ASSESSMENT OF GROWTH DEVELOPMENT IN CHILDREN · ASSESSING GROWTHAND DEVELOPMENT the latter case, the standard deviations are used essentially as percentiles (see Fig. 1); the given

THE ASSESSMENT OF GROWTH AND DEVELOPMENTIN CHILDREN

BY

J. M. TANNERFrom the Sherrington School of Phvsiology, St. Thomas's Hospital, London

(RECEVED FOR PUBLICATnoN JULY 2, 1951)

During the last decade or two, as part of thegeneral application of preventive medicine to humanaffairs, an increasing interest has been taken in thegrowth of children. To a large extent this followedthe realization on the one hand that malnutritioncould cause a retardation of growth in the child,and on the other, that differences in size did actuallyexist between children belonging to different socialclasses. From this it was a short step to theassumption that the rate of growth itself affordedan index of the nutrition, or at least of somethingcalled the 'general condition of the child; and onthis premise, both in relation to groups and toindividuals, paediatricians, public health officers andthe School Medical Service began to take regularmeasurements of the children under their care.Having got the measurements it was necessary tohave something with which to compare them, andstandard figures from supposedly good samples ofsupposedly healthy children were soon forthcoming.The Baldwin-Wood tables, for example, a 1923revision of figures first published in 1910, werewidely used for a time and found their way intomany textbooks of paediatrics. Alongside thesalutary results of all this activity, two bad effectswere clearly to be seen. When standards were firstpublished what is implied by 'the spread of thenormal' and 'the limits of the normal zone' wasnot at all generally understood. Anxious parents,consulting the oracular weighing-machine, plaguedtheir practitioners with complaints of their childrenbeing five pounds under- or over-weight for theirheight and age, and this despite both mother andfather being miracles of thinness or rotundity. Alsoit began to be quite uncritically assumed that thefaster you grew the better it was, and since the moreyou ate the faster you grew-particuilarly in weight-an era of stuffing babies and children regardless ofall psychiatric or humanitarian principles began.

Only recently have any voices been raised againstthis trend, but there are signs that these are nowmaking themselves heard, and animal evidence onfeeding and longevity (Ball, Barnes and Visscher,1947), though probably not strictly relevant, willdoubtless help to redress the balance.

Meanwhile, more and more standards have beenpublished, most using height and weight combinedwith other anthropometric measurements and some,in addition, assessments of maturity by hand,radiograph or bodily appearance. The situation hasgrown somewhat confusing and a general clarifica-tion would seem useful at the present juncture. Itis the aim of this paper, therefore, to give a coherentaccount of the standards in use and the principleson which they are constructed, using language asnon-technical as is possible without shirking theissues involved. It is foolish to pretend that any ofthe methods so far proposed are ideal or even verysatisfactory, and the reader must not imagine thatat the end he will emerge with a finally chosenfoolproof, automatic system for use on all occasions:it is hoped, rather, that he may be brought to aclearer conception of the methods at presentavailable, the foundations on which each is based,and the uses to which each can and cannot be put.A new arrangement both for graphing and reportinggrowth progress is suggested in Figs. 5 and 8, butthe suggestion is a tentative one requiring practicaltest, and the arrangement is certainly not as suitablefor some periods of growth as for others: at puberty,for example, it seems likely that some slight com-plications will have to be introduced if the precisionof the standards is to be maintained.The paper is divided into sections: the meaning

of abnormal; percentiles versus standard deviations;distance versus velocity standards; distancestandards available (measurements consideredsingly); use of distance standards for assessing

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ASSESSING GROWTH AND DEVELOPMENT

velocity; multiple measurement distance standards;a suggested form for combined distance, velocityand standard-score difference standards; standardsfor maturity; conclusion.

The Meaning of ' bnormal'The point of any standard of whatever sort is to

enable the physician, nurse or whoever it may be togive at least a tentative answer to the question, ' Isthis child abnormal ? ' If the answer is no, theanxious mother is reassured; if yes, further stepsare taken to eradicate or minimize the abnormality,and to remove, if possible, its source. But thisquestion is not quite as simple as may appear atfirst sight and we must begin by getting clear in ourminds just what the question implies and just whatsort'of an answer it is possible to give.We shall consider in this section only one single

measurement; let us say of stature. If we measurea very large number of 6-year-old children, allhealthy so far as we know, we shall find a few shortones, a few tall ones and a lot of middling height.If we plot a graph of the number of children alongthe y axis against stature along the x axis we willhave a series of points, and if we join these by asmoothed curve we shall have the frequencydistribution curve illustrated in Fig. IA and IB;this is a Gaussian or normal curve of distribution.In Fig. IA a series of vertical lines have been put in,delimiting the percentiles of the distribution; by thisis meant that 1% of the population are smaller thanthe stature given by the vertical line marked 1,2 -50 are smaller than the stature given at theline 2 5, and so on. For this sort of distributioncurve the mean stature of the group and the 50thpercentile coincide; just half the population arebelow the mean stature and half above it. Now ifwe have a 6-year-old child M we can immediatelycompare his stature to that of this standardizingpopulation by seeing which percentile on the figurehe lies nearest. If his stature is the same as thatof the 95th percentile we can say that only 500 ofhealthy children of this age are taller than M. If itlies at the 99th percentile, only I 00 of healthychildren are taller. If M is as tall as this thenobviously the suspicion is aroused that he is4 abnormally ' tall; in other words, that he is notreally a member of this healthy population to whichhe is being compared, but of another, unhealthypopulation.Now suppose we have a second group of children,

all of whom have acidophil adenomata of thepituitary, mid-brain tumours and so forth. This isthe abnormal population, and on average itsmembers will be taller than the members of thenormal population. But the two populations may

overlap in distribution, and we then get the situationhypothetically illustrated in Fig. 2; in general theunhealthy population is likely to be a mixture comingfrom various causes of ill-health with varying effects,producing a frequency distribution which is notGaussian and has a large scatter. We can nowreturn to child M, stature at the 99th percentile,with a clear idea of what we mean by affirming ordenying that he is abnormal. Since the populationsoverlap in this region it is not possible to say withcertainty that M belongs to one or to the other.All we can state is the probability of his belonging toone or the other, and this probability we can stateprecisely if we know the distributions of the twopopulations. In practice we usually do not knowthe distribution of the unhealthy population and welay down arbitrary 'limits of normality '. It isessential to recognize that these are arbitrary, andto understand what they imply. Suppose we takethe stand that anybody over the 95th percentile shallbe called ' abnormally tall '. Most, perhaps, of theactually abnormally tall would be picked up by thisprocedure, but at the expense of including in thiscategory five out of every 100 normal children. Ifwe adopt the 99th percentile as the limit, then wemay pick up fewer real abnormals, but we shallonly call one normal person in every 100 abnormal.The limits of normality we should adopt mustdepend on the use to which they are going to be put;if the result of being classified as abnormal wasimmediate and serious operation, we should haveto put the limit even beyond the 99th percentile,to ensure we operated on very few normals, but ifstature is being used as a first screening test forsuspected malnutrition, say, with a result nothingmore drastic than a visit to the specialist and someextra milk in the mornings, our limits could be muchlower, perhaps even at the 80th, or in this particularexample, its lower equivalent the 20th, percentile.This sort of problem, though stated here in some-what academic terms, arises acutely sometimes inpaediatric practice, as, for example, in whether ornot to explore for a possible tumour in a girl whobegins to menstruate somewhat earlier than usual.

Percentiles versus Standard DeviationsStandards of growth in current use employ either

the percentile division outlined above or else adivision of the healthy population by standarddeviations* (e.g. Sontag and Revnolds, 1945). In

* The standard deviation (a) is a measure of the spread of afrequency distribution. It is particularly appropriate to Gaussiandistributions, in which the correspondence of various multiples of ato various percentiles can be seen from Figs. IA and lB. It isestimated from a sample of readings as the square root of the sumof the squares of the desiations of the readings from their meandivided by one less than the number of readings.

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ARCHIYES OF DISEASE IN CHILDHOOD

PERCENTILE

STATURE, PEICETtLES

B

-3 -Z-2

STANDARDDEVIATIONDIVISION

STATURE. STANDARD DEVIATION UNTS

NORMAL DISTRIBUTION

PEAKED AND POSITIVELY SKEWED DISTRIBUTION

F

957. POPULATION LIMITS FOR UPPER 95- PERCENTILE AND +1-65 6 COMPARED.

SAMPLE SIZE 100, d UNITY, NORMAL DISTRIBUTION

FKG. 1.-To illustrate the relation of percentile and standard deviation divisions of A and B a normally

distributed population, C and D a peaked and positively skewed distribution. E and F show the sampling limitsof the upper 95% point in a normal distribution.

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ASSESSING GROWTH AND DEVELOPMENTthe latter case, the standard deviations are usedessentially as percentiles (see Fig. 1); the givenchild's stature is found to be greater than the meanby a certain figure and this figure is so many, say,2 3, standard deviations (a). By reference to a tableof the Gaussian curve it is found that only 1% of the

PP L'L r.A : -

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FIG. 2.-Possible overlap of a healthy and unhealthypopulation (hypothetical).

population are taller than 2- 3a above the mean,and the interpretation and the laying down of limitsproceeds as before. In other words, provided thepopulation distribution is Gaussian, as in Fig. IAand B, 2 -3a corresponds to the 99th percentile,-2-3a to the first percentile, *1 65a to the 95thpercentile, -1 65a to the fifth percentile, and

O- 67a to the 25th and 75th percentiles.This reasoning, however, breaks down if the

distribution of the healthy population for somemeasurement is not Gaussian, but skewed, as inFig. IC and D. Here a distribution curve similarto that usuallv found for body weight is given; it isnot Gaussian, but has a higher peak and a longertail out to the right. (Weight, it may be noted, isthe most highly skewed of all the commonly usedmeasurements with the exception of subcutaneoustissue thickness; most length measurements haveGaussian distributions, and breadths, depths andsome circumferences tend to be a little skewed inthe same direction as weight.) In such a skeweddistribution percentiles can still be drawn in, as inFig. IC, though the 50th percentile no longercorresponds either to the peak of the curve or tothe value of the arithmetic mean. But as can beseen from Fig. ID the standard deviations no longercorrespond to the same percentiles as for theGaussian curve. We can no longer say that a childof +2-3a is exceeded in weight by 1,' of thehealthy population; clearly he is exceeded by more.Thus the use of standard deviation divisions isfraught with errors of interpretation unless thepopulation distribution is Gaussian.

There are, however, two advantages in the use ofstandard deviations rather than percentiles. First,

there is the relatively unimportant one that thepresentation of standard data is simplified; all thatneed be given is the mean and the standarddeviation, the table of the Gaussian curve forpassing from standard deviations to percentiles beingin any book of elementary statistics. Secondly,there is a more telling advantage of a biometricalnature. All the standard data published are dataon samples of healthy children, not the completemeasurements of every healthy child in the country(let alone the extra ones needed by the mathe-maticians to make their population infinite). Mostof the samples consist of a few hundred children ateach age; the published standards, however, arefor the whole healthy population. We find the95th percentile for our sample, and from thisestimate the 95th percentile for our whole popula-tion. The estimate is subject to a certain amountof error; all we can say with confidence is that thepopulation 95th percentile lies between the twolimits illustrated in Fig. IE by the two verticalinterrupted lines (unless we have been so unlucky asto have struck a sample which would only occurless than five times in 100, in which case the popula-tion value will lie actually outside these limits). Inthe same way we can calculate the standard deviationfrom our sample and estimate the 95th percentile ofthe population as 1 -65 standard deviations, but inthis case the limits between which our populationfigure is fairly sure to lie are much narrower,provided the distribution is Gaussian. This isillustrated in Fig. IF; compare the position of thevertical interrupted lines with Fig. IE. Looked atanother way, it requires more children in thestandardizing sample to estimate the percentiles forthe population to a given degree of accuracy thanit does to estimate the standard deviation. In fact,it needs, in a Gaussian distribution, just four timesas many to estimate the 95th percentile with thesame accuracv as the 1 65a level, and 14 times asmany to estimate the 97 5 percentile with the sameaccuracy as its corresponding 2a level.The question can be sumned up thus: if the

distribution of the measurement is Gaussian or verynear it, then standard deviation divisions and limitsof normality are preferable. But if the distributionis non-Gaussian, then percentile division has to beused since the standard deviation method will notlocate the point required; in technical language, itis biased. Just where the degree of skewness in thedistribution balances the loss of precision due to thelarger sampling error is a nice point and one notpractically clear (a small bias may be permissibleif a great gain in precision accompanies it). Con-sequently it is not possible to choose flatly betweenthe two methods at present; perhaps the most

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ARCHIVES OF DISEASE IN CHILDHOOD

rewarding approach to skewed distributionsultimately may be to use transformations (e.g. logweight or index weight 0-8 instead of weight) whichwill turn them into Gaussian ones, but at present toolittle is known about most anthropometric distribu-tions for this to be practicable. An equivalent andpractically simpler approach would be to tabulatethe standard deviations and values corresponding,in the various skewed anthropometric distributions,to the first, fifth, 50th, 95th and 99th percentiles.

Distance versus Velocity StandardsWe have now discussed what we mean by

abnormal, and how we judge whether a given childreaches or does not reach our arbitrary limits ofnormality. We must next consider what sort ofstandards exist for judging children, and whatadvantages and disadvantages each possesses. Letus take first the measurement of one single dimensiononlv, such as stature. There are four questions wemay ask about a given child M. A. Is M abnorm-ally tall or short at a particular age, sal 6 ? B. DidM grow abnormally fast or slowly during aparticular period, say 5 to 6 ? C. Was M'sdeceleration from the period 5 to 6 years to theperiod 6 to 7 years abnormally large or small ?D. Was M's curve of growth in stature abnormal inany respect from birth to age 7 or to adulthood ?Growth is a form of motion, and question A seeks

to characterize the motion by the distance achievedin a certain time, B by the velocity over a certainperiod, C by acceleration and D by a more complexconsideration of the whole curve of motion frombirth onwards. Question D is the most searching,but we may dismiss it at once, for it will be manydecades before any acceptable standards forindividual birth-to-maturity curves are available.Question C is almost equally impracticable atpresent and we are left with a choice betweendistance and velocity standards, answering questionsA and B respectively.

Velocity Standards. Which question is the mostrewarding to answer varies somewhat with circum-stances, but other things being equal, it seems to melikely that the testing of velocity, or increments ofgrowth, is to be preferred. Pathogenic factors wouldusually affect rate of growth directly and distanceachieved only after the altered rate has had timeto produce its result, so that one would expectearlier diagnoses of abnormality to be made byreference to rate. In this opinion also I am in thebest possible company, for Shuttleworth hasadvocated using increments since 1934. All thesame, velocity standards have never been seriouslyused up to the present and indeed very few usablestandards exist. The reason for this appears to be

threefold. First, the consultant paediatrician mayonly see a child once and, it is said, may never knowanything about the child's increment. This is anargument which carries no weight in relation to theschool medical officer and the general practitionerwho have or could often obtain measurementrecords extending over several years. and for theseto be made available to the consultant is a notinsoluble administrative problem. Second, thedetermination of annual increment involves twomeasuring errors instead of one, and records areusable only if the measurements are made withreasonable care and accuracy and without lookingat the card first to see what the previous figures were.Third, and by far the most important, velocitystandards are extremely hard to come by, becausethey must give not only the average increments butalso their variability, and to do this involvesmeasuring children not just once but twice or moreat yearly or shorter intervals. Velocity standards,in other words, must come from what students ofchild growth call longitudinal rather then cross-sectional growth studies, the former term referringto the measurement of the same children at differentages, the latter to the measurement of differentchildren at different ages. Longitudinal studiescarried over several years involve a good deal ofmoney, administrative labour and the ability to waita long time for results. Fleming's study (1933),confined to stature and head merasurements, is theonly one so far carried to the stage of publicationin this country, though three studies are in progressat present, one at the Institute of Social Medicineat Oxford, another at the National Children's Home,Harpenden, under the joint sponsorship of theMinistry of Health and the Sherrington School ofPhysiology of St. Thomas's Hospital, London, and athird at the Institutes of Child Health and Educationof London University. We are at present, therefore,dependent on the United States for this type of data:a short description of the major studies completed orin progress there will be found elsewhere (Tanner,1949a), as well as a more extended one if required(Tanner, 1948). Even after the longitudinal studyhas been made there has been a further difficulty.Due to some children inevitably leaving in mid-course, the investigation always produces in the enda mixture of longitudinal and cross-sectional data,and there has been considerable confusion as tohow proper velocity standards can be obtained fromsuch records. Techniques have recently becomeavailable, however, as described previously (Tanner,1951a).There are four sets of data which seem useful for

velocity standards. Robinow (1942) has given meanincrements and standard deviations from birth to

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age 6 for height and weight on approximately 100children from upper middle class homes in Ohio;they were studied at the Fels Institute and theincrements are reported in three-monthly periodsto one year and six-monthly thereafter, the sexesbeing combined. Simmons and Todd (1938) havegiven yearly increments with standard deviations forheight and weight from 3 months to 13 years, withthe sexes separate. The annual increments are basedon numbers which vary from about 50 to 150 ofeachsex for the various incremental periods, and thechildren are also mostly from upper middle classhomes in Ohio. Palmer and his associates (Palmerand Reed, 1935; Palmer, Kawakami and Reed,1937) have published annual increment figures forheight and weight from age 6 to 14 for boys andgirls separately, the data coming from the U.S.Public Health Service Survey of Hagerstown inMaryland, 1922-28. The numbers in this study arelarger, ranging from about 200 to about 800 yearly,and all social classes are included. The standarddeviations of the increments are given, but not theform of the frequency distributions. Probably thisstudy is rather too old to be used as a standardnowadays; there has been considerable increase inthe size of children at all ages during this centuryand data before about 1930 are to be avoided ifpossible: indeed the increase is still going on andthe more recent the standardizing series the better.Lastly, Meredith and Meredith (1950) have publishedfrom thelowaChildWelfare Research Station velocitystandards for annual increments from 4 to 8, thedata being obtained from approximately 200 healthychildren of north-west European ancestry andcoming mostly from the professional and managerialclass. The 10th, 30th, 70th and 90th percentiles aregiven for weight, stature, sitting height, arm length,leg length, shoulder width, hip width, and chest,upper arm and calf cirumferences. The sexes arecombined, there being no significant differences overthis age range.

Avaihble Distae S nHeigbt man Weight. There are considerable

numbers of distance standards available for heightand weight, and a few which include additionalmeasurements. These standards are obtained fromcross-sectional studies, or from mixed longitudinalstudies treated as though they were cross-sectional.Tlhe best height and weight standards available forEnglish (and probably Scottish and Welsh) use atpresent are probably those of Gore and Palmer(1949) for age 0-5 years and Daley (1950) forage 6-17.Gore and Palmer report on a cross-sectional

sample made in 1947 of children in London infant

welfare centres; 5,684 children were weighed butunfortunately only 921 had their length (or height)measured. Mean weights and standard deviationsare given weekly to 4 months, monthly to 1 yearand three-monthly thereafter. Boys and girls arereported separately, and each mean is based onbetween 80 and 200 children. The main criticismof this standard is that no frequency distribution ofweights are given, and no percentiles, so that onemust use the standard deviation method withoutactually knowing whether this is justified, and withweight the initial assumption must be that it is not.Gore and Palner's height data are much scantier;means and standard deviations are given forsix-monthly periods from 1 to 5 years, but some ofthe figures are based on less than 30 subjects. Alsothe technique of measurement is not given, and thisis a rather crucial matter in measuring the length ofsmall children.

TIhere are at present two possible sources ofstandards for the 5-17 age groups. Daley (1950)has reported the height and weight measurementstaken in 1949 on 21,000 London school childrenand gives the means, standard deviations, 10th, 50thand 90th percentiles and the complet frequencydistributions for each year, girls and boys separately.The 1st, 5th, 95th and 99th percentiles can thus beeasily computed for the weight distributions, whichare all skewed. Two objections can perhaps be laidagainst these figures; first that London childrenmay not be a very good sample of all childrenthroughout the country, and second that thesechildren were weighed in their usual indoor clothesand by many different measurers and this alwaysintroduces inaccuracies and leads to standarddeviations somewhat larger than they should reallybe. The weights reported include clothing (Daley,personal communication); to obtain nude weightprobably about 7% should be subtracted. The firstobjection is probably not of much importance, sinceeven if some small difference in mean weight andheight exists between London and elsewhere this canbe offset by using slightly altered percentile limits, aslong as the scatter of the data in both places issimilar.MEAsuREmEmr TECHNiaQUE. The second objection

is more serious. It must be emphasized quite clearlythat all anthropometric measurements, includingheight and weight, need considerable care and effortin the taking, and unless done properly are notmerely useless, but confusing. It is not sufficientto let an unskilled person measure height withoutdetailed previous instruction, and it is not sufficientto weigh children now in one set of clothes and nowin another. To take nmesurements properly demandsvery little more time and patience than to take them

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in a slovenly fashion, and unless the measurer iswilling to expend this little extra energy it is betterto leave measurement alone. Krogman's (1950)handbook on the measurement and interpretationof height and weight should be consulted in thisconnexion, also the remarks of Baldwin (1924).Briefly, stature should be measured with the subjectstanding as erect as possible, with heels, shouldersand buttocks touching an upright wall, the headpoised so that the subject looks straight forward(external auditory meatus and lower border of orbitin the same horizontal plane), the occiput eithertouching or not touching the wall according tolength of the head, and the heels together. A scalecarefully ruled on manila paper should be stuck tothe wall at an appropriate level, and a woodeni-shaped block should be brought down with thebottom face on the top of the subject's head andthe rear face held against the wall. The subject istold to make himself as tall as possible withoutlifting his heels from the ground, and this is assistedby having him take a deep breath. Variation due totime of day is eliminated as much as possible bythis latter procedure. Platform height scales aregenerally inaccurate and get more so with use andshould not, therefore, be used; Krogman founderrors of up to an inch on a selection of them.Height should preferably be taken with bare feetand in any case without shoes. It is useless tomeasure height with shoes on and apply a correctionfor heel height, for the simple reason that thelumbar curve is altered by the heel of the shoe beingthere. Weight should be taken on a beam scaleand in the nude wherever possible. If not in thenude, standard clothing must be worn; either asmock as used in x-ray departments or else drawersfor boys and pants and a brassiere for older girls.The point is that the weight of the clothing mustbe the same for each child, and unless some standardarrangement is adopted it will not be the same (seeKrogman's table of various weights of sumner andwinter clothes, etc.). Weights should be recordedas nude weights, the standard clothing weight beingsubtracted.The technique for other anthropometric measure-

ments need not be described here, as investigatorsusually seek the help of a standard text beforeplunging into these. But a word about the recordingof age in standard tables may be said. Some tableshave their label ' 6 years ' refer to all children from52 to 6-1 ('age at nearest birthday'), others to age6 to 7; the user should make sure which he is dealingwith in any given case. Also the width of the ageinterval makes a difference in the actual constructingof the standards. As the means and usually alsothe standard deviations of most anthropometric

measurements rise with increasing age, the scatteramongst a group of children covering a six-monthrange is somewhat greater than the scatter of agroup all ofwhom are exactly the same age. In theactual use of standards, however, it would probablybe best to compare the child to be tested againstthe scatter of children of exactly that child's age.It is consequently desirable for standards to be madeusing the smallest age ranges that the magnitude ofthe data allows; three-monthly groupings are to bepreferred to six-monthly or yearly. Alternativelyone could correct for the gradually increasingstandard deviation, but this does not seem ever tohave been done in practice. The same considera-tions apply to the form of the distributions;if the height distribution of children all exactly6 years old is Gaussian then that of children6-6j years old will be slightly positively skewed andplatykurtic; this difficulty reaches a climax atpuberty.

Returning now to the main discussion, the secondset of figures covering the 5-17 age range are thoserecently published by Sutcliffe and Canham (1950).These are based on a cross sectional sample of 17,000children taken in 1947 and drawn in a more or lessrepresentative fashion from rural and urban areasover most of England. The 10th, 25th, 50th, 75thand 90th percentiles and the standard deviationsare given for each year, for boys and girls separately.The curious feature of this data, however, is thatthe 10th and 90th percentiles for weight aresymmetrical about the 50th percentile at all ages,which is contrary to practically all other publishedfigures. It would seem that either these percentilepoints have been calculated on the assumption of aGaussian distribution for weight, or else by somesmoothing process. The 'indices ' tabulated at theend of the book are, it appears, calculated on theassumption of a Gaussian distribution for weight,and so it seems wise to avoid using them at leastuntil more stringent tests of the weight-distributionsare published. It is noticeable also that though themedians for both height and weight agree fairlywell between Sutcliffe and Canham's figures and theLondon ones, the standard deviations of the formerare considerably lower. This is partly because theage group marked, for example, 6 years, refers onlyto the three-month range 511/12, 60/12, 61/12,and partly because the standard deviations werecalculated not from the raw data but from thepercentiles, assuming a Gaussian distribution(Sutcliffe, personal communication). It seems, asbetween the two sets of standards, that the Londonones are at the moment preferable, though areworking of Sutcliffe and Canham's excellent datais very desirable.

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Other Anthpometric rds. Astonishingthough it may appear, there are at present noBritish standards for any anthropometric charactersother than height and weight; however, thisdeficiency will shortly be at least partly remedied,when the results of a Ministry of Health Surveymade in 1945 under the direction of Dr. E. R.Bransby, are published: about 2,500 children, aged5 to 18, were measured, and 20 measurements weretaken including height, sitting height, arm length,shoulder and hip widths, chest, waist, upper arm,knee, wrist and ankle circumferences, subcutaneoustissue folds and weight.The main American, standards with which the

English should be compared, are those of Vickersand Stuart (1943), Simmons (1944), Gray and Ayres(1931), O'Brien, Girshick and Hunt (1941), Stuartand Meredith (1946) and Meredith (1946). Vickersand Stuart's data comes from middle and lowersocial class Boston children, and list means,standard deviations, range, 10th, 25th, 50th, 75thand 90th percentiles six-monthly from birth to10 years for boys and girls for height, sitting height(or crown-rump at early ages), hip and chest width,head and chest circumference and weight. Simmonsgives for Ohio upper social class boys and girlsfrom 3 months up to 17 years means and standarddeviations for 25 measurements including height,sitting height, shoulder, chest and hip width, chestcircumference, arm length, and head length, breadthand circumference. Gray and Ayres give the meanand standard deviations for ages 1 to 19 ofprivate school children of middle and uppersocial class for 15 measurements, including height,sitting height, shoulder, chest and hip width,chest circumference and weight: their monographis still one of the prime sources of information inthis field.The U.S. Dept. of Agriculture survey reported by

O'Brien, Girshick and Hunt comprises measure-ments on 147,000 children of all social classes,aged 4 to 17, and is the biggest survey of its kindyet made. Means and standard deviations for eachyear are given for 35 measurements, but most ofthese, being intended for use in tailoring design,are not those thought to be best suited for medicalpurposes; however, height, hip width, leg length,chest, upper arm, thigh and calf circumference andweight are given.

Stuart and Meredith's are perhaps the bestcontemporary American standards, and the paperin which they are introduced is certainly the beststatement of the problems involved in supplyingand using standards since Shuttleworth's note of1934. Dealing with the selection of measurementsthey strongly deprecate reliance on height and

weight alone and point out that the time required totake three or four more anthropometric measure-ments is only a couple of extra minutes or so, andthe value of the examination is thereby enhancedout of proportion to the extra time spent.

' It must be remembered that height is only oneaspect of size, and that the stockiness or linearityof skeletal build is only one factor in determiningbody weight. Furthermore, body weight does notdifferentiate between the amount of protoplasmictissue and the amount of fat or water stored inthese tissues; nor does it distinguish betweenrelatively inert tissues such as bone, and activeprotoplasmic tissues, principally muscle. It isimportant to recognize that heavy weight for agemay be due in one case to stocky bones, in anotherto exceedingly well-developed muscles, in a third tolarge accumulations of subcutaneous fat and in afourth to a relatively well balanced amount of allthese. When a change occurs in weight for age it isimportant to know which of these tissues has changedsufficiently to bring this about.'

In an endeavour to estimate the various tissues bysimple means, Stuart and Meredith recommend fivemeasurements in addition to height and weight,namely hip width and chest circumference (thesetwo with stature giving a guide to linearity orectomorphy), calf circumference (to measuremuscular development) and subcutaneous tissuethickness under the scapula and above the crest ofthe ilium. Directions for taking the measurementsare given in full except for the subcutaneous tissuefolds which should be measured with the calipersdesigned for the purpose by Franzen (1929, frontis-piece) and used extensively by nutritionists andconstitutional anthropologists (Meredith and Stuart,1947). Stuart and Meredith (1946) give percentilestandards for boys and girls from 5 to 18 years; theseare illustrated in Fig. 3, which is reproduced fromtheir paper. Their tables give 10th, 25th, 50th, 75thand 90th percentiles at half-yearly intervals: the dataare from Iowa school children of the professionaland managerial classes measured between 1930 and1945. These measurements and standards, it may beremarked, were deliberately published for theguidance of school medical officers in assessingchildren's health and growth progress. For anexample of their use see Stuart and Kuhlnan (1942).

These American distance standards are quotedhere partly as examples in standard construction andpartly because of the lack of British data. It doesnot seem likely that they could be used for Britishchildren without some modification of procedure,since American children, apparently of all socialclasses, are bigger, on average, than British. Thedifference in mean height is about 3 to 6 cm. fromage 5 to 17, with the gap widening a little at thebeginning of puberty, probably due to Americanchildren beginning their adolescent spurt slightly

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BOYS

~

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='_I__ ._'

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From Use of Body Measurements in the School Health Programn'by Stuart and Meredith (1946).

FIG. 3.-Stuart and Meredith's percentile distancestandards: the five lines in each graph represent the 90th,75th, 50th, 25th and 10th percentiles. Iowa children of

professional and managerial class.

earlier. The mean weight difference is about 3 lb.at the beginning of this age range and rises to about10 lb. by the end. The standard deviations forheight are about the same, but the American spreadin weight is greater than the British at all ages.Those interested in standards for more recondite

measurements will find lengths of arm and leg bonesby radiograph from 6 months to 12 years in Maresh(1943) and Andersen and Green (1948), and fatmuscle and bone breadths of the calf as determinedradiologically in Stuart and Sobel (1946), Lombard(1950), Reynolds (1948), and Reynolds and Grote(1948). Regression standards and standards formaturity are discussed below.Use of Distance Standards for Assessing VelocityBefore considering more complex standards of

the wreight-for-height-for-age type, we must pauseto illuminate, if we can, one particularly murkycorner of this field. There are a considerable numberof authors who endeavour to use distance standardsfor judging velocity. Two alternative w-ays of doingthis are illustrated in Fig. 4. In Fig. 4A the child'sheight measurement is simply plotted from year to

year in the typical percentile distance chart. Startingout at about the 80th percentile the child falls backto the 10th percentile between 5 and 7, and picks upagain thereafter. The graph illustrates this well,but it takes us no further than simple illustration.The child in Fig. 4A never reaches our boundary ofabnormality by reference to distance standards, evenat age 7: common sense suggests that the incrementsfrom 5 to 6 or 6 to 7 are abnormally small, butFig. 4A does not provide a test of this question; forthis we need velocity standards with percentilecharts of velocity from year to year.The same is true of Fig. 4B, which is a rather

more complicated way of dealing with the samedata, but has some illustrative advantages. Hereby developmental age is meant the age that theaverage child is when he reaches so many cm. ofheight: the same concept is used in constructingintelligence quotients and in making the skeletalratings discussed below. Thus the average childprogresses exactly up the diagonal line in Fig. 4B,with chronological and developmental ages alwaysequal. The particular child we are considering,however, is in advance of average at age 2, thendrops slightly behind in height, until at age 7 heis only the height of the average child of 6. Thismethod has the disadvantage that usually neitherdistance nor velocity percentiles are shown; andhaving a 'height developmental age a year lessthan chronological at age 4 implies considerablydifferent conclusions from having the same differenceat age 12, as may be seen by comparing percentilepositions in 4A to developmental age advancementin 4B. Distance percentiles could be put in such achart to remove this objection, but the trouble withvelocity percentiles would remain. Admittedlydevelopmental age in several measurements can

be plotted at once on this type of graph-we canput in weight developmental age, hip width develop-mental age and also skeletal and mental age-butthe interpretation remains highly subjective. Thebest example of the use of this graph will be foundin Wilkins' recent textbook (1950).The method of Fig. 4A certainly has a great deal

to commend it. Particularly when the record extendsover several years the visual comparison of thesubject's curve to the standard ones may be mostilluminating. Also the situation may arise when achild suffers a succession of somewhat decreasedvelocities, none overstepping the limits of normality,but cumulatively producing an abnormally smallchild, as revealed, eventuallv, by the distance chart.It would seem perhaps best to use two percentilecharts side by side in assessing growth in singlemeasurefents, one chart of distance and the otherof xelocity. Such a combined chart is given in

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ASSESSING GROWTH AND DEVELOPMENTFig. 5A, B, C, D. The data are those of the BrushFoundation from Simmons (1944) and Simmons andTodd (1938); standard deviations have been put ininstead of percentiles because the data are onlygiven in this form; percentiles would probably bepreferable.The two standards together enable one to assess

both size and velocity and should therefore be morecritical than any single-measurement standards usingthe same measurements now in use: only experiencewill show whether the expectation is borne out in

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CHRONOLOGICAL AGE, YEARS

2 5 4 5 a 7 e 10 112 15 14 I5 16 17

CHRONOLOGICAL AGE, YEARS

FIG. 4.-Growth of a hypothetical child with retardationfrom age 5 to 7. 4A. Plotted on the normal percentiletype of distance standard. 4B. Plotted as chronologicalage versus developmental age. Note that neither method

gives a test for abnormality of velocity.

practice. For more precise standards still one wouldhave to use deviations from growth curves overseveral years; it might be sometimes practicallyimportant to do so, particularly in orthodontic work(see Count, 1942). A system of standards usingdistance and velocity data for single neasurementsand in addition, the relation of one measurement toanother, is given below.

Multiple Masurment Distance S dardsSo far we have discussed only the use of single

measurements for detecting abnormality. We haveseen that a battery of such measurements, aboutseven in all, is the procedure recommended onbiological grounds, but we have not discussed howthe results of these seven measurements should berelated together to give us an overall diagnosis.But if a child's scores on the seven measurements aresix 75th percentiles and one 97th percentile, whatare we to say ? He is abnormal on one measure-ment, according to our single-measurementstandards, but normal on six others. Again, if wehad two children of the same age, one at the 95thpercentile for height, weight and hip width and theother at the 95th percentile for height and hip widthbut the 5th percentile for weight, we would come toradically different opinions about the two; one isquite simply a large child, the other a child with a largeskeleton and a probably abnonmally small amountof muscle or fat or both. Clearly the relationshipsbetween two or more measurements give us addedinformation about the child, information that wehave so far neglected.The complexity introduced into the situation as

soon as we take two measurements instead of oneseems not to be widely realized; with the secondmeasurement we are well into the statistical jungle,populated only by a few semi-domesticatedmathematicians and an occasional exotic psycho-logist. The trouble conies about this way: if weagree to call abnormal all children falling below thefifth percentile in height or in weight, then thenumber of normals called abnormal will no longerbe five in 100, but more. Out of every 100 normalswe shall 'reject ' (used from hereon to signify 'callabnormal') five on the basis of height and five onthe basis of weight. If height and weight bore norelation to each other our total rejection wouldbe 5-5 = 10, but since they are related some of ourheight-rejected children will be the same individualsas the weight-rejected, and the total rejected willbe somewhere between five and 10. If we use heightand weight in this way, in other words, we havealtered our definition of' abnormal ', for we definedit in the single-measurement case so as to rejectjust 500 of normals (or other fixed percentage).

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2 4 6 a 10 12 14 16AGE, YEARS

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DISTANCE STANDARD VELOCITY STANDARDERESO IRRESPECTIVE OF AGE REGRESSION WITHIN AE. 9-10

FIG. 5.-To illustrate suggested form for standards using two measurements only: a combination of distancevelocity and regression data. Data in A, B, C, D and F are from Simmons (1944) and Simmons and Todd(1938) on Brush Foundation boys; for E from Daley (1950) for London County Council boys aged 5 to 16.The i 1*65 a and± 2-3 a lins correspond to the 5th, 95th and Ist, 99th perentiles in A and B; in C, D and E

probably about the 2nd, 93rd and 1/10th, 97th percentiles: in F uncertain.

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It will be seen that Stuart and Meredith's standards,amongst others, are subject to this uncertainty ininterpretation.

Constructio of Standards. We can meet thissituation only by arranging our consideration of thetwo or more measurements so that in the end only5°o of normals are rejected by our total procedure,whatever it is. We have to combine height andweight somehow. This is very simple to do; wecan use a thousand combinations: height/weight,height! 2s weight, height/ 3x'weight, height/log.weight, log. height-log. weight, heightz, weightg,anything. For each we can find a figure suchthat 5'o of normals are rejected. But thevarious combinations will differ in the number ofabnormals picked out for that 50. normal rejection;some will be powerful enough to pick out most of theabnormals, others will detect very few and hencehave little practical value. It is in choosing our com-bination, that is in deciding the relative stress to belaid on height, weight, subcutaneous fat and so on indiagnosing abnormality, that we find ourselves statisti-cally pathless, except in one set of circumstances,which we had better describe before going further.When the characteristics of the abnormal,

unhealthy population are known, besides those ofthe normal population, then we are in no doubt asto the correct procedure. In this case, we cancalculate a line so that it separates, on the basis oftwo or more measurements, the abnormals fromthe normals with 50. (or any other chosen figure)normals rejected and the minimum percentage ofabnormals undetected. Those above the line arenormal, those below abnormal, only 50. of normalsare misclassified, and our objective is achieved.The line is called a discriminant function. If thescatter of normal and abnormal populations is thesame for, for example, height and weight, andthe correlation of height and weight is the same inboth populations, the line is a straight one, but if thescatters or correlations are different, as is much morelikely in practice, the line is curved, an equationof the second degree (Smith, 1947). Not having anydata available on groups of known well-nourishedand ill-nourished children to take as an example,we must be content with an illustration from datapreviously reported (Tanner, 1951b). This is asituation in which we are trying, a trifle foolishly, todiscriminate men from women (normals fromabnormals) by shoulder and hip widths: if we havetwo measurements, biacromial and bi-iliac, the linewhich best discriminates is the one marked ' overall'in Fig. 6A; its equation is

3 biacromial diam. -bi-iliac diam. -82=0

plus women. Parallel to this line we can draw others,misclassifying 50o of the men only or 10O of the men,as shown. The 500 line, the one we particularlywant, is approximately

3 biacromial diam. -bi-iliac diam. -81 =0

In short, we have calculated a combination of twomeasurements which, if more than 81, indicatesnormality, and if less than 81, abnormality. Thecombination we have calculated is the best combina-tion; that is, it detects the largest possible numberof abnormals for 5 normals rejected. One can tryto distinguish men from women by the use of theratio hip width'shoulder width, for example, butfor 5O. of men misclassified, a much greater numberof women remain undetected among the men thanby using the discriminant function line. The use ofthe discriminant can be extended to any number ofmeasurements; in the example given the equation

2 biacromial diam. , 0 53 subischial (leg) length-1 25 bi-iliac diam.-81 =0

discriminates better than the two-measurementequation above.

In practice there are great difficulties in setting-upstandards this way, desirable though they would be.To use them we must know the characteristics ofboth populations, and this we seldom do. If wewanted, therefore, to use these standards as a screenfor malnutrition from the usual variety of causes-economic hardship, maternal inefficiency, familydisorganization, psychological disorder of child orparents-we would have to have located childrenwhom we knew were quite definitely malnourished,and this is not easy. Stuart (1948) has well saidthat the therapeutic test of giving the child a knownadequate food intake in a holiday surrounding withknown psychological stabilization is the only sureway of telling whether a child has suffered retarda-tion of growth progress through malnutrition. Ifthe screen is to include lack-or excess-of growthprogress through other factors such as the variousendocrine disorders, the abnormal populationbecomes yet more difficult to locate and handle;its distribution is likely to be skewed and perhapsmultimodal.*When we do not know the characteristics of the

abnormal population, or when they are simply toocomplicated to handle, we are forced to choosesome combination of the measurements, locate thefifth percentile level for our normal limit, and hopethat we are picking out as many abnormals with itas possible. There are no statistical grounds toguide us, and if we choose one combination rather

and it misclassifies the minimum number of men * That is, haling several peaks instead of one.

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than another, it is on an empirical or intuitive basisthat we do so. The combination can be chosen ina number of ways, three of which are illustrated inFig. 6B, C and D.

In Fig. 6B we follow the straightforward idea ofusing -1 65a for biacromial and -1 65a forbi-iliac as lower limits of normality for the men,but since these lines would exclude from theunhatched area not 500 of men but more, the limitsare set at -2 0a, which is the multiple of eachstandard deviation which does lead, empirically inthis sample, to 5° misclassified. Here we aregiving equal importance to both measurements inthe diagnosis. Should we do the same if we hadheight and weight and were trying to discover if achild were malnourished ? Most would say not;more importance would be given to weight, but howmuch more ? Twice as much so that the lowerweight limit is something like 1 8a and the lowerheight limit 2 -2 ? Or three times as much ?

Several alternative ideas, some used in practice,suggest themselves. Fig. 6C illustrates one. Herethe regression* of one measurement on another istaken for males and the -1 655 limit for thebiacromial-predicted-from-bi-iliac diameter used asthe separating line (marked -1 65a , in figure).Correnti (1948-49) has used an elliptical area withthe regression line as the major axis, rather thanthe -1 65ac t line parallel to the regression line;his arrangement has some advantages. Or someratio, biacromial/bi-iliac diameter, weight/height,height! 3 ,weight and so on can be used. Lastly themethods of Fig. 6B and C can be combined as inFig. 6D, which gives some importance to bothabsolute size of measurement and the relation of onemeasurement to another.- Regression standards have been widely used, andmust be discussed at some length. They willprobably be familiar to the reader, though perhapsnot under this name. The weight-for-height-for-agetables are the commonest example, the best knownbeing those due to Baldwin and Wood (1923;Baldwin, 1924, 1925) and to Faber (1929). In thistype of standard the expected weight is givencorresponding to the various possible heights, andthis is done for each year of age separately. Supposewe have a boy aged 10 whose height is 140 cm. andweight 72-5 lb. Finding 10 years in the table, we

* If we hase tso measurements x and v we can relate them bymeans of a line which predicts the most likely salue Y for any gisensalue of X. This line

Y=a-bXwhere a and b are constants, is called a regression line. Unless themeasurements are perfectlv correlated one with another the predictionof Y from a value of X is subject to a certain amount of error mostof the points do not actuall- lie quite on the line, but round about it.The amount of this error in prediction is measured by the statistica es, the standard error of estimate. Its interpretation is that of allthe values actually obtained for Y at a gisen value of X about 95 °O liewsithin the range =2 a es from the predicted value ofY.

look up the expected weight of 10-year-old boys of140 cm. height and find it to be 78 5 lb. The boyis 6 lb. below the average weight for his height atthis age. If the tables have been properly con-structed, we should also find the percentile spreadabout the expected weight figure, or the standarddeviation around the expected figure (the standarderror of estimate, in the usual terminology of theregression equation). The Baldwin-Wood tablesgive only the mean expected figure, however, andFaber gives only the 10th and 90th percentiles.Let us suppose the standard deviation around theexpected value is 9 lb.; the boy is then 6/9=0 67standard deviations below the expected mean, andif we pretend for the moment that weight has a moreor less Gaussian distribution for given height, thenthis corresponds to about the 25th percentile, whichis not very far down the total list of boys. Aregression standard (for increments this time) isshown graphically in Fig. SF, the central line beingthe expected weight increment for height increnentand the parallel lines the - I 65a and - 2 - 3a limitsfor the estimate. (The data are from Simmons andTodd (1938) and a linear regression of weightincrement on height increment and also homosce-dasticity* has been assumed, perhaps unjustifiably,for illustrative purposes and because data on thepoint are lacking.) In Fig. SF the lower 1 65alimits for weight increment and height incrementhave also been indicated. If we were judging by theregression standard, the child designated by B inthe figure would be called abnormal; if we werejudging by weight increment only, B would benormal, being just above the 1 65a level. Child Cwould be normal in either case, and child Aabnormal, but if we used the technique shown inFig. 6B, giving equal importance to both variablesand rejecting 5°. only, then even A would probablybe judged normal, as the lower limit for weightwould be somewhere about 1 -8 to 2 -0a.

This is merely repeating what is already shown inFig. 6; in each drawing A, B, C, D, 500 of normalsare rejected, but not the same individuals in each.In Fig. 6 we have the discriminant function linewhich we know is the best one and we can comparethe other techniques with it. The regression method(6C) in this example comes out better than any setof horizontal and vertical boundaries drawn afterthe manner of 6B; it detects only two fewerabnormals than the discriminant. Whether regres-sion standards are preferable to standards of the6B type in all or even most circumstances in childgrowth is not known at present. The efficiency ofany regression depends first on the correlation

Equality of vanrability in Y (wseight) for each broad disisionof X height).

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45

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FIG. 6.-Four possible sorts of multiple measurement standards. In each case the batched area represents the

area of abnormality, defined so that 5oo of normals are called abnormal. Males are taken as normals, females

as abnornmal. Fig. 6A. Discrinminant lines, giving best separation of normials and abnormals. Fig. 6B. Equal

importance given to both measurements singly; 25 fewer abnormials detected than by discrimiinant. Fig. 6C,

regression standard ; 2 fewer abnormals detected. Fig. 61), combination of B and C; 31 fewer abnorm-als

detected.

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between the two measurements (since if there is nocorrelation the relating together of the two is simplyan irrelevance), and second on the disease process,whatever it is, altering one measurement and notthe other. If the disease causes both measurementsto alter proportionately, then their relationshipstays the same, and, if the child's point falls on theregression line to start with it merely moves up ordown the regression line (see Fig. 6C) and not awayfrom it. In such circumstances the technique of Fig.6B would be better, for by this method the propor-tionate increase or decrease will be detected, thechild moving from, say, a position of-1-0a in bothmeasurements to the abnormal position of -2-3ain both.The construction of regression standards is a

simple matter. If two anthropometric measure-ments are adequately related by a straight line, andif the y-axis measurement is distributed in a Gaussianform for each broad division of the x-axis measure,then the expected value Y' of any measurement forthe value X of another measurement is

Y'=a+bX

where a and b are constants obtained for thestandardizing data by simple statistical procedures;b is known as the regression coefficient. Thestandard deviation around this expected value Y',a et is also simply estimated, and if r is thecorrelation between the whole series of X and Ymeasurements at this age a At\,1- r2 wherea, is the standard deviation of all values of Y.(In this section and above I have assumed largesair ples and avoided discussing problems ofestimation, not because they are unimportant, butbecause they would complicate the expositionintolerably.) The principle can be extended to morethan two measurements; Y' can be predictedfrom X, Z, A and B by, for example,

Y' =a+bX+cZ+dA+eB

with a a est of a I -R2 where R is the multiplecorrelation ofY with X, Z, A and B. If the relation-ship of one measurement to another is not adequatelyrepresented by a straight line, but requires a curvedone, the same principles still hold. The situation isthen as illustrated in Fig. 5E; curved percentilelines run either side of the curved line of expectedweight.

In using the regression standard one may calculatefrom the standard the expected weight, say, for therneasured height, and then compare the differencebetween this and the actual weight with the figurefor a et, as in the example above. For this pro-cedure to be valid it must be emphasized that twoconditions must be met. The distribution of weights

for any given broad division of height must beGaussian, and the standard deviation of the weightsmust be the same for all height divisions (i.e. nor-mality and homoseedasticity of weight arrays). Ifthe former condition is not met then percentilesmust be used, and if the latter is not met, thendifferent standard deviations or percentiles must beused for each division of height, a laboriousbusiness. These considerations apply wAhetherthe regression line is straight or curved, rectilinearitybeing a separate issue. Since in general one cannotfind transformations which simultaneously reducethe relation to one of rectilinearity, homoscedasticityand normality of array distributions, it is necessaryto decide which reduction is the most important.This would seem to be the production of a Gaussiandistribution in the arrays, with homoscedasticity ofarrays as the next desideratum. Rectilinearity comeslast. Some standards have been proposed-forexample, the Wetzel grid discussed below-in whichrectilinearity has been achieved over considerableranges, but at the expense of non-Gaussian arraydistributions. Though such standards can be usedwith percentiles instead of standard deviations, theirconstruction does not seem a very appropriate one.

Regression standards in current use are divisibleinto two classes: those which operate over arestricted age group, which we will call within-ageregression standards'. and those which operate quitewithout reference to age at all, which we will callirrespective-of-age regression standards. Fig. 5F isan example of the former, and Fig. 5E of the latter.In Fig. 5F the standard holds only for the agerange 9-10 years, and is one of a set of similarregressions, one for each year of age. The Baldwin-Wood and Faber tables are regressions of this sort.But instead of this we can ignore age and simplyuse a weight-for-height regression covering the wholeperiod of growth, as in Fig. 5E.

It is essential to have clear the difference betweenthese alternatives. In the first case, we test thechild M on the basis of weight-for-height at his age,and place him in relation to the expected mean andstandard deviation for boys of his chronological age.In the second, we test M on the basis of weight-for-height at his height and place him in relation to theexpected mean and standard deviation for boys ofhis height. Thus, if we have a boy aged 10 who isadvanced for his age both in height and weight,the first method will predict his expected weight bya regression coefficient appropriate to 10-year-olds,and compare his deviation from the expected valuewith the a t for 10-year-olds. However, the boymay perhaps be better regarded as nearer theaverage I1-year-old state, since he is about an11-year size, and the regression coefficient for

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1 1-year-olds is larger than that for 10. The expectedvalue would therefore be somewhat different, andso the deviation would be different. Also the awould probably be larger at 11 than at 10, and theresult of the test pretending the boy was 11 wouldbe different from that made keeping him at 10.Only in one circumstance will this not be true; ifthe expected weights for both year groups are thesame, and the deviations from expected weights ineach of the groups are proportional to the standarddeviations of the groups, then the test result will bethe same whichever group the boy is tested in.(This is now on the assumption that we are usinga transformation of weight which brings it to aGaussian distribution.) For the expected weightsto be the same the regressions must be the samefor both age groups and the coefficient must beequal to the average weight gain from 10 to 11divided by the average height gain: for the secondcondition above to be satisfied we must have thesame height-weight correlation at both 10 and 11.When these conditions are met for all age groupsthen there is no difference between the two alterna-tive regression methods. If the condition of equalcorrelations at all ages is met, as it is fairly closelyat least up to the last two or three years of growth(Tanner, 1951a), then the conditions reduce tomean yearly gain in weight/mean yearly gain inheight being constant, and equal to standarddeviation of weight/standard deviation of height,the latter ratio being the same for all age groups.These conditions are not met by weight and heightin their usual measurement scales, but they are metby using standard scores as described below.

Considerable numbers of distance regressionstandards have been suggested, most of them of thewithin-age variety, which have the advantage ofbeing nearer rectilinearity for most combinations ofmeasurements than irrespective-of-age regressions.Most of these standards aim at predicting bodyweight from various skeletal and/or muscularmeasurements. Pryor's (1936, 1941) tables predict-ing weight from height and hip width are of thebest know-n and are given in Holt and McIntosh'stextbook (1940). The idea is that the two skeletalmeasurements give a fair idea of skeletal size andbuild, and then weight ought to follow accordingly,but weight in fat and weight in muscle are not, ofcourse, distinguished. The most thorough studiesof weight prediction by various combinations ofmeasurements are those of Franzen (1929), McCloy(1936, 1938) and Dearborn and Rothney (1938).The first of these accounts in particular deserves tobe better known than it is at present; it covers withclarity and distinction a great deal of the groundsurveyed in this paper. Franzen discussed the

prediction of weight from four skeletal measure-ments, but suggested that for nutritional purposesweight prediction standards are not as good asprediction of upper arm girth, calf girth andsubcutaneous tissue thickness over the biceps.The former two are predicted from height, chestbreadth, chest depth and hip width, and sub-cutaneous tissue is predicted from height, chestbreadth, chest depth and shoulder width. Franzen'sregression standards were tested in the field byMitchell (1932) who used them successfully to pickout malnutrition in Porto Rican children and relatethis to such factors as family income and over-crowding. Mitchell's paper also seems to be lesswell known than it deserves. Massler and Suher(1951) have recommended a ratio type of standard,weight being predicted by (calf circumference)2stature divided by a constant, which is independentof age over the range 5 to 17. No percentile limitsor tests of distribution are given.The Wetzel Grid. A consideration of the Wetzel

grid (1941, 1943, 1944) standard falls due at thisjuncture. Armed with the discussion above,courage, a magnifying glass and steady nerves, thereader will be able to make out that the grid,reproduced in Fig. 7, is in essentials simply aweight-for-height regression distance standard,presented with a recommendation to use it as avelocity one. The regression standard is neatlycombined with a distance-for-age standard, and isof the irrespective-of-age type, with a logarithmictransformation of both weight and height used toget the regression from the curve of Fig. 5E aboveto a straight line, at least from age 6 onwards.Look first at the left hand portion of Fig. 7: thegraph is one of log weight vertically against logheight horizontally. Consider a child M of height130 cm. and weight 26 kg.; locate the point, ringedin the figure, which corresponds to these figures.Look at the physique channel' lines runningnorth-eastward, and it will be seen that M lies inchannel Bl, near the B1-B2 boundary. Since themiddle channel corresponds to the average child,this Bl position tells us that M weighs a bit less thanthe average child of his height. If we go up tothe 130 cm. vertical line till we get to the middle ofthe centre channel M we find the weight of theaverage child of this height is actually 28 kg. Thisinformation, then, is the same as that given by aweight-for-height distance regression except that itis less precise, since no standard deviation 5 cst aboutthe mean expected weight is given. We cannotjudge how far down amongst his height group aweight of 2 kg. below average brings M. That itbrings him to the BI-B2 border does not of itselftell us what we really want to know, which is his

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percentile position. The channels may be actuallymisleading in this regard to the unwary; from theirgraphic presentation as of equal width one mightreadily assume that the distribution of log weightfor log height was Gaussian and homoscedasticabout the mean of channel M. Whether or not thisis so still cannot be discovered from the publishedstudies; Hopkins (1947) gives a graph of log weightagainst log height for girls aged 6-12, and in thisit looks as if log weight is still skewed, particularlyfor the larger girls. For a given size (that isauxodrome 100, see below) the distribution of logweight is certainly heavily skewed with an excessof cases in the B channels below the mean (Wetzel,1941), so that being in channel B2 at what almostamounts to a given log height implies a percentileposition considerably nearer the 50th than doesbeing in A2. Also one must remember that thoughthese lines are called physique channels', M'sposition in them really tells us very little indeedabout his physique in the true sense. It takes agreat deal more than simple weight for height tocharacterize a human body, in which connexion theremarks of Stuart and Meredith quoted above arepertinent.Now consider the line passing in an east-south-east

direction through M's position on the grid. It iscalled 'isodevelopmental level' and marked 70.Follow it down to the right hand portion of thechart and consider this portion. It is seen to besimply a percentile chart of growth with age, thesame as those in Figs. 3 and 4A and 4C, except thatthe vertical scale is neither height nor weight, but acomposite of the two. If, for example, M was130 cm. tall but weighed 29 kg. instead of 26 kg.,his level on the right hand chart would be 80; ifhis weight were 26 kg. but his height 120 cm. insteadof 130 cm., his level would be about 67. A changein weight of 3 kg. is not a great deal, yet it producesa far greater effect on isodevelopmental level thana change of 10 cm. of height, which is quite a lot.The composite measurement is of the same natureas surface area, also obtained from a combinationof weight and height, but it gives much greateremphasis to weight as opposed to heigbt than doesthe DuBois expression for surface area. The ideaof using a composite of the two measurements tomeasure size for age is undoubtedly a good one,but this particular composite is probably not thebest available. Presumably what is theoreticallyrequired is something approximating the generalsize factor for body build, and at least in adults,as I have pointed out elsewhere (Tanner, 1949c),this is very closely approximated by the DuBoissurface area. Returning now to M, we disclose hisactual age as 10 years, say. Follow the 70 line to

the right till it meets the vertical 10 year line at theringed point. A percentile line goes.through thispoint; M lies on the '82nd percentile of size for age.This is approximately the same information as isobtained by reference to Meredith and Stuart'scurves of Fig. 3, or those of Figs. 4A, SA and C;it is not quite so full, however, in that it gives onlya somewhat questionable size rating instead ofseparate height and weight ratings. Note also thatWetzel gives his percentiles in the opposite sense tothose in Figs. 3 and 5, marking the children fromthe bottom up, so to speak. In addition, the middleof the percentile lines given in Wetzel's chart is not,as one might expect, the 50th percentile, but the67th, or in the more usual terminology, the 33rd.A 'size developmental age is given by referenceeither to this 67th percentile or, by some laterauthors, to a 50th percentile precisely as for theheight age graphed in Fig. 4B; the size develop-mental age is the age at which the 67th (or 50th)percentile crosses the horizontal line reached bythe child, in the case of M 83 years for the 67thpercentile, about 8!1 years for the 50th.

Wetzel now recommends this procedure to befollowed for M every year, when a series of pointswill be produced on both left and right hand portionsof the chart. These, plotted in solid dots, are for thesame hypothetical child who gave the points inFig. 4A and B. The dots on the right hand portionare precisely similar to those in Fig. 4A except thatWetzel's measure of size is plotted instead of height.From the point of view of interpretation thesituation is just the same as in Fig. 4A; graphicallythe drop in velocity between S and 7 years is shownquite well, but no tests of whether the drop isabnormally large or not can be made. We areagain using a distance standard for judging velocity.The dots on the left hand chart require a little moreanalysis. Wetzel assumes, it seems from a prioriconsideration, that from about 6 years onwards ahealthy individual travels a straight course up oneof the channels, in other words, maintains a constantratio of log height :log weight. This is certainly trueof the mean values of such data as of the BrushFoundation (Simmons, 1944) and is very nearly truefor the mean values of the London County Councildata (Daly, 1950). If a child slips out of his channelin a southerly direction, as does the one illustratedin Fig. 7, then he is said to be gaining too littleweight for his gain in height, and if he deviates tothe north he is said to be gaining too much weightfor his height. Again, the method is very aptlyillustrative, and by using logarithms Wetzel hasobtained a straight line regression for weight onheight over a fairly large age range, which is certainlydesirable, though not at the expense of producing

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skewed or heteroscedastic weight arrays; andwhether or not these are produced we do not know.But again it suffers from the disability of distance

m standards used as though they were velocity ones.Over the straight line portion the standard laysdown that increment log weight=k. increment logheight, a velocity regression of a similar nature toFig. 4E. But no figure for a t is given, and no dataas to the distribution of increments of log weightfor given increments of log height; weight incre-

b ments are usually somewhat positively skewed, butone's suspicion is that taking logarithms may over-correct. An apparently empirical tolerance limitof 2 channel deviation in 10 isodevelopmental levelsis mentioned, but its source is not clear and itassumes quite uncritically homoscedasticity of arrays

from age 6 on and, presumably, since deviations ineither direction are subject to the same rule, a

Gaussian distribution in arrays. What has beensaid above about any regression standard for weighton height not necessarily distinguishing abnormalsif the disturbing influence affects both measurementsproportionately applies, of course, also to the grid.Apart from these points, however, the grid does seema neat way of recording weight, height and weight-for-height data so long as the user understandsclearly its simplicity of approach and the limitationsto the information it gives. Various tests of its use

in practice have been made and various opinionspassed (Bruch, 1942; Simmons and Greulich, 1943;Stuart and Meredith, 1946; Dreizen, Mann andSpies, 1948; Mann, Dreizen, Pyle, and Spies, 1948;

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Krogman, 1950). It does seem to me that the gridhas little or no advantage over percentile graphs forheight and weight combined with a weight-on-heightregression standard, and it cannot compare inusefulness and accuracy with the simultaneous useof distance and velocity charts as outlined in Fig. 5and discussed in the following section.

Other Standards. Correnti (1948-49) has recentlypublished a weight-for-height auxogram, which hasa much firmer biometrical foundation than theWetzel grid, and seems in many respects preferableto it. The auxogram is a height-on-weight regres-sion, the variables untransformed, the regressiontherefore curvilinear. At each year of age the meansof height and weight are plotted, and around theman ellipse, containing some particular percentage(say 900O) of the total children of that age. Thosewithin the ellipses are normal, those without are not.The ellipses are calculated on the assumption of ajoint Gaussian distribution of height and weight foreach age, and this is certainly a questionableassumption. Also the auxogram is subject to thecriticism of distance standards being used forjudging velocity.TuxFoRD s INDEx. Another distance standard

recommended for use as a velocity one is Tuxford's(1939, 1942) index (Campbell and Weir, 1-948).Tuxford uses the ratio weight/height rather than aregression equation for comparing the two measure-ments, and his method essentially gives simply themean weight height at each age from 5 to 16 forboys and girls. He found, however, that this ratiodecreases approximately in a straight line withincreasing age, so that instead of giving a distancetable for weight/height at each age, a linear correc-tion for age brings back the mean weight/height tovery nearly 1 -00. Tuxford's index (1942 edition)is founded on the 1938 London County Councildata given by Menzies ( 1940), and for boys is

T.1. Wt. (kg.) 335-age in monthsHt.(cm.) 48

and for girlsWt. (kg.) 308 age in monthsHt. (cm.) 42

The mean of the index is not exactly 1 00 for eachage in these data, but comes fairly close to it exceptfor boys at age 14 where T.I.=0-987, and for girlsaged 5. No standard deviation or percentile spreadat any age is given, so that even as a distancestandard the index is impressionistic only. Tuxfordsays that values below 0-95 deserve investigation,but the basis of this statement is not clear, and itseems to assume that the scatter of weight/height isthe same at each age, which certainly cannot bethe case. If a value of 0 - 95 is a warning at

adolescence, then something much nearer unityshould be the warning at, say, 6 years. Even if wehad percentile limits, however, one would still besomewhat uncertain how precisely to interpret anabnormal ratio: ratios may look simple but theyare biometrically a bit complicated and present tothe statistically unsophisticated several pitfalls,some of which I have discussed elsewhere (Tanner,1949b).Tuxford also recommends using his index to judge

velocity, and this in very much the same way as thechannel system in Wetzel's grid. In health theTuxford index is assumed to be constant from yearto year, this being the equivalent of straightprogression up the channel. This time the standardis weight/height increment= -c. age increment,but again no figure for e t is given and no data asto the distribution of weight/height increments forgiven age increments. Tuxford suggests that achange of index of 0-02 over a year should beregarded with suspicion, but whether this appliesequally at all ages is not clear. It is interesting tocompare the use of Tuxford's index and the Wetzelgrid in one of the articles (Wetzel, 1942) in whichWetzel first fully introduced his system. Wetzelcriticizes the Tuxford index and alleges that it doesnot show that the particular boy used as an exampleis retarded in growth progress, whereas the grid does.Unfortunately for his thesis, however, Wetzel usesTuxford's index quite wrongly, applying theempirical distance criterion where he should applythe velocity one; used properly the index shows thefalling weight-for-height at exactly the same timeand with the same force as does Wetzel's channelsystem. Neither, however, can be considered verysatisfactory.

Velocity Regression Standard. There have so farbeen very few attempts to construct a propervelocity regression standard of the sort shownin Fig. 5F. Bransby (1945) has suggested andtentatively used a standard for weight attained afterso many years at school for height increment duringresidence at the school. Further subdivisions weremade by age at entry to school and weight at entry.Thus a standard curve of weight attained for givenheight increment was provided for each 2 lb. weightgroup and each year of age at school entry. Inother words, the 10-year-old 62 lb. child had astandard curve covering the rest of his schoolcareer, the 10-year-old 64 lb. child another, and the11-year-old 64 lb. child a third. The material wasinsufficient for percentile limits to be accurately laiddown, but the approach is an interesting one andmight repay more extensive study. This methodcombines velocity in one measurement with distancein another, a perfectly simple and useful possibility

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in regression standards. Also two values of thesame anthropometric measurement at different agescan be used if desired; for example, in constructinga standard for weight at age 1 or 2 or more byregression on birth weight (Asher, 1950; luing-worth, 1950) or in comparing the growth of childrenof different economic groups (Greenberg and Bryan,1951). Bransby and Hammond (1950) are currentlyconsidering whether standards of this general sortfor subcutaneous tissue change over fairly shortperiods would have screening value for the assess-ment of malnutrition. Stuart and Reed (1951) havedealt with the same problem by fitting straight linesfor each individual to the growth in volume ofsubcutaneous tissue by radiograph of the calf overthe age range 1 to 6 years: the fit is good but theresidual variance about the line is significant, whichis not the case for muscle and bone lines. Thecauses of a significant departure from the line arethen sought. This method begins to approach atest of hypothesis, D above (page 14), of growthbeing normal over a whole range of years, and mayturn out to be a most powerful technique.

Suggested Form for Combined Distance, Velocity andStand score Difference Standards

It is possible that a small simplification of theregression type of standards could be made alonglines rather vaguely suggested elsewhere (Tanner,1950. 1951a) and if this simplification is combinedwith both velocity and distance standards an overalltest for abnormality more adequate than any so faravailable might perhaps be achieved. The use ofthe distance and velocity standards as suggested inFig. 5A, B, C, D, implies finding first of all thestandard deviation score or percentile for the twomeasurements, let us say height and weight, and itis easy to see that the difference between these scoresfor the two measuremzents relates height and weightto one another in the same sort of way as does theregression equation. If X cm. is the height of achild age 6 say, x cm. the average height of6-year-olds, and o, the standard deviation of6-year-olds, then the score z=X -x is called the

standard score for the child. All standard scoreshave a mean of zero and a standard deviation ofunity. The mean difference of the two standardscores will be zero, and the standard deviation ofthis difference will be V2(l-r), where r is thecoefficient of correlation between the two variablesconcerned. Thus if a child has standard scores forheight and weight of -I -2 and-0 8 respectively.his standard-score difference is

Z%wt-Zht= -08-12-2

The test for whether such a difference could havearisen in a normal healthy population or whetherit indicates that the child is abnormally under-weight for height is made by comparing thisheight-difference with its standard deviation. Ifthe correlation between height and weight at theage considered is 0-75, then the standard deviationof the height-weight difference is </2(1- -75)=0-7 units. The ratio of height-weight difference toits standard deviation is therefore-2 0=--30,

0o7which is far out beyond even the first percentile(which it will be recalled is at 2 3a) and undoubtedlysignifies abnormally low weight for height.

This procedure seems to me rather simpler thanthe usual regression computation, and gives thesane information. Admittedly the example aboveis badly chosen, in that the distribution of the Yvariate should be Gaussian for each broad divisionof X, and these distributions should have the samestandard deviation. However, it should not be toodifficult to allow for skewness of weight arrayseither by the use of tables transforming weight, assuggested in the footnote to Fig. 8, or by adjustment

GROWTH PROGRESS CHART

FIG. 8.-Increment 1-2 years entered under 2 yearcolumn. Ring in black standard scores coming below5th or above 95th percentile; in red scores coming below

1st or above 99th percentile.The chart is accompanied by three tables:

A. Pearl's tables to convert increments to per year.B. Tables for turning measurements to standard scores;

incorporating transformation for non-normallydistributed measurements.

C. Tables for percentiles corresponding to standardscore differences for each pair of measurements ateach age if necessary.

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of the final value corresponding to the figure of-3 0 in the example above. If the within-age typeof regression (see page 24 above) is wanted it wouldbe necessary to give a table of correlation coefficients(or actually of X 2(1-r)) for each pair of anthropo-metric dimensions at each year of age, and this is thepreferable form if the regression is at all curvilinear.If the irrespective-of-age regression is required, thenthe standard scores are obtained by reference tothe mean and standard deviation of the measure-ments at all ages, and the correlation is the overallcorrelation for the whole age range. However, oneof the advantages of standards couched in this wayis that when the regression is rectilinear, theconditions for the two types of regression tests to beidentical, as outlined above on page 25, are met ifthe correlations at each age are the same. For theheight-weight correlation the published figures showlittle trend during growth up to the last two orthree years (Wilson, 1935: Simmons, 1944). Itseems that a figure of about 0 75 would coveradequately both boys and girls, the former for age Ior less to age 16, the latter from I or less to age 13.The correlation for weight increment-height incre-ment is about 0 40 from 2 till 12 (Simmons andTodd, 1938).The form of the report suggested is given in

Fig. 8: the upper block contains the actual figuresfor weight and height and any other measurementstaken, at each age, and the figures for their velocity.The I to 2 year velocity is placed in the 2-year-oldcolumn and all velocities are given as so muchper year since the intervals between successiveexaminations are inevitably different on differentoccasions; for example, 360 days one time but380 the next. Pearl's tables (1940) giv,ing theproportion of a year lying between any two datescan be used to facilitate the conversion. Thelower block in Fig. 8 contains the standard scores,obtained by reference to the standard tables used,that is tables embodying the lines of Fig. 5A, B,C, D. One new item appears here; this is weight -height, one standard score being subtracted fromthe other. Reference to a third table completesthe job: in this are listed the percentile pointscorresponding to the standard scores and thestandard score difference for each year, the tablebeing constructed on the basis of the distributionof the standardizing data. If the correlationsbetween two measurements are equal each yearthen this system is equivalent to either regressionstandard: if not. then it is equixvalent to thewithin-age type only: but it could be extendedto the irrespective-of-age type by reference toanother table wherein standard scores for weightsappropriate to v arious height groups were entered.

The construction of British standards of this sortwould probably be immediately possible for heightand weight. The distance data have been discussedabove and though, so far I am aware, no means andpercentiles for height or weight increments haveyet been published in this country, several localauthorities and secondary schools must have thedata in their files. Pending their production,however, it might prove possible to use the Americanvelocity data after a little experience had been gainedin their interpretation, or to use, as a temporaryexpedient, British mean increments obtained cross-sectionally with percentile limits from the Americandata.The interpretation of such standards is subject

to the uncertainties discussed above, and it seemsat present impossible to suggest anything morepositive than caution in using multiple standardscores, or if this is impossible, reliance on one soleitem such as weight increment standard score minusheight increment standard score. or wvhichever isfound to work best in practice.

Standards for MaturityThe advent of the adolescent spurt in growth

bedevils all the standards so far discussed. Thereason for this is that there is a wide spread betweenindividuals in the time at which the spurt starts,and so, with some children suddenly speeding uptremendously and others not at all, the scatter ofthe normal increases greatly. Consequently ourstandards, though perfectly valid still, become farless potent for detecting abnormality. We need tocombine them with some index of whetheradolescence has started or not.

In longitudinal growth studies several ways havebeen used for indicating the relation of a child at anytime to his adolescent spurt. For girls menarchealage is an excellent indicator, a given girl being scoredso many months before or after the menarche; thetime of maximal velocity in height has also beenmost effectively used (Shuttleworth, 1937, 1938, 1939).Neither of these are available, however, except inretrospect; one cannot tell how much before themenarche a girl is until, obviously, she has reachedit. In the circumstances considered in this papertwo, or perhaps three. methods are available: theseare the rating of secondary sex character develop-ment. the skeletal (wrist and hand) development,and, possibly. tooth eruption development.

Standards for secondary sex character (S.S.C.)development in the case of boys have been given indetail by Greulich and his associates (Greulich.Dorfman, Catchpole. Solomon and Culotta. 1942)Five stages are described, stage I being pre-pubertal,stage 2 beginning growth of testes, penis, pubic hair,

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stage 3 a further development of testes, penis andpubic hair and often the beginning of facial hair,stage 4 further development again, with face hairdefinite and axillary hair beginning, and stage 5near adult. These stages are, of course, far morefully described and illustrated by Greulich, so thata scaling on a rapid clinical examination should beperfectly feasible. For girls, similar scales for breastsand pubic hair separately have been illustrated byReynolds and Wines (1948), and a rating combiningthe two characters would be simple to arrange.Since the breast and pubic hair begin developingabout two years before the menarche on an average,S.S.C. ratings cover just the period when theadolescent spurt is maximal. (The menarche occursshortly after the point of maximal velocity instature.)

Several possible ways of incorporating theseratings into growth standards suggest themselves.First, simple standards for the time at which eachstage occurs and the normal limits of this should beestablished; second, height and weight, and indeedall anthropometric standards during puberty,should be couched in terms of S.S.C. maturity groupas well as, or instead of, chronological age; thirdly,regression standards using simply S.S.C. maturityratings as one variable could be constructed;fourthly, a S.S.C. age could be developed in exactlythe same way as skeletal age below.

Skeletal (Wrist-hand) Maturity. These standardsgo a little further. The maturation of the skeletoncan be followed by x-rays and judged by whethersuch and such an epiphysis has appeared, whetheranother has closed, what shape a third has and so on.This skeletal maturation does not follow chrono-logical age exactly, and especially at puberty thetwo part company. If the boy is an early maturer,his adolescent spurt in height and other anatomicaland physiological measurements comes early, hissecondary sex characters develop early and his boneappearances hasten to adulthood. Thus skeletalradiographs enable one to judge how far along inadolescence is a given child (and are quite closelyrelated to S.S.C. groups in this), and they also,stretching back to birth, enable one to rate as maturebeyond his years a child of any age whatsoever.The technique at present used is to take a radiographof the left hand and wrist, a simple matter that canbe -ery satisfactorily done with a small. portabledental machine. A set of standards is then con-sulted, the original one due to Todd (1937) havingbeen recently superseded by a new edition fromGreulich and Pyle (1950). Skeletal developmenthas from the start been dealt with in the same wayas mental age: a given boy's radiograph is matched toa particular standard and if that standard represents

the development of the average boy of age 104,one lists the boy's skeletal age as 101 years.In practice the matching of films with standardsdemands a certain amount of skill and practice,and unfortunately wrist and hand changes seem tobe minimal just at the beginning of puberty, thustending to make the ratings least reliable and finely-spaced just when one wants the information most.The information one does get, however, is veryvaluable and this technique has deservedly gaineda wide reputation for usefulness. Recently, arefinement of it, for use more in special than ingeneral circumstances, perhaps, has been proposedby Pyle and her associates (Pyle, Mann, Dreizen,Kelly, Macy and Spies, 1948). In this, besides thewhole appearance of wrist and hand being used toobtain the skeletal age, each individual bone orpart in the radiographs is assigned a skeletal ageand the range of the most advanced to the leastadvanced bone is given. This refinement is known,for historical reasons, as the red graph method.Malnutrition and certain other states are believedto increase the variability of maturation in thebones of hand and wrist besides retarding itgenerally.The incorporation of skeletal maturity into general

standards follows the same lines as that of S.S.C.maturity above (Bayley, 1943; Gray, 1948). It isnot yet known to what extent the skeletal ages ofAmerican and British children are the same in termsof chronological age. Although the pattern ofmaturing is probably very similar in both countries.it may well be that the American children on whomthe standards are founded are somewhat ahead ofthe average British child in maturity at any givenage. If so, then while the average American childof chronological age 101 will have, being average.a skeletal age of 101 on the Greulich-Pyle standards.the British average child of 101 would have askeletal age of somewhat less. No British standardsare yet available.

Tooth Eruption Development. Tooth eruptiondevelopment has not as yet been used as a measureof maturation, but there seems no good reason whyit should not at least be tried; a measure of toothage could readily be obtained, it would seem, fromthe figures in Palmer. Klein and Kramer's paper(1938) on the Hagerstown children or fromHellman's study (1943) in New York (see also Boas.1933: Bengston, 1935: Doering and Allen. 1942:Meredith, 1946: Hurme, 1948). Tooth age wouldhave its main application in the prepubertal years.and might be of particular interest as girls erupttheir teeth somew hat earlier than boys, and this ata time when the sexes are otherwise little distin-guished in development. Not much is known at

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32 ARCHIVES OF DISEASE IN CHILDHOOD

present about the relation of tooth eruptionmaturity to skeletal maturity.

ConchloIt would be eminently satisfying if a survey of

growth standards such as this started by propound-ing the statistical principles upon which suchstandards could be based, went on to list theinevitable results of their application with theappropriate data for use in each circumstance, andwound up with a few simple instructions in the useof a few master tests. But though satisfying, it wouldbe at present wildly inappropriate. We lack as yetany comprehensive theory of the construction ofnormal standards involving numerous measure-ments all of which change as time passes, all of whichare interrelated and most of which are not quitedistributed in Gaussian form; some mathematicalbackground exists (see for example, Box, 1950;Greenhouse and Mantel, 1950; Votaw, Kimball,and Rafferty, 1950; Wilks, 1941) but as yet it is apatchy one. We lack, for the most part, good seriesof standardizing data, at least for this country.And we are far from any simple and satisfactorygeneral test of healthy growth in the child.

SummaryThe current standards available for assessing

whether or not a child is growing normally arepresented and reviewed; the theoretical backgroundand the limitations of each one are discussed.The meaning of the assessment 'abnormal' is

discussed, and the view presented that the assessorhas in mind two populations, one healthy, the otherunhealthy, probably overlapping; limits of normalityare arbitrarily fixed for the purpose in hand,arranging inevitably to misclassify a certain propor-tion of normals as abnormal.The relative merits of standards couched in

percentile and in standard deviation terms arediscussed.The use of velocity or rate-of-growth standards

as opposed to distance or size-at-age standards isadvocated, and the use of standards for distance asthough they were standards for velocity isdeprecated.No British velocity standards are available; the

American ones are discussed.The British and American distance standards

available are reviewed and the opinion given thatthe currently best British height-weight standarddata are those of Gore and Palmer for 0 to 5 yearsand Daley for 5 onwards, both being fromLondon County Council children.The use of height and weight only is deprecated

and the optimal choice of a few measurements is

discussed; the proper technique for taking heightsand weights is given. No British standards exist formeasurements other than height and weight; someof the relevant American data are reviewed.The combination of two or more measurements

into a standard is considered and its two possibleregression forms, exemplified by weight-for-height-for-age and weight-for-height-irrespective-of-age, arepresented. The use of each is discussed and theWetzel grid and Tuxford's index shown to bespecial examples of such standards.A suggested system of standards is presented

tentatively for experimental trial; various measure-ments are considered in relation to age, and inrelation to each other irrespective of age; bothdistance and elocity are tested for each measure-ment. The difficulty in interpreting multiple testsof this sort is stressed.

Standards for maturity, such as skeletal age byhand and wrist radiograph, secondary sex character,age and tooth development age are reviewed.

I wish to thank Mr. M. J. R. Healy for reading themanuscript and suggesting numerous improvements,Professor Henry Barcroft for his interest in and supportof this work, and Mr. R. H. Whitehouse for the figuresand calculations. I have also greatly benefited from adiscussion of these problems with Professor HaroldStuart and Dr. R. B. Reed. Part of the expenses weredefrayed from the William Hyde Award of the ResearchBoard for the Correlation of Medical Science andPhysical Education.

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ASSESSMENT OF GROWTH DEVELOPMENT IN CHILDREN · ASSESSING GROWTHAND DEVELOPMENT the latter case, the standard deviations are used essentially as percentiles (see Fig. 1); the given