PðxÞ¼



N r

n x



The mean of x is nr/N and its variance is



1 



N n

N 1



When N is large and n is small compared to N, the hypergeometric distribution can be

approximated by the

binomial distribution

. [STD Chapter 20.]

Hyperparameter: A parameter (or vector of parameters) θ

that indexes a family of possible

prior distributions

for a parameter θ

Bayesian inference

, i.e. θ

is a parameter of a

distribution on parameters. An investigator needs to specify the value of θ

in order to

specify the chosen prior distribution. [Kendall’s Advanced Theory of Statistics, Volume 2B,

2nd edition, 2004, A. O’Hagan and J. Forster, Arnold, London.]

Hyperprior: A

prior distribution

on a hyperparameter. [Bayesian Theory, 2000, J. M. Bernardo and

A. M. F. Smith, Wiley, New York.]

Hypothesis testi ng: A general term for the procedure of assessing whether sample data is con-

sistent or otherwise with statements made about the population. See also null hypothesis,

alternative hypothesis, composite hypothesis, signi ﬁcance test, signiﬁcance level,

type I and type II error. [SMR Chapter 8.]

211

ICM: Abbreviation for iterated conditional modes algorithm.

IDA: Abbreviation for initial data analysis.

Idempotent matrix: A matrix, A, with the property that A ¼ A

.[Linear Models, 1971, S. R. Searle,

Wiley, New York.]

Identification: A parametric model is said to be identiﬁed if there is a unique value θ

of the

parameter vector θ that can produce a given probability distribution for the data. If the

model is not identiﬁed consistent estimation is generally precluded. More formally, two

values of θ, θ

and θ

are called observationally equivalent if they produce the same

distribution of the data Y (i.e. f(Y; θ

)=f(Y;θ

) for all Y). θ is locally identiﬁed at a parameter

point θ

if there does not exist a value θ

such that θ

and θ

are observationally equivalent.

θ is globally identiﬁed if for any parameter point there is no other observationally equivalent

point. [Econometrica, 1971, 39, 577–591.]

Identification keys: Devices for identifying samples from a set of known taxa, which have a tree-

structure where each node corresponds to a diagnostic question of the kind ‘which one of a

named set of attributes does the specimen to be identiﬁed possess?’ The outcome determines

the branch of the tree to follow and hence the next diagnostic question leading ultimately to

the correct identiﬁcation. Often there are only two attributes, concerning the presence and

absence of a particular character or the response to a binary test, but multi-state characters or

tests are permissible. See also decision tree.[Journal of the Royal Statistical Society, Series

A, 1980, 143, 253–92.]

Identitymatrix: A diagonal matrix in which all the elements on the leading diagonal are unity and all

other elements are zero.

Id l e col um n meth od: See Taguchi’s idle column method.

Ignorability : A missing data mechanism is said to be ignorable for

likelihood

inference if (1) the joint

likelihood for the responses of interest and missing data indicators can be decomposed into

two separate components (containing the parameters of main interest and the parameters of

the missingness mechanism, respectively) and (2) the parameters for each component are

distinct in the sense that there are no parameter restrictions across the components. The

component for the missingness mechanism can then be ignored in statistical inference for the

parameters of interest. Ignorability follows if

missing values

are missing completely

at random or missing at random and the parameters are distinct. [Biometrika, 1976, 63,

581–592.]

Il l conditioned matrix: A matrix X for which XX

has at least one

eigenvalue

near zero so that

numerical problems arise in computing ðXX

1

. Linear Regression Analysis, 2nd edition,

2003, G. A. F. Seber and A. J. Lee, Wiley, New York.]

Image restoration: Synonym for segmentation.

212

Immig ratio n-emig ration models.: Models for the development of a population that is aug-

mented by the arrival of individuals who found families independently of each other.

[Branching Processes with Biological Applications, 1975, P. Jagers, Wiley, New York.]

Immune proportion: The proportion of individuals who are not subject to death, failure, relapse,

etc., in a sample of

censored survival times

. The presence of such individuals may be

indicated by a relatively high number of individuals with large censored survival times.

Finite mixture models

allowing for immunes can be ﬁtted to such data and data analysis

similar to that usually carried out on survival times performed. An important aspect of such

analysis is to consider whether or not an immune proportion does in fact exist in the

population. See also cure models.[Biometrics, 1995, 51, 181–201.]

Imperfect detectability: A problem characteristic of many surveys of natural and human popula-

tions, that arises because even when a unit (such as a spatial plot) is included in the sample, not

all individuals in the selected unit may be detected by the observer. For example, in a survey of

homeless people, some individuals in the selected units may be missed. To estimate the

population total in a survey in which this problem occurs, both the sampling design and the

detection probabilities must be taken into account. [Biometrics, 1994, 50,712–24.]

Importance sampling: The estimation of expectations of random variables with respect to a

distribution of interest (the target distribution) using samples from another distribution

(the trial distribution). One motivation is that sampling from the trial distribution can

serve as a variance reduction technique, another that it may be easier to simulate from the

trial distribution than from the target distribution. More formally, let gðxÞ be the target

density we wish to integrate and gðxÞ

hðxÞ the trial distribution. Then

gðxÞdx ¼

gðxÞ

hðxÞ

dx ¼

gðxÞ

hðxÞ

hðxÞdx ¼ E

gðxÞ

hðxÞ



;

as long as hðxÞ 6¼ 0, where E

denotes expectation with respect to h. This gives a Monte

Carlo estimator



gðxÞ¼

i¼1

gðX

hðX

where X

~hðxÞ. The Monte Carlo variance of



gðxÞ is minimized if the importance sampling

function h(x) is proportional to the target distribution g(x). Hence, a good importance

sampling function is almost proportional to the target distribution. [Statistical Science,

1998, 13, 163–185.]

Imprecise probabilities: An approach used by

soft methods

in which uncertainty is represented by

closed, convex sets of probability distributions and the probability of an event is speciﬁed as

an interval of possible values rather than only as a precise one. The amount of imprecision is

the difference between the upper and lower probabilities deﬁning an interval. See also belief

functions.[Journal of the Royal Statistical Society, Series B, 1996, 58,3–57.]

Improper prior distribution: In Bayesian statistics a

prior distribution

is called improper if it

depends on the data or does not integrate to 1. [Bayesian Data Analysis, 2004, A. Gelman,

J. B. Carlin, H. S. Stern and D. B. Rubin, Chapman and Hall/CRC, Boca Raton.]

Imputation: A process for estimating

missing values

using the non-missing information available for

a subject. Many methods have been developed most of which can be put into the following

multiple regression

framework.

¼ b

mij



213

where

is the imputed value of y for subject i for whom the value of y is missing, the x

mij

are the values of other variables for subject i and the b

are the estimated regression

coefﬁcients for the regression of y on the x variables obtained from the subjects having

observed y values;



is a residual term. A basic distinction between such methods involves

those where the residual terms are set to zero and those where they are not. The former may

be termed deterministic imputation methods and the latter stochastic imputation methods.

Deterministic methods produce better estimates of means but produce biased estimates of

shape parameters. Stochastic methods are generally preferred. See also multiple imputation

and hot deck. [MV1 Chapter 1.]

IMSL ST AT /LIBRARY: A Fortran subprogram library of useful statistical and mathematical proce-

dures. [Visual Numerics Inc. Corporate Headquarters, 12657 Alcosta Boulevard, Suite 450,

San Ramon, CA 94583, USA.]

Incidence: A measure of the rate at which people without a disease develop the disease during a

speciﬁc period of time. Calculated as

incidence ¼

number of new cases of a disease over a period of time

population at risk of the disease in the time period

it measures the appearance of disease. See also prevalence. [SMR Chapter 14.]

Inc i dental parameter prob l em: A problem that sometimes arises when the number of parame-

ters increases in tandem with the number of observations. For example, models for

panel

studies

may include individual-speciﬁc ﬁxed intercepts, called “incidental parameters”,in

addition to the “structural parameters” of interest, making the number of parameters tend to

inﬁnity as the number of individuals tends to inﬁnity. In some models, such as logistic

models with individual-speciﬁc ﬁxed intercepts, this leads to inconsistent

maximum like-

lihood estimates

of the structural parameters. [Econometrica, 1948, 16,1–32.]

Inclusion and exclusion criteria: Criteria that deﬁne the subjects that can be accepted into a

study, particularly a

clinical trial

. Inclusion criteria deﬁne the population of interest, exclu-

sion criteria remove people for whom the study treatment is contraindicated. [Statistics in

Medicine, 1994, 9,73–86.]

I ncl us io n p r o ba bility: See simple random sampling.

Incomplete beta function: See beta function.

Incomplete block design: An experimental design in which not all treatments are represented in

each block. See also balanced incomplete block design.[Planning of Experiments, 1992,

D. R. Cox, Wiley, New York.]

Incomplete contingency tables:

Contingency tables

containing

structural zeros

Incomplete gamma functi on: See gamma function.

Incubation period: The time elapsing between the receipt of infection and the appearance of

symptoms. The length of the incubation period depends on the disease, ranging from days

in, for example, malaria, to years in something like AIDS. Estimation of the incubation

period is important in investigations of how a disease may spread and in the projection of the

evolution of an epidemic. [Statistics in Medicine, 1990, 9, 1387–416.]

Independence: Essentially, two events are said to be independent if knowing the outcome of one tells

us nothing about the other. More formally the concept is deﬁned in terms of the probabilities

of the two events. In particular two events A and B are said to be independent if

214

PrðA and BÞ¼PrðAÞPrðBÞ

where Pr(A) and Pr(B) represent the probabilities of A and B. See also conditional proba-

bility and Bayes’ theorem. [KA1 Chapter 1.]

Ind ependent component analysis (ICA ) : A method for analyzing complex measured quanti-

ties thought to be mixtures of other more fundamental quantities, into their underlying

components. Typical examples of the data to which ICA might be applied are:

electroencephalogram (EEG) signal, which contains contributions from many differ-

ent brain regions,

person’s height, which is determined by contributions from many different genetic and

environmental factors.

[Independent Component Analysis, 2001, A. Hyvarinen, J. Karhunen and E. Oja, Wiley,

New York.]

Independent sampl es t-test: See Student’s t-test.

Independent variables: See explanatory variables.

Index of clump ing: An index used primarily in the analysis of

spatial data

, to investigate the pattern

of the population under study. The index is calculated from the counts, x

; x

; ...; x

obtained from applying

quadrant sampling

ICS ¼ s



x  1

where



x and S

are the mean and variance of the observed counts. If the population is

‘clustered’, the index will be large, whereas if the individuals are regularly spaced the index

will be negative. The

sampling distribution

of ICS is unknown even for simple models of the

underlying mechanism generating the population pattern. [Spatial Data Analysis by

Example, 1987, G. Upton and B. Fingleton, Wiley, Chichester.]

Index of dispersion: A statistic most commonly used in assessing whether or not a random variable

has a

Poisson distribution

. For a set of observations x

; x

; ...; x

the index is given by

D ¼

i¼1

ðx

xÞ

=x

If the population distribution is Poisson, then D has approximately a

chi-squared distribution

with n  1 degrees of freedom. See also binomial index of dispersion.[Biometrika, 1966,

53, 167–82.]

Index number: A measure of the magnitude of a variable at one point (in time, for example), to its

value at another. An example is the

consumer price index

. The main application of such

numbers is in economics. [The Making of Index Numbers, 1922, I. Fisher, Houghton,

Mifﬂin, Boston.]

Index plot: A plot of some diagnostic quantity obtained after the ﬁtting of some model, for example,

Cook’s distances

, against the corresponding observation number. Particularly suited to the

detection of

outliers

. [ARA Chapter 10.]

Indianbuffetprocess : A

stochastic process

used in

unsupervised pattern recognition

when deriving

a particular probability distribution. The process is deﬁned by a culinary metaphor based on

Indian restaurants in London that offer lunchtime buffets with an apparently inﬁnite number of

dishes; N customers enter such a restaurant one after another. Each customer encounters a

215

buffet consisting of inﬁnitely many dishes arranged in a line. The ﬁrst customer starts at the left

of the buffet and takes a serving from each dish, stopping after a Poisson(α)numberofdishes

as his plate becomes overburdened. The ith customer moves along the buffet, sampling dishes

in proportion to their popularity, serving himself with probability

,wherem

is the number of

previous customers who have sampled a dish. Having reached the end of all previous sampled

dishes, the ith customer then tries a Poisson



number of new dishes. [Technical Report

2005–001, Gatsby Computational Neuroscience Unit, University College, London.]

Indicator variable: Synonym for

binary variable

. Also used for a

manifest variable

that is thought to

be related to an underlying

latent variable

in the context of

structural equation models

Indirect least squares: An estimation method used in the ﬁtting

of structural equation models.

Ordinary least squares

is ﬁrst used to estimate the

reduced form

parameters. Using the

relations between structural and reduced form parameters it is subsequently solved for the

structural parameters in terms of the estimated reduced form parameters. Indirect least

squares estimates are consistent but not unbiased. [Econometric Methods, 4th edn, 1997,

J. Johnston and J. DiNardo, McGraw-Hill, New York.]

Indirect standardization: The process of adjusting a crude mortality or morbidity rate for one or

more variables by using a known

reference population

. It might, for example, be required to

compare cancer mortality rates of single and married women with adjustment being made for

the likely different age distributions in the two groups.

Age-speciﬁc mortality rates

in the

reference population are applied separately to the age distributions of the two groups to

obtain the expected number of deaths in each. These can then be combined with the observed

number of deaths in the two groups to obtain comparable mortality rates. See standardized

mortality ratio (SMR) and direct standardization.[Statistics in Medicine, 1987, 6,61–70.]

Individualdifferences scaling: A form of

multidimensional scaling

applicable to data consisting

of a number of

proximity matrices

from different sources, i.e. different subjects. The method

allows for individual differences in the perception of the stimuli by deriving weights for each

subject that can be used to stretch or shrink the dimensions of the recovered geometrical

solution. [MV1 Chapter 5.]

INDSCAL: Acronym for individual differences scaling.

In fa nt mortal ity rate: The ratio of the number of deaths during a calendar year among infants

under one year of age to the total number of live births during that year. Often considered as a

particularly responsive and sensitive index of the health status of a country or geographical

area. The table below gives the rates per 1000 births in England, Wales, Scotland and

Northern Ireland in both 1971 and 1992.

1971 1992

England 17.5 6.5

Wales 18.4 5.9

Scotland 19.9 6.8

NI 22.7 6.0

I nfect ious peri od: A term used in describing the progress of an

epidemic

for the time following the

latent period and during which a patient infected with the disease is able to discharge

infectious matter in some way and possibly communicate the disease to other susceptibles.

[Analysis of Infectious Disease, 1989, N. G. Becker, Chapman and Hall/CRC Press,

London.]

216

Inference: The process of drawing conclusions about a population on the basis of measurements or

observations made on a sample of units from the population. See also frequentist inference

and Bayesian inference. [KA1 Chapter 8.]

Infertile worker effect: The observation that working women may be relatively infertile since

having children may keep women away from work. See also healthy worker effect.

[Journal of Occupational and Environmental Medicine, 1996, 38, 352–8.]

Infinitely divisible distribution: A probability distribution f(x) with corresponding

characteristic

function

ðtÞ, which has the property that for every positive integer n there exists a

characteristic function 

ðtÞ such that



ðt Þ¼½ðtÞ

This implies that for each n the distribution can be represented as the distribution of the

convolution (sum) of n independent random variables with a common distribution. The

chi-

squared distribution

is an example. [KA1 Chapter 4.]

Influence: A term used primarily in regression analysis to denote the effect of each observation on the

estimated regression parameters. One useful index of the inﬂuence of each observation is

provided by the diagonal elements of the

hat matrix

.[Technometrics, 1977, 19,15–18.]

Influence statistics: A range of statistics designed to assess the effect or inﬂuence of an observa-

tion in determining the results of a regression analysis. The general approach adopted is to

examine the changes that occur in the regression coefﬁcients when the observation is

omitted. The statistics that have been suggested differ in the particular regression results

on which the effect of deletion is measured and the standardization used to make them

comparable over observations. All such statistics can be computed from the results of the

single regression using all data. See also Cook’s distance, DFFITS, DFBETAS,

COVRATIO and hat matrix. [ARA Chapter 10.]

Influential observation: An observation that has a disproportionate inﬂuence on one or more

aspects of the estimate of a parameter, in particular, regression coefﬁcients. This inﬂuence

may be due to differences from other subjects on the explanatory variables, an extreme value

for the response variable, or a combination of these.

Outliers

, for example, are often also

inﬂuential observations. [ARA Chapter 10.]

In f o rmati o n matr ix: See Fisher’s information.

Information theory: A branch of applied probability theory applicable to many communication

and signal processing problems in engineering and biology. Information theorists devote

their efforts to quantitative examination of the following three questions;:

What is information?

What are the fundamental limitations on the accuracy with which information can be

transmitted?

What design methodologies and computational algorithms yield practical systems for

communication and storing information that perform close to the fundamental limits

mentioned previously?

See also entropy.[Information Theory and Coding, N. Abrahamson, 1968, McGraw-Hill,

New York.]

Informative censoring:

Censored observations

that occur for reasons related to treatment, for

example, when treatment is withdrawn as a result of a deterioration in the physical condition

217

of a patient. This form of censoring makes most of the techniques for the analysis of survival

times, for example, strictly invalid. [Statistics in Medicine, 1992, 11, 1861–70.]

Informative missing values: See missing values.

Informative prior: A term used in the context of

Bayesian inference

to indicate a

prior distribution

that reﬂects empirical or theoretical information regarding the value of an unknown param-

eter. [KA1 Chapter 8.]

Informed consent: The consent required from each potential participant prior to random assign-

ment in a

clinical trial

as speciﬁed in the 1996 version of the

Helsinki declaration

intended to

guide physicians conducting therapeutic trials, namely: in any research on human beings,

each potential subject must be adequately informed of the aims, methods, anticipated

beneﬁts and potential hazards of the study and the discomfort it may entail. He or she

should be informed that he or she is at liberty to abstain from participation in the study and he

or she is free to withdraw his or her consent to participation at any time. The physician

should then obtain the subject’s freely-given informed consent, preferably in writing.

[Journal of the American Medical Association, 1997, 277, 925–6.]

Initial data analysis (I D A): The ﬁrst phase in the examination of a data set which consists of a

number of informal steps including

checking the quality of the data,

calculating simple summary statistics and constructing appropriate graphs.

The general aim is to clarify the structure of the data, obtain a simple descriptive summary,

and perhaps get ideas for a more sophisticated analysis. [Problem Solving, A Statistician’s

Guide, 1988, C. Chatﬁeld, Chapman and Hall/CRC Press, London.]

Inliars: A facetious term for

inliers

Inliers: A term used for the observations most likely to be subject to error in situations where a

dichotomy is formed by making a ‘cut’ on an ordered scale, and where errors of classiﬁca-

tion can be expected to occur with greatest frequency in the neighbourhood of the cut.

Suppose, for example, that individuals are classiﬁed say on a hundred point scale that

indicates degree of illness. A cutting point is chosen on the scale to dichtomize individuals

into well and ill categories. Errors of classiﬁcation are certainly more likely to occur in the

neighbourhood of the cutting point. [Transformation and Weighing in Regression, 1988,

R. J. Carroll and D. Ruppert, Chapman and Hall/CRC Press, London.]

Innovati onal outlier: See additive outlier.

Instantaneous countprocedure: A sampling method used in biological research for estimating

population numbers.

Instantaneous deathrate: Synonym for hazard rate.

Institutional surveys: Surveys in which the primary

sampling units

are institutions, for exam-

ple, hospitals. Within each sampled institution, a sample of patient records is selected.

The main purpose of the two-stage design (compared to a simple random sample) are to

lessen the number of institutions that need to be subsampled, and to avoid constructing

a sampling frame of patient records for the entire population. Stratiﬁed sampling

involving selecting institutions with differing probabilities based on some institutional

characteristic (e.g. size) is typically used to lessen the variability of estimators. See also

cluster sampling.[A Concept in Corporate Planning, 1970, R. L. Ackoff, Wiley, New

York.]

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