# Ethel Elderton's papers

We list below some of Ethel M Elderton's papers, giving a short extract from the introduction to give an idea of the contents of the paper.

Click on a link below to go to the papers published in that year

1907     1909     1910     1912     1913     1914     1915     1919     1920

1923     1927     1928     1929     1931     1932     1933     1935
1907
1907.1: Edgar Schuster and E M Elderton, The Inheritance of Psychical Characters, Biometrika 5 (4) (1907), 460-469.

In April 1905 Messrs Heymans and Wiersma sent to all Dutch doctors (about 3000 in number) and to some others, six forms, each containing in all ninety questions concerning psychical characters, and their direct or indirect expression.

The recipient was requested to select from his friends and relations one family (containing father and mother and one or more children - where possible grown up), concerning which he happened to have exact knowledge, but otherwise at random, and to answer each question for each member of the family by underlining one of the alternative characteristics mentioned in the question.

Of the six forms sent, one referred to the father, one to the mother, and the remaining four to the children. The ninety questions were divided into six classes according to the nature of the characteristics to which they referred.
...
Conclusions. In conclusion we claim that we have made some of Messrs Heymans and Wiersma's numerical results more intelligible - to the initiated - by expressing them, by means of the statistical constants calculated, in a form which renders them comparable among themselves, and with similar results obtained for widely different characters in other places. It is no part of our present purpose to institute such comparisons, to examine the value of the original material, or to inquire how far the measured resemblance between parents and children is due to their having similar inborn characteristics and how far to the moral influence of the former on the latter. We will however point out, that after allowing for the effect of assortative mating the mean coefficients of resemblance between fathers and sons, and between mothers and daughters, calculated for one set of characters by the contingency method and for another set by the fourfold correlation method, come in each case to very nearly 1, the value proposed originally for the parental inheritance coefficient by Mr Galton.
1909
1909.1: Ethel M Elderton, On the Association of Drawing with Other Capacities in School Children, Biometrika 7 (1/2) (1909), 222-226.

An interesting paper has recently been published by E Ivanoff discussing the association of power of good drawing in boys and girls with other capacities. The relationships, however, are not expressed in terms of any modern statistical measure of correlation, and it is accordingly not easy to determine whether the drawing capacity is highly of slightly correlated with other characters, or what are the relative degrees of association between drawing and these characters. It seemed therefore worth while considering the data from another standpoint, and expressing it in a form more readily intelligible to the statistician. Each characteristic is divided into three categories, a 'mean' group, and a group above and a group below the mean. The classification of a group which contains 40 to 80% of the total frequency as 'moyens' is not to be commended. It corresponds, however, to a division into markedly good, markedly poor, and a middle group of 'indeterminates.' Thus for example Ivanoff uses for categories of attention 'Attentif,' 'Distrait' and 'Indéterminé,' and for temper 'Doux,' 'Violent' and 'Indéterminé,' while for most special studies including drawing he uses a 'moyens' group. He does not give, but from his data it is possible to deduce, contingency tables with 9-fold groupings. The coefficients of mean square contingency deduced from such tables will be comparable among themselves, but possibly 30 to 50 per cent below the true value of the correlation coefficient; eight tables were worked out by the fourfold table method and showed on an average 40 per cent. increase on the contingency values. It is only needful to bear this in mind when we are considering the absolute importance of the contingencies investigated.
1910
1910.1: Karl Pearson, Alice Lee and Ethel M Elderton, On the Correlation of Death-Rates, Journal of the Royal Statistical Society 73 (5) (1910), 534-539.

The discovery of possible inter-relationships between diseases by an examination of their death-rates as affected by varying environment, occupation, or race, has not been without fascination for more than one investigator. Personally I have considered the problem more than once, but always failed to make progress owing to the existence of spurious correlations, which I did not see how to meet....
...
It was only after reading Dr Maynard's paper in the current number of Biometrika, and thinking over the difficulties to which he draws attention, that another way of tackling the problem occurred to me. We reduce all our sub-populations to a standard population, or population with a standard age-distribution. The assumption made in doing this is, practically, that the particular standard population used is immaterial.
...
Miss Ethel M Elderton has kindly worked out for me the case of the 40 American cities dealt with by Dr Maynard, confining her attention, however, to the cancer and diabetes death-rates.
...
... it is proper to emphasise that the arithmetical work is excessively laborious; the determination of the corrective factor, the work of finding ten correlation coefficients, and of evaluating the determinants must not be undertaken without this word of warning, because the enormous amounts of arithmetic carried out by Miss Ethel Elderton and Dr Alice Lee are scarcely indicated in the mere statement of the results provided above.

1910.2: Ethel M Elderton with the assistance of Karl Pearson, A first study of the influence of parental alcoholism on the physique and ability of the offspring, Eugenics Laboratory Memoir Series X (Dulau and Co., London, 1910).

An attempt is made in this paper to measure the effect of alcoholism in the parents on the health, physique and intelligence of their offspring. The question of intemperance is one of the chief problems of our national life, and as such is beset with difficulties. It is surrounded with prejudices and has been too often treated with rhetoric, so that it is extremely difficult to free the mind from preconceived opinions and approach the subject with a purely judicial and calm statistical spirit. Yet if we are to deal with the drink question in a satisfactory and permanent fashion, reform must be guided by an instructed public opinion. No greater evil is done to a good cause, than when statistically undemonstrable statements receive, owing to emotional appeals, general credence, and then wider experience shows them later to be inexact. Nor again when we demonstrate that certain social results do not flow from alcohol, ought we to be charged with asserting that other results which we have not considered may not be directly due to it. The desire to know before acting, and the mind which refuses to express an opinion before knowledge, are so unfamiliar to many workers in the field of social reform, that the possibility of starting an inquiry without any bias as to its result seems to them almost an iniquity, the mark of an abnormal temperament.

1910.3: Karl Pearson and Ethel M Elderton, A second study of the influence of parental alcoholism on the physique and ability of the offspring, Eugenics Laboratory Memoir Series XIII (Dulau and Co., London, 1910).

A second study of the influence of parental alcoholism on the physique and ability of the offspring being a reply to certain medical critics of the first memoir and an examination of the rebutting evidence cited by them.
1912
1912.1: Ethel M Elderton, On the Relation of Stature and Weight to Pigmentation, Biometrika 8 (3/4) (1912), 340-353.

It is well-known that pigmentation differs widely from race to race. Further stature certainly and weight probably are racial characters. We might therefore anticipate that in investigations of stature and weight we should find a differentiation in these characters associated with the different pigmentation classes within the population of any town. This would arise not only because the chief classes of pigmentation are supposed to have originated from separate racial types, but because in many large towns there are considerable foreign elements not yet blended with the native population, e.g. in England and Scotland, we find Italian, Irish, Jewish and even Polish groups. In many cases these non-native elements form a considerable percentage of the population, and if, as often happens, they are the poorer section, then we may discover a relation between physique and environment which is not causal but racial in origin. Little attention seems to have been paid to this point in considering, for example, the effects of overcrowding on the weight and stature of children. The children who dwell in four-roomed homes are not necessarily of the same race as those who live in one or two-roomed homes. In a town like Glasgow, the Irish and Italian contingents are possibly more likely to be in one or two-roomed homes than the native Scottish, and a similar state of affairs probably occurs in those London school districts which contain large foreign contingents.

Before we have investigated the racial homogeneity of a population or before we have shown that racial differentiation does not indicate any economic differentiation, we ought not to lay much stress on the association of physique- measured by stature and weight-with environment. There is little doubt that a comparative study of native and foreign elements in our big towns, from the standpoints of both physique and economic condition would be of much service. Meanwhile it occurred to me that if an investigation were made of the relation of stature and weight to pigmentation a positive result would indicate the general importance of the problem. A negative result would show that within a homogeneous population pigmentation had little or no relation to stature and weight. It would not demonstrate that a large foreign element might not modify the conclusion, unless we were absolutely certain that in the material considered we were really dealing with a heterogeneous population.

In the present inquiry I have worked with Glasgow data, which I selected because I thought that I should include considerable Italian and Irish elements. For the schools, however, where the stature and weight were known as well as the pigmentation, the surnames do not suggest that the foreign element is extensive. Hence I think my inquiry is concerned only with the problem of whether in a fairly homogeneous population pigmentation is related to stature and weight.
1913
1913.1: Karl Pearson and Ethel M Elderton, On the Hereditary Character of General Health, Biometrika 9 (1/2) (1913), 320-329.

In dealing with the heredity of general health we have to meet at once certain fundamental difficulties. We have first, the question of environment and secondly the question of variety in health caused by what we may term accident. If we deal with families living in widely differentiated environments we shall have, or certainly may have, a spurious correlation of health in parents and offspring; the resemblance in health will be emphasised. On the other hand, when a single member of a family is exposed to a specially differentiated environment, i.e. goes to the West Coast of Africa, or spends his life in India, or catches enteric at a particularly unfavourable moment, the correlation of general health may be decidedly weakened in the case of parent and offspring. These difficulties of differentiated environment and what we may, perhaps, term accident cannot be wholly overcome, but we may endeavour to meet or measure them. In the first place we can confine our observations to one social class and thus go a long way to get differentiated environment removed. If, as in the present paper, we deal essentially with the professional classes, there is great uniformity of general environment. The food supply is sufficient, the doctor is always at command, physical exercise is fairly general and markedly insanitary houses or occupations are practically avoided. We do not think therefore that, for the data of the present paper, differential environment is a marked factor in producing correlation. On the other hand we do consider it possible that "accident" will weaken the relationships sought. The reduction in health-correlations below the values for other physical characters, might indeed be taken as a measure of random action on health, comparable with the random action of death itself in reducing the correlation of duration of life, which has already been discussed by one of us. Indeed heredity of general health is almost as significant for the problem of natural selection, as heredity of duration of life.
1914
1914.1: Ethel M Elderton, Note on Infantile Mortality and Employment of Women, Biometrika 10 (1) (1914), 193-196.

The author of this Report emphasises the difficulty of determining the effect of women's employment and points out that

"It would be possible to draw positive conclusions as to the relative importance of this particular factor only by point-to-point comparison of the infant mortality for a period of years in two large communities, or two classes of large communities, in which all the material conditions were substantially common, with the single important exception that in one a considerable proportion of the married female population of child-bearing age were at work outside of their homes and in the other community with which the comparison was made none of the women were so employed.

To admit of entirely sound conclusions, it would be necessary that the populations - and especially the women - of both communities should be of like ages, races, and physical health, that their living conditions should be practically identical, and that, in a general way, the child-bearing women should be of about the same grade of intelligence. In default of some such comparison on a broad scale of the mortality of the infants of working and non-working women of similar ages, races, intelligence, and living conditions, no one can determine accurately how many of the deaths of working women's infants are due to the mother's work and how many to the other conditions of their lives and environment."

The author illustrates the point by taking the six New England States and giving the infant death-rate, percentage of women of 16 years and over who are breadwinners, percentage of foreign-born to the population and percentage of population living in towns of 4000 and more inhabitants, and showing that, though the states with the highest infant mortality have also the largest number of women employed, they have also the largest percentage of foreign-born and of those living in urban surroundings, and that it is therefore impossible without further investigation to assign the infant death-rate to any of these three factors.

A further investigation has been undertaken into the 32 Massachusetts cities and the death-rate under a year is given, the percentage of foreign-born, the births per 1000 of the population, the percentage of women gainfully employed and the percentage illiterate, and a comparison is made between the ten cities with the highest and the ten cities with the lowest infant death-rate and percentage of women employed and the other factors enumerated. The conclusion is reached that "These comparisons indicate, superficially at least, that a more direct relation exists between infant mortality and the birth-rate, the percentage of foreign-born, and the percentage of female illiteracy than between infant mortality and the employment of women."

There can be no doubt that a direct study of the infant mortality in relation to women's employment can only properly be made, when we confine our attention to women, employed and unemployed, who are actually mothers and live in the same town, and when we correct for age, and if possible home conditions. Still if we take a series of different towns the right method must be to correct by the method of partial correlation for such divergent factors as we are able to ascertain and allow for in the series of towns investigated. I have endeavoured to apply modern statistical methods to the data of this Report ...

1914.2: Ethel M Elderton, Height and Weight of School Children in Glasgow, Biometrika 10 (2/3) (1914), 288-339.

In 1905-6 an enquiry was made in the Public Schools of the School Board for Glasgow as to the height and weight of all the scholars, the occupation of the parents, the number of rooms occupied etc. By permission of Sir John Struthers, of the Scottish Education Office, these schedules were most kindly placed at the disposal of the Galton Laboratory. The number of children concerning whom the enquiry was made is over seventy thousand of ages 5 to 18 years. The schools from which these children came were divided into four groups according to the district in which the schools were situated.

Group A comprised schools in the poorest districts of the city.
Group B comprised schools in poor districts of the city.
Group C comprised schools in districts of a better class.
Group D comprised schools in districts of a still higher class with which are included four out of five Higher Grade Schools.

The data were originally used by the Galton Laboratory with the object of discovering how far the physique of school children, judged by their height and weight, is affected by the occupation of the father and the employment of the mother. With this end in view the necessary data were entered on cards. Children over 14 were excluded and all children who had not both parents alive were also excluded; this left us with 30,965 girls and 32,811 boys.

The object of the present paper is to ascertain what is the average weight of a child of a given age and a given height.

1914.3: Ethel M Elderton, Report on the English Birthrate, Part I: England North of the Humber, Eugenics Laboratory Memoir Series (Dulau and Co., London, 1914).

The fall in the birthrate has received much attention of late years. The fact of the fall is not disputed but differences of opinion exist as to the importance of the fall and as to the circumstances which have caused it.

The fall considered by some as a natural outcome of increased prosperity; they assert that animals, when richly fed, breed less freely and conclude that the same applies to man; the fall in the birthrate they find due to an improved environment and recognise a natural process, not an artificial one.

Others regard the falling of the birthrate as due mainly to the deliberate limitation of the family, but regard this limitation as a mark of civilisation and as an advantage to the race; where there are fewer to provide for, there the few will have better opportunities; when the family is small, the children have greater advantages and a better chance of success in life.

Others, and, probably the greater number, regard the fall in the birthrate as a serious menace to our national efficiency. They point out that this fall has not been uniform in different physical and mental classes of the community; that a low birthrate in itself may not be a serious matter but that a differential birthrate, if it favour the less fit, may be a very dangerous social factor.

The birthrate is generally based on the number of births per 1000 of the population and there is a tendency to account for the fall in the birthrate by insisting on a diminishing marriage rate and on a later age of all marriages.

The first aim of the present paper will be to show in graphical form how great the fall in the birthrate has been and to correct as far as possible for differences due to changes in the marriage rate and in the age distribution of married women.

Secondly we shall try to discover in what type of district the fall is most marked.

Thirdly we shall inquire whether there are any facts which indicate whether the fall is due to a natural decrease in fertility owing to an increase in prosperity, or whether it is due to deliberate limitation of the family.

Fourthly, if we must conclude that the fall in the birthrate is due to deliberate limitation of the family, we shall try to discover whether there are any social or economic changes which have caused or increased that limitation.

Fifthly we shall discuss whether the fall occurs uniformly in all sections of the community or whether it belongs especially to any classes differentiated in physique and mentality.
1915
1915.1: Ethel M Elderton and Karl Pearson, Further Evidence of Natural Selection in Man, Biometrika 10 (4) (1915), 488-506.

The second author of the present paper writing in 1894 a commentary on the statement that "no man, as far as we know, has ever seen natural selection at work," remarked: "Every man who has lived through a hard winter, every man who has examined a mortality table, every man who has studied the history of nations has probably seen natural selection at work." The emphasis is here to be laid on the word "probably," because the seeing depends on the power and validity of the scientific means adopted to analyse the observed facts. In a paper communicated by the same author to the Royal Society in June 1912, it was shown from the Registrar-General's series of ten yearly life-tables that when allowance was made for change of environment in the course of the fifty years a very high association existed between the deaths in the first year of life and the deaths in childhood (1 to 5 years). This association was such that if the infantile death-rate increased by 10% the child death-rate decreased by 5.3% in males, while in females the fall in the child death-rate was almost 1% for rise of 1% in the infantile death-rate. The method of investigating by life-tables could not be extended beyond 1900, because the life-tables for the next ten years (1901-1910) were not then out, and indeed have only just appeared (December 1914). While the infantile death-rate as shown from the life-tables had risen from 1871-1900, the child death-rate had fallen for the same period. During the next decade 1900-1910 both death-rates have fallen together; such a secular change does not in any way modify the argument of the paper, which lies in the statement that whether two death-rates rise together or rise and fall simultaneously we can draw no inferences at all, until they have been corrected for secular change. Most economic, demographic and physical variates are changing continuously with time, and no comparison of time graphs or calculation of correlations will demonstrate of necessity anything but spurious association, until the time factor has been eliminated. It is the deviations from the continuous curves of secular change which may turn out on careful analysis to be truly indicative of causal relationship between the variates under consideration.

1915.2: Ethel M Elderton and Karl Pearson, The Influence of Isolation on the Diphtheria Attack- and Death-Rates, Biometrika 10 (4) (1915), 549-569.

The problem of the advantages of isolation, not only in the case of diphtheria but of other diseases of an infectious character, is likely, owing to modern views as to "carriers" and other sources of transmission, to be much discussed in the near future. It is therefore well to consider what may be learnt from the statistics available. The questions which naturally arise are of the following kind:

(i) In districts with a maximum of isolation is there a minimum of incidence?

(ii) In districts with a maximum of isolation is there a minimum death-rate from the disease isolated?

There cannot be the slightest doubt that, if these two questions were answered in the affirmative and we could show that the incidence was markedly less and the death-rate significantly smaller in districts where isolation was most stringently carried out, then these results would be advanced as a strong argument in favour of isolation.

To the trained statistician, however, no conclusion based upon such results without much further analysis would have any validity. To illustrate this point, let us consider the hypothetical case that medical or popular opinion in a given town has been persistently in favour of increasing the isolation-rate, and further suppose that in this district improved economic conditions have increased the immunity, or bettered sanitation lowered the incidence, while at the same time new methods of treatment have lowered the death-rate of the disease; it will be clear that in considering the statistical results over a course of years we should find a high isolation-rate negatively correlated with both the incidence- and the death-rates. Thus if we considered this correlational as a causal nexus, we should be raising an apparently strong argument in favour of a maximum of isolation, which would be based on the statistical fallacy, that when two quantities are both changing continuously with the time, this must of itself denote a causal relation.

In precisely the same way a positive correlation between the isolation rate and the attack- or death-rates by no means justifies us in asserting that isolation is worse than non-effective. It is conceivable that in the period or the district under consideration with an increasing isolation-rate there might be decreased immunity in the population, greater virulence of the disease, or even a limit to the available isolation accommodation, so that in the case of attacks of an epidemic nature the isolation rate would not increase proportionately to the cases, or indeed might even diminish. Further, if apart from the changes in a single district, we consider a great variety of districts, it may chance that the greatest isolation-rate occurs in those districts where the disease has been found most prevalent, because it appeared the most obvious remedy, and thus a greater attack- or death-rate would be no real measure of the futility of high isolation.

If, however, it should turn out that on the whole the higher isolation rate is associated with the higher attack-rate or the higher death-rate then it will be clear (i) that there is ground for demanding a closer investigation as to the advantages of isolation, and (ii) that we may be overlooking the real method, or at least one or more important factors, of the transmission of the disease. It is conceivable that isolation of all cases during attack may be of far less importance than isolation of certain special cases for a shorter or longer period well subsequent to the attack, and after they would normally have resumed their ordinary avocations.

The main problems which arise are accordingly these:

(i) Have isolation-, attack- and death-rates changed continuously with the time, and are the apparent correlations really suggestive of causal relationships?

(ii) Are associations between isolation-rate and attack- and death-rates really spurious arising from the fact that where the attack- and death-rates have been severe there the remedy which appeared nearest to hand was more isolation?
1919
1919.1: W Rowan, E Wolff, P L Sulman, K Pearson, E Isaacs, E M Elderton and M Tildesley, On the Nest and Eggs of the Common Tern (S Fluviatilis). A Cooperative Study, Biometrika 12 (3/4) (1919), 308-354.

This paper may be looked upon as a continuation of that published in Biometrika, Vol. x. pp. 144-168. It is based upon a census of the eggs made July 3rd-20th, 1914, and contained in Rowan's Fifth MS Report on the Faunistics of Blakeney Point, the Field Station under Professor F W Oliver's direction on the Norfolk coast. The year was a record year for the common tern, a marked contrast to 1913, the young were abundant as well as the eggs, and many of the birds were still laying. Some peculiar nests were found: (a) one entirely of seaweed, (b) another of large wood shavings, (c) one of selected small pebbles, (d) a very large nest - the largest yet met with. Some of the nests are illustrated in Plate II and will suffice to indicate the considerable differences between their make up and environment.

1919.2: Ethel M Elderton, Life-History Albums, Biometrika 12 (3/4) (1919), 373-374.

The Personal and Family History Register compiled by Dr Taylor is extremely interesting, and if people could be persuaded to keep the records asked for and to forward the book when completed to some central agency such as is intended, the statistical data then available should be most useful. In this register under one cover all the children of one family have their life histories recorded, and if the individuals are to be studied only in their childhood this is an advantage, but if it is hoped by means of a register to provide the life history rather than the child history a separate volume for each child would be preferable; then as each child left the home the book could go with him to be continued and completed. Francis Galton in the Life-History Album issued years ago preferred this second plan and arranged that each child in the family should have its own album.

To the statistical worker in Eugenics so many problems in heredity are still unsolved, problems dealing with fertility, with inheritance of disease, with age at death, etc. that no record of personal history seems adequate which does not provide the data from which such problems can be attacked. In the Personal and Family History Register information as to date of birth and date of death is sought for parents, grandparents, great-grandparents, etc. up to the sixty- four ancestors in the seventh generation, and such a record is interesting, but one feels that cause of death and some information as to general health, if obtainable, would make the data more useful. Further there is no space assigned for collaterals. In the introduction the following occurs: "It is of interest to obtain data also on collaterals (uncles, aunts, cousins, etc. and alliants (members by marriage). These extras can be inscribed on a page marked ' Special Happenings' or on separate sheets or cards, and placed in the pocket at the end." Our experience is that even when a special space is provided for an entry the information required is not always given, and I think that except in a very few cases extra data of this kind will not be given, and I am inclined to think that knowledge of the brothers arid sisters of the parents is of more importance for determining the hereditary characteristics of an individual than knowledge of the great-grandparents. Cousins, we found, were as closely related to one another as grandparents to their grandchildren, and the data concerning them could be more easily obtained and would be more reliable than those concerning individuals who lived perhaps 100 years ago.

Personally I feel that careful details concerning the life history of a baby, interesting as they may be, are of little value to the student of Eugenics, unless the hereditary history is fully given.
1920
1920.1: Ethel M Elderton, On the Inheritance of the Finger-Print, Biometrika 13 (1) (1920), 57-91.

The inheritance of finger-print types when once those types have been analysed and classified seems an almost ideal subject for the study of heredity in man. It would appear at first sight that they would present most excellent material for comparing various theories of inheritance and measuring the intensity of heredity between the different grades of kinship. Yet as far as I am aware nothing has hitherto been published on the subject either from the Biometric or the Mendelian standpoint. By 1903, data had been collected and reduced showing the degrees of inheritance for many physical characters in both animals and man and the collection and reduction of data for the heredity of mental and moral characteristics in man had been started. It would appear strange that finger- print types should remain unregarded, - the "arch," the "loop," the "whorl," the "composite" were familiar to many and seemed by their easy determination for the purpose of criminal indices to be most appropriate for the study of heredity. Two chief difficulties, however, stood in the way. First the great labour of collecting in adequate quantities the finger-prints of relatives; and secondly the still more important fact that while four or five broad categories were adequate for a criminal index, they were inadequate for scientific distinctions. Galton at first ran up his four or five categories to 53, and the continual appearance of transitional forms led him further and further in the sense of finger-print continuity. Without exaggeration one can say that he sought for years for quantitative measures of the finger-print, which might be applied to any type, and that, when he had appreciated continuity, it was this failure to obtain quantitative measurement which ultimately led him to put the problem on one side. Nevertheless those who were intimate with him in the last ten years of his life know the prominent part which the inheritance of finger-print types played both in his thoughts and activities.
1923
1923.1: Karl Pearson and Ethel M Elderton, On the Variate Difference Method, Biometrika 14 (3/4) (1923), 281-310.

Every one is familiar with data which show a secular trend with time, say the deaths from tuberculosis as measured by the corrected death-rate from 1865 down to the present or again the falling birth-rate per married woman between 15 and 50. Now the data for such matters do not when plotted take the form of smooth curves corresponding to continuous mathematical functions; they exhibit general trends with the time, but they rise and fall with apparent, but not indeed necessary irregularity, above and below a sort of average curve representing the secular trend. The words "sort of average curve" are vague and intended to be so, because much of the matter in dispute turns on the manner in which the curve representing the secular trend is to be determined. The curve which represents this secular trend may be a long period periodic term or it may not. Generally we have absolutely no reason to suppose it is so, but we may imagine it so, if we have a monomania for the representation of time-functions by periodic analysis. We have, however, no reason for supposing that increased consumption of apples or bananas, or increasing expenditure on the navy, per head of the population are periodic in their nature; they may rise or fall according to circumstance ...

Of course in any case in which it seemed reasonable to use a harmonic curve, one would naturally do so, but in the cases we have chiefly in mind this is certainly not so, and it is far more reasonable to suppose that the secular trend can be given by a single high order parabola, or by the series of such parabolae involved in a good smoothing process, than by any products of periodic analysis.

1923.2: Ethel M Elderton, A Summary of the Present Position with Regard to the Inheritance of Intelligence, Biometrika 14 (3/4) (1923), 378-408.

Intelligence is defined in the Oxford Dictionary as meaning primarily "the faculty of understanding" and it is in that sense that I propose to use the word. Secondary meanings for the word intelligence have grown up, meanings that have rather the sense of extent of knowledge, and it is that idea that we must banish from our minds. People with good intelligence will be capable of acquiring information readily and will assimilate it; but it is possible to be a regular repository of information and yet to be singularly lacking in the power to use it; such power lies in intelligence, that faculty of using one's existing information to arrive at a right decision in some new field of thought or at a reasoned course of action under unusual circumstances, and it is this power which will make the difference between a well informed intelligent person and a well informed unintelligent one. We shall expect a correlation between intelligence and acquired knowledge but not by any means necessarily a very high one. Is this faculty of understanding inherited or is it largely, if not wholly, the product of opportunity, of environment and of education? No one would suggest that all the children in one school are equally intelligent but are the variations we see due to differences in natural ability or to a different home environment, or to an unsuitable educational environment, or are the variations due chiefly to one of such causes, while the others are of some but of much less importance?
1927
1927.1: B Perott and Ethel M Elderton, Correlation Between Prognosis Based on Condition of the Tuberculous Patient at Entry to a Sanatorium and the Issue, Annals of Human Genetics 2 (1/2) (1927), 63-75.

The problem before us is the discovery of the simplest way of estimating the probable issue for the tuberculous under sanatorium treatment from the condition of the patient at the time of entry. The material on which this paper is based was collected by the first named author when he was the Chief Physician, Director and Lecturer of the Imperial Sanatoriums in Russia, Finland.
1928
1928.1: Ethel M Elderton and Margaret Moul, On the Growth Curves of Certain Characters in Women and the Interrelationship of these Characters, Annals of Human Genetics 3 (3/4) (1928), 277-336.

In Volume 11, Parts I and II, of the Annals of Eugenics, Professor Ruger of Columbia University and Miss Stoessiger of the Galton Laboratory discussed the growth curves for certain characters in men. The material had been collected in Francis Galton's first Anthropometric Laboratory which was established at the Health Exhibition at South Kensington in 1884. Just over 7000 men passed through the Laboratory and roughly 1850 women, but about 100 of these women did not complete all the tests; in this paper we are considering the growth curves for about 1800 women. The task before those who computed the curves for the women was far less arduous than that of Professor Ruger and Miss Stoessiger as they had not a third of the number of cases, but this paucity of numbers has its drawbacks. For the men it was found that there were not enough cases of males under 12 to give accurate measures of growth and that from 12 to 17 the numbers were really insufficient for a discussion of variability. Among the women the difficulty is even greater, for though the proportion of women at the younger ages relative to all the women is similar to the proportion of men, the total being less, we have much smaller frequencies on which to base means and standard deviations. Taking the numbers of males and females in five year age groups, choosing in each case the table with the largest total frequency, we give in Table A the number of males and females in each age group per 1000. Persons over 70 are so few that they have been omitted from this table.
1929
1929.1: Karl Pearson, G B Jeffery and Ethel M Elderton, On the Distribution of the First Product Moment-Coefficient, in Samples Drawn from an Indefinitely Large Normal Population, Biometrika 21 (1/4) (1929), 164-201.

Note. Ethel M Elderton computed the "Table of the product moment $T_{m}$ function."

1929.2: Ethel M Elderton, Note on Variability in Girls and Boys (Glasgow) for Height and Weight, Biometrika 21 (1/4) (1929), 429-430.

In a memoir published in Vol. x. (pp. 288-339) of this Journal, I dealt with the regression curves of weight and height on age of a very large number of Glasgow children. These children were grouped in four classes of schools, A, B, C, D, according to the economic conditions of the district. In that paper although they were necessarily computed I did not publish the standard deviations for each age-group, as I was seeking only the change in height and weight with age. My numbers were so large that it was possible to obtain standard deviations with a relatively small probable error. I have since found several investigators inquiring for reliable measures of the variability in stature and weight of boys and girls. Accordingly I give here two Tables. The first provides the Means, Standard Deviations, and Coefficients of Variation of the entire population of children not divided into the groups A, B, C and D. The second gives the Means, Standard Deviations, and Regression Coefficients of Weight on Height for school ages of the four grades. The ages are central ages.
1931
1931.1: Ethel M Elderton and Margaret Moul, Table of the Values of the Differences of the Powers of Zero, Biometrika 22 (3/4) (1931), 306-308.

At the time when the first quarter of this table was originally worked (for a special problem during the War) the authors (Karl Pearson and Ethel M Elderton) of it were unaware of Cayley's paper. Later being informed of it, they checked the original work by reduction from Cayley's numbers, ... [The table presented] is probably the most extensive table of the differences of the powers of zero yet published. ...Laplace has indicated the importance of the differences of the powers of zero in the theory of probability for problems allied to that of De Moivre, and further illustrations will be given in the forthcoming Part II of the Book of Tables for Statisticians and Biometricians.

1931.2: J Wishart, T Kondo and E M Elderton, The Mean and Second Moment Coefficient of the Multiple Correlation Coefficient, in Samples from a Normal Population, Biometrika 22 (3/4) (1931), 353-376.

Note. The paper is by John Wishart but an Appendix by Tsutomu Kondo and Ethel M Elderton gives "Tables of the Mean Value and Squared Standard Deviation of the Square of a Multiple Correlation Coefficient."
1932
1932.1: E M Elderton and T L Woo, On the Normality or Want of Normality in the Frequency Distributions of Cranial Measurements, Biometrika 24 (1/2) (1932), 45-54.

It is well known that the general appearance of the distributions of anthropometric characters led Quetelet and afterwards Galton to the assumption that such characters were normally distributed. The normal curve was then introduced into anthropometric discussions, and became almost as much a fetish in anthropometry as in the theory of astronomical observations.

It is, however. undoubtedly true that a number of antitropometric characters, if taken in not too large samples, roughly obey the normal law. With larger and larger populations the deviation becomes more and more obvious. Some recent craniometric investigations suggested that the approximate normality of a considerable number of anthroponmetric characters might be due to such characters depending upon a variety of elements of growth, and when the number of such elements was reduced there might be a distinct weakening in the normality of distribution. Thus while the stature of adults in samples of, say, a thousand may be approximately normal, cubit is less so, and head length or breadth still less so, although these latter cover several bones of the skull. This is more or less in accordance with the idea that the normality of a distribution arises from the action of a multiplicity of a large number of contributory causes each supplying a small amount of the variation.
1933
1933.1: E M Elderton, The Lanarkshire milk experiment, Annals of Human Genetics 5 (3/4) (1933), 326-338.

This experiment was carried out in 1930 and a paper was published in that same year by Dr Leighton and Dr McKinlay.

For four months in Lanarkshire in certain schools 5000 children were given 2 pint of raw milk a day and 5000 children in these same schools were selected to act as a control series; in another set of schools, 5000 children were given 2 pint of pasteurised milk and another 5000 children in these same schools were selected to act as a control; the children were measured and weighed at the beginning and end of the experiment.

"Student" [William Gosset] in a paper "The Lanarkshire Milk Experiment" published in 1931 in Biometrika, Vol. XXIII, pp. 398-406, dealt with the difficulties of comparison which may be restated briefly from his paper:

(1) Raw milk and pasteurised milk were never given in the same schools.
(2) The initial heights and weights of the children in the control series were greater than those of the children who were milk fed.
(3) The children were weighed in their clothes and the first weighing was in February and the second in June; had there been no selection of cases this would not have mattered but it seems possible that the slightly poorer children who were given milk would lose less weight from change of clothes than the children in the control series who are assumed from their greater height and weight to be slightly more prosperous.

"Student" suggested that the experiment should be carried out on identical twins and if identical twins were more numerous and could with ease and certainty be discriminated from other twins they would be ideal subjects for such an experiment. In the absence of such data Professor Pearson suggested that, from the original cards, enough children of each class - controls, raw milk feeders, pasteurised milk feeders - could be found and paired who would have the same initial height and weight within reasonable limits.
1935
1935.1: Catherine M Thompson and Ethel M Elderton, Strength of Vision in Relation to Eye and Hair Pigmentation, Biometrika 27 (1/2) (1935), 266-268.

Note. This paper was written up by Karl Pearson.

Many years ago Francis Galton raised the question of whether it was not desirable to select candidates for the Civil Service not only by their intellectual powers and the capacity to satisfy a medical examiner, but, especially in the case of tropical appointments, by physical characters which do not enter into the customary medical inquiry. For example, was it more profitable to send young men of light or dark complexion to hot countries. What hair and eye pigmentation were more suited to India or again to Central Africa.

Last year my colleague, Professor Fawcett, asked me with a like end in view whether I knew of any data associating vision with pigmentation. Besides much data not yet reduced taken in the Anthropometric Laboratory at University College, London, I had on loan and in course of reduction data from the Cambridge Anthropometric Laboratory. This latter material offered in the case of some 1500 young men, between 18 and 22 years of age, the means of determining for one visual character, strength of sight, the relation to pigmentation. It did not, however, provide the effect of bright light of various intensities on modifying this relation of sight and pigmentation, and for this reason could scarcely be of service for Professor Fawcett's purpose. The results appeared of sufficient interest in themselves to deserve publication in the Miscellanea of this Journal. The material was extracted from the Cambridge data and tabled by Miss Catherine M Thompson, a student in the Department of Statistics in University College, London. The constants were then worked out by Dr E M Elderton, and partly, under her supervision, by Miss Thompson. The Editor is solely responsible for the arrangement of the material and the conclusions drawn from it. He would state, however, that the Right Eye is known from other investigations to be more long-sighted than the Left.

Last Updated September 2021