CHAPTER 10

THE DIMENSIONS OF QUANTIFICATION IN HISTORICAL RESEARCH

Chukwuemeka Tony Nwosu, PhD

Introduction

More than any other new approach the influence of quantitative history has been quite pervasive. In the case of economic and social history something approaching a transformation has taken place, there is almost no branch of historical research that has not been affected. Infact, there are two reasons that account for this development. First, the cardinal shift in emphasis from the individual to the majority which occurred earlier in this century has major quantitative implications. Thus, for as long as historians concentrated on the doings of the great, they hardly needed to account. However, once they became profoundly interested ineconomic growth, social change as well as the history of entire communities, questions of number as well as proportion assumed a critical significance. Infact, Economic and Social historians who turned for guidance to the social sciences had to face the fact that the quantitative element in both economics as well as sociology was noticeable. Although, if historians proposed to deal with the same sort of questions as economists and sociologists, they could hardly avoid using-or at least-testing-their methods. Secondly, the next reason is technological in nature. The computer came of age during the 1960s, it became cheaper as well as more accessible, while both the kind of data it could handle as well, the operations it could carry out were expeditiously diversified, in ways which were indeed suitable for the requirements of historical research. For the first time, a whole range of quantitative exercises which would have defined unaided human effort became practicable as a result.

The theme of this work is to offer a valid historical context that, quantitative history is founded on the persuasion that in making quantitative statements historians should take the burden to count rather than content themselves with impressionistic estimates. It seeks to bring into focus and address the various variables associated with quantification in history and that quantification has still shown itself, as a powerful addendum or augmentation to the historians’ toolkit in historical analysis.

Quantitative History

A good example of the difference which this can make is the Atlantic Slave Trade. Historians until recently had assumed that the number of Black Africans shipped to the New World between fifteenth and nineteen centuries totaled somewhere between fifteenth and twenty million. It is important to note that this figure was based on little more than the guess work of nineteenth century writers, a lot of them prominent in the campaign to abolish the slave trade.

Phillip Curtin, in his quantitative study, The Atlantic Slave Trade: A Census (1969), concluded that the number had been markedly exaggerated. He showed that the total was most unlikely to have been more than ten and a half million or less than eight million, by first critically evaluating and then adding together the figures for particular periods and areas of trade. Whatever the total, it still represents an appealing blot on the record of western civilization; however, this adjustment has no bearing on the moral outrage of posterity. But Curtin’s figures provide for the first time a solid basis for considering the effects of the trade on the societies of tropical Africa and those of the Americas.

For historians who do wish to generalize, however, quantitative methods offer certain merits. Infact generalizations are implicitly quantitative in character, although, this may not always be clearly brought. As Lee Benson says, historians who use words like “typical”, representative”, “significant”, “widespread”, “growing”, or “intense” are making quantitative statements whether or not they present figures to justify their assertions. Benson contends in the same passage, of “the impressionistic approach long dominant in American historiography, and the present writer have intermittently been worried by this kind of thing as a historian. It seems fair to say, nonetheless, that these techniques have more often been applied to individual bits of information than to broader statements.

Historians make quantitative statements more frequently than might at first be supposed, in the course of their work. Certainly, questions like ‘what was Charles I’s revenue in 1642?’ or ‘how large was the liberal vote in the general election of 1906?’ calls for an answer as numerically accurate as the sources can permit, and the reader of a reputable secondary work would expect nothing less. As earlier stated, many of the broader generalizations which historian incessantly make are by implication quantitative also-for instance, ‘the British working class was literate by 1914’ or ‘women married late in early modern England,’ Note however, a statement of this kind may reverberate the observation of a thoughtful contemporary, or it may arise from a comparison of a number of well authenticated instances. So how can we tell whether the contemporary was right, or that the examples cited are typical? It is only a quantitative analysis can put these statements beyond reasonable doubt, by revealing the incidence of literacy as well as the range and frequency of the ages at which women actually married. Most historians were indeed reluctant to accept this postulation. G.M. Trevelyan, in the 1940s explained the evidential base of his subject in these words:

The generalizations which are the stock-in-trade of the social historian must necessarily be based on a small number of particular instances, which are assumed to typical, but which cannot be the whole of the complicated truth.

The probable challenge associated with this method is that the particular instances can all too easily be selected to confirm what the historian expected to find, and conviction may be lent to unwarrantable presumptions. Nowadays the findings of the ‘qualitative’ historians like Trevelyan are being increasingly refined by the quantitative analysis of data systematically assembled to reflect an entire society. In this regard and for this purpose not only the main trend is revealed but also the variations as well as exceptions which highlight the distinctive experience of a particular group or locality. However, Curtin’s work on the slave trade was significant not only for establishing a total, although for also quantifying the concentration of the trade in the eighteenth century and the exceptional losses sustained by Angola as well as the Niger Delta area as compared with the other catchment areas. Infact, at its most ambitious, quantitative history seeks to illustrate an entire historical process by measuring as well as comparing all the relevant key factors: why did the population of England increase so dramatically during the eighteenth century? What effects did the construction of railways in the mid-nineteenth century have on the development of the American economy? At this juncture, quantitative history stakes its claim to be not simply an ancillary technique, however, to take over the centre stage of historical enquiry.

An immense scholarly effort has been invested in quantitative research, and increasingly sophisticated statistical techniques have been applied during the past thirty years. Furthermore, the findings are often presented in a highly technical and inaccessible manner, as will be clear from a glance at any recent volume of the Economic History Review or the Journal of Economic History. Without doubt, this poses a challenge for non-quantitative historians who are reluctant to take these findings on trust and yet are uncomfortably aware of the authority which is attached to quantitative statements of all kinds in the present era. Besides, it is pertinent to state that the clarion call which is periodically made that all historians should have some instruction in statistics is scarcely realistic. Though no specialized knowledge is required to understand where quantitative historians get their figures from or in broad specification or terms the uses to which they can be put. On what it can achieve and what it cannot a non-technical discussion of these issues is sufficient to indicate both the strengths and weaknesses of the quantitative approach.

Demographic History

Another dimension of quantitative approach has to do with what is referred to as demographic history. Thus, the field in which a quantitative approach is most significant and where arguably it has made its greatest contribution is demographic history. Obviously, demography without numbers is an absurdity, accordingly in this area the quantitative historian can fairly claim to be indispensable. In other words, demographic history involves a great deal more than merely working out the size of a given population in the past-difficult though even that can be in the absence of reliable census data. Also, germane than the total is the breakdown in terms of age, gender as well as household size. Undoubtedly, calculations of this kind may reveal the ratio of producers to dependants, the proportion of households with living-in servants, as well as other indicators of significance to the economic and social historian. On the contrary, the most challenging task facing the demographic historian is to determine the causes of population change over time-or the lack of it. The first step here is to reconstruct the birth rate, the marriage rate as well as the death rate. Furthermore, each of these ‘vital’ rates are in turn influenced by many different factors which lend themselves to quantification with greater or lesser ease-the incidence of contraception and abortion, the age of marriage, the illegitimacy rate, the impact of famines and epidemics etc. The attraction of this kind of enquiry for many is that it uncovers patterns which relate to the whole of society, rather than just that segment of it illuminated by literary sources or evidence. For instance, in the case of pre-industrial societies which lived so much closer to the margin of subsistence than our own, it can be argued demography was the determinant of social as well as economic life. On these grounds demographic history, is central to the kind of ‘total history’ written by Annales School with its primary interest in the early modern periods.

However, defined, demographic history majorly depends on two types of sources. Thus, the first lists all the members of a country or community alive at any particular point in time. Although this is of course the basic function of the modern census, which was invented in the Scandinavian countries in the mid-eighteenth century. Since 1801, in Britain a census of the whole population has been taken at ten-yearly intervals and it is generally conceded that after 1841 (when the name of each individual was noted for the first time) errors in the totals are statistically infinitesimal. Also, other listings survive from earlier periods-tax returns, returns of church communicants, declarations of political loyalty etc. The margin of error is very uncertain and inconsistent, though comprehensive in intent, however, these were seldom so in practice. One obvious effect of the relatively recent origin of census-taking is that it has proved extraordinarily difficult to establish the relationship between demographic change as well as the onset of industrialization in late eighteenth century Britain. Basically, this is where the second type of source comes in-the recording in sequence of the ‘vital’ events in a given area. From 1538, for English history the most significant source is the parish registers kept by the Anglican incumbents who were required by law to record all baptism, marriages as well as burials in their parishes; the system persisted until the beginning of civil registration in 1837. E.A. Wrigley and R.S. Schofield from a sample of parish registers have calculated national rates of births, marriages and deaths and have used these to project the total population of England back from 1801 as far as the mid-sixteenth century. As a result, they are able to pinpoint small variations in the growth rate much more precisely than before, and to demonstrate the preponderant influence which changes in the marriage-rate had on the long-term rate of population growth.

Other Fields in which Quantitative Methods Apply

It is also worthwhile to say that the second field in which quantitative methods have proved significant is the history of social structure. At this juncture it is important to note that there is infact a close connection between this field as well as demographic history, simply because the same sources loom large in both. Note however, that any source which list an entire population or records its ‘vital’ event offers, at least potentially, the possibility of classifying that population into social groups. Besides, this is most easily attained in the case of groups defined by age or gender. Though historians are becoming increasingly resourceful in abstracting other aspects of social structure from demographic data. A case in point is the changing size and structure of the household. The evidence of both pre-census listings and family reconstruction has effectively undermined the traditional notion that pre-industrial society in Western Europe was characterized by large, complex households of the extended family type. From the mid-nineteenth century the ever-increasing scope and precision of the questions asked in the census means that a whole range of social issues is opened up to quantitative analysis-occupation, status, religious affiliation, rural migration to the towns, and so on. The ‘new urban history’ in the United States is largely based on the premise that the changing social structure of a city can be reconstructed by analyzing the manuscript schedules of the U.S. Census in conjunction with other nominative data (notably tax records, city directories and registers of births, marriages and deaths).

Probably, it may seem startling and astonishing that quantitative methods have much relevance to the third field to be considered here, that is, political history. Indeed, the customary concern of the political historian is, after all, with ‘unique’ events and with the actions and motives of individual statesmen. As soon as the field of enquiry is broadened to include the political system as a whole, quantitative history comes into effect. Thus, this is evident in the realm of electoral behaviour. The concept of psephology- the study of present-day elections-is largely a matter of juggling with numbers, so too the study of elections in the past demands a quantitative approach. Undoubtedly, for any period up to the development of opinion polls in the 1950s the quantification of political attitudes presents major challenges (and it can be argued that it still does). Nonetheless the historian has other advantages which are denied to the modern psephologist. Before the coming of the Ballot Act of 1872 parliamentary elections in Britain were conducted in the public and votes were individually recorded. Where registers of votes can be analyzed in conjunction with other nominative data on income, status or religion, the way is open to firmer conclusions about the basis of party affiliation in nineteenth century Britain.

Quantitative methods have also been usefully applied to economic history and have had a decisive impact. Economics –like demography –is a highly quantitative discipline. Therefore, the principal elements in an economic system-prices, incomes, production, investment, trade and credit-all lend themselves to precise measurement; indeed, they demand it if the workings of the system are to be clearly understood. Economic historians collected quantitative economic data, from the beginning of economic history as a distinct specialism in the late nineteenth century, usually as one aspect of whatever research they were engaged on. However, it is only in the last thirty years or so, that historians have tackled the challenge of constructing extended statistical sequences, often from varied as well as imperfect sources, as a means of illuminating long-term economic trends. R.B. Mitchell as well as Phyllis Deane’s Abstract of British Historical Statistics (1962) represents the most systematic attempt to do this for Britain so far. But it is some of the French quantitative historians who have pressed this approach furthest: the exponents of ‘serial history’ (l’histoire serielle) aim to build up extended sequences of prices, crop yields, rents and incomes which together will enable them to construct a model for France’s development during the early modern period-and ultimately Europe’s as well. If anything, the claims of the ‘new economic history’ (or ‘cliometrics’) in the United States are in the meantime greater.

Statistical Know-How: An Addition to the Historians Tool-Kit

At times, it is imagined that the application of quantitative methods on a large scale displaces the traditional skills of the historian and calls for an entirely new breed of scholar. Indeed, in all intent and purposes, nothing could be further from the truth. Note however, that statistical know-how can only be effective if it is treated as an addition to the historian’s toolkit, and subject to the normal controls of historical method. The obligation to subject quantitative data to tests of reliability is at least as great as in the case of literary sources, given the special authority which figures carry in our numerate society. As soon as the figures have been verified, their interpretation as well as their application to the solution of specific historical challenges requires the same qualities of judgment as well as flair as any other kinds of evidence. It is significant to realize that each of these two stages presents its own challenges. To have any validity at all, conclusions about social movements must have a statistical basis.

Where a historian is lucky enough to find a set of readymade statistics-say a table of imports and exports or a sequence of census reports, in that case the historian is saved an immense amount of work. However, the reliability of such sources must never be taken for granted. The historian needs to exactly know how the figures were put together. Were the returns made by the man-on-the-spot distorted by his own self-interest-like the tax-collector who understated his takings and pocketed the difference? Were the figures conjured out of thin air by a desk-bound official, or totted up by a subordinate who was not competent in arithmetic? More importantly, both of these possibilities arise in the case of the impressive-looking statistics published by British Colonial administrations in Africa which were often based on returns made by poorly educated and underpaid chiefs. Also, how much scope was there for errors of copying as the figures were passed on from one level of the bureaucracy to the next? Could the same item have been counted twice by different officials? Where statistics were compiled from questionnaires, as in social surveys or the census, we need to know the form in which the questions were put in order to determine the scope for confusion on the part of the respondents, and we have to consider whether the questions on - income or age, for example-were likely to elicit frank answers. Against this backdrop, only an investigation of the circumstances of compilation, using the conventional skills of the historian, can provide the answer to these questions. Though it has proved extremely useful to classify, arrange, and summarize the available information, it may be even more rewarding-to judge from some of the ventures that have already been made-to attempt more complex methods of descriptive statistical analysis by the use, for example, of mathematical model or of scaling techniques.

Customarily, what interest historians in their calling and craft is less a single set of figures than a sequence overtime which enables them to plot a trend. For the historian the figures must accordingly be tested not only for their reliability but also for their comparability. No matter how accurate the individual totals in such a sequence may be, they can only be regarded as a statistical sequence if they are strictly comparable-if, that is, they are measuring the same variable. However, it needs only a slight discrepancy in the basis of assessment to render comparisons null and void. Oftentimes a classification which seems clear and consistent enough on paper may be applied differently overtime, or between one place and another, which is one basic reason why comparative criminal statistics have to be treated so cautiously. With respect to English census, the increasing refinement of the occupational schedule in every count since 1841 means that it is difficult to quantify the growth as well as decline of specific occupations. Notwithstanding even the most seemingly straightforward statistical sequences may conceal pitfalls of this kind. Thus, comprehensive commercial statistics for England date back to 1696, when the post of Inspector- General of Imports and Exports was created. But because the official table of values drawn by the first Inspector-General was applied almost without modification until the end of the eighteenth century, during which time some prices rose while others fell, the figures as they stand cannot be used to calculate the changing balance of trade.

Quantitative procedures by no means preclude, nor indeed can they possibly eliminate, the use of value judgments, speculations, intelligent guesses, or “the imagination and intuitive feel which the historian, and for that matter the social scientist, should bring to his subject. For instance, consider the official cost - of - living index which measures the cost of a typical “shopping-bag” against the current wage rate. Infact in Britain the index, begun in 1914, ought to provide a reliable picture of the declining standard of living during the Depression of the 1930s. But during the Inter-war period the price side of the index continued to be based on the same ‘shopping-bag’, even though changing patterns of consumption meant that the weighing given to the various items (fresh vegetables, meat, clothing, etc) in 1914 no longer corresponded with the actual make-up of the average family budget.

Be that as it may, quantitative history is not based on ready-made statistics. The advantages of a statistical approach to public issues began to be canvassed only in the late seventeenth, century; and it was only during the nineteenth century that the state acquired the resources of manpower and money to undertake such work, and only in the present century that statistical information has been gathered in a really comprehensive way by both government and private bodies. Frank Knight once observed that Lord Kelvin contended that “if you cannot measure, your knowledge is meager and unsatisfactory.” For most of the questions that interest historians, the likelihood is that the figures will have to be labouriously constructed from the relevant surviving materials. It is infact not easy to construct quantitative data in such a way that valid statistical inferences can be drawn from them. The historian seeks for data from varied and scattered source materials and the issues of reliability and comparability will be posed, not once, but many times over. In this regard, the classification of the data in tabular form now becomes the task of the historian; and the criteria on which that classification is based raise questions of historical judgment rather than statistical method.

The construction of statistics, above all, raises acute challenges of selection. Inspite of the foregoing, it is true and incontrovertible, that quantitative enquires whose scope is so narrowly defined that all the relevant data can be assembled: W.O. Aydelotte’s quantitative collective biography of all the members who sat in the parliament of 184-47 (the period of Sir Robert Peel’s Premiership leading to the split in the Tory Party over the Corn Laws) is a case in point. Monographs on the composition of the British House of Commons, which are now fairly numerous and cover a time-span of six centuries, have brought to light significant continuities and changes in the social structure of the British political elite. Crane Brinton, in his well-known quantitative study of the members of the Jacobin Clubs, reached the conclusion that the Jacobins represented “a complete cross-section of their community” and that: “The Jacobins of 1794 were not a class, and their enemies the ‘aristocrats’ were not a class. The Terror was not chiefly then a phase of the class-struggle, but even more a civil war, a religious war. Donald Greer, on the basis of a quantitative analysis of the victims of the Terror, argued that the lower classes, by the definitions he used, supplied 70percent of the victims and the upper classes less than 30 percent and that: “The split in society was perpendicular, not horizontal. The Terror was an intra-class, not an inter-class war. Just as we have seen, one of the main attractions of the quantitative approach is the opportunity it offers for making statements not just about small elites, but about whole classes or societies over long period of time.

While the vase bureaucracy employed by most modern states can gather comprehensive national statistics with relative ease, no historian, however well endowed with research assistants and computer time, can hope to survey all the primary sources needed for a quantitative study of, say, farm-size in Tudor England or personal incomes in early Victorian Britain. Contemporary Statisticians have developed reliable methods for taking a random sample, that is, one in which every element making up the whole has an equal chance of being included in the sample. However, in a recently completed project the enumerators’ returns for the 1851 Census were prepared for computer analysis in a bid to provide answers to a number of questions about social as well as economic structure which fell outside the scope of the report on the census published at the time; a 2 percent sample was chosen which comprised the total population of one in every fifteen enumeration districts and which were 945 as a whole. All the census information about these 415,000 individuals was fed into the computer, with the result that historians can now get a much clearer idea about variations in education, land tenure, household composition, the size of the labour force in different businesses, and many other issues.

The Historian and Statistical Inference: The Coefficient of Correlation

The historian can set about putting the data to work, once it is established that the figures are reliable, comparable as well as representative. The figures amount sometimes to an unequivocal answer to the question in hand, and all that remains is to devise the best way of presenting them clearly on the printed page-whether by table, graph, histogram, ‘cake’ or pyramid as well. Besides, some elementary processing may be desirable, such as the calculation needed to work out percentages or averages. Accordingly, the findings of economic historians in matters such as exports or production often lend themselves to straightforward exposition, known in the trade as ‘descriptive statistics’; an excellent instance is the forty-odd pages of tables and charts which appear at the end of E.J. Hobsbawm’s economic history of Britain since 1750, Industry and Empire (1968). Meanwhile, as historians have extended the application of quantitative methods, they have increasingly found that what counts is not so much the explicit meaning of the figures as inferences that can be drawn from them.

Furthermore, it is important to state that the drawing of such inferences may be essentially a statistical operation. In the case of an extended series of export statistics, for example, the researcher may wish to abstract the long-term trend of growth or decline, the regular fluctuations of slump and boom, and the irregular fluctuations caused by war, plague and the vagaries of government policy; only the sophisticated techniques of time series analysis will make this feasible. Infact, more complex statistical techniques are employed by Wrigley and Schofield in their backward projection of the English population from the nineteenth to the sixteenth century: there must be few historians who can follow them through that labyrinth. More importantly, from the historians’ point of view, a particularly useful kind of statistical inference is the coefficient of correlation, that is, the demonstration of a relationship between two variables. Note that, it is often important to know whether such a relationship exists and of what type-say between party affiliation and voting behaviour, or between the duration of marriage and the number of offspring. Moreso, if reliable quantitative data are available for each variable, the relationship can be worked out by statistical means. Although the computer can be of great assistance in this kind of project. Imagine that, for every one of the five hundred members of a legislature, the researcher has assembled information under twelve headings (which might include age, education, party, constituency, income, occupation, and voting record on six different issues) and wishes to test each of these twelve variables against all the others. The working out by hand of each of these correlations would be an almost impossible task; a correctly programmed computer, on the other hand, would print out the required tables in minutes. Thus, the outcome might be that a hitherto unsuspected correlation was revealed, suggesting a fruitful new line of research. It is significant, however not to exaggerate the importance of a statistically verified correlation: it does not take account of the possibility of coincidence, nor will it reveal which variable influenced the other; it may be, infact, that the two variables are determined by a third, as yet unidentified variable. Historians, on all these points, must fall back on a commonsensical way as well as their training, craft and their knowledge of the period as well as its challenges.

It is fundamental to state here that most historians who make inferences from quantitative data do not need to use statistics at all; instead, they treat the figure as an indicator or index’ of some other, usually much less tangible phenomenon for which direct quantitative evidence is not available. Invariably, it is tempting to infer political attitudes from statistics of voting behaviour, or the influence of a book from its sales, or the intensity of religious belief from the returns of Easter communicants, but none of these inferences can be taken for granted, nor does their validity depend on statistical principles. However, in each case it depends on a historical informed awareness of other factors which may have affected the figures. Were voters open to corruption, or responsive to personalities rather than policies? Was the book brought as an item of conspicuous consumption and put away unread? Can we assume that taking communion had the same significance for peasant congregations as it did for the clergy who compiled the returns. Importantly, the application of demographic data to family history has proved to be a minefield. To take just one example, it cannot be assumed without a great deal of supporting qualitative evidence that a narrow age-gap between husband and wife (as was already the case in early modern England) indicates a more affectionate and companionable marital relationship. Though at the point where numerical data touch on a major historical question, quantitative methods in themselves often resolve nothing. In this regards, three leading proponents of quantitative history have conceded:

Statistical manipulations merely rearrange the evidence; they do not, except on an elementary level, answer general questions; and the bearing of the findings upon the larger problems of interpretation in which historians are interested is a matter, not of arithmetic, but of logic and persuasion.

Indeed, statistics may serve to reveal or clarify a particular tendency; but how we interpret that tendency-the significance we attach to it and the causes we adduce for it-is a matter for seasoned historical judgement, in which the historian trained exclusively in quantitative methods would be woefully deficient.

However, there is one quantitative approach to history which claims to have transcended these limitations to some extent and which has as a result generated heated controversy. During the 1960s in the U.S., its first champions originated what is referred to as ‘cliometrics’ to distinguish their approach, and the term is not widely understood-although those who reserve judgement on its claims prefer to retain the inverted commas. ‘Cliomtrics’ proceeds on the assumption that certain areas of human behaviour are best understood as a system in which both the variables and the relationship between can be quantified; when the value of one variable changes, the effect which this has on the system as a whole can be calculated. Therefore, the field of human behaviour which is most suited to this approach is economics. In other words, ‘Cliometrics’ is simply a fancy label for what is often called ‘the new economic history’. It draws its inspiration from econometrics-that is, the techniques that statisticians have evolved to analyze economies of the present as well as to predict their future development. In proceeding from known to unknown variables the economist applies a theory of the relationship between the elements in an economic system (capital, wages, prices, etc); when an economic theory is expressed in mathematical terms, it is known as a model. Undoubtedly, econometrists are concerned to test and apply models by statistical means. For instance, in input-output analysis a model is employed in order to calculate what inputs an economy (or one sector within it) requires to achieve a given production target.

Indeed, for those historians with the necessary training in statistics, it is easy to see the appeal of econometric methods. Howbeit, they hold out the prospect of filling in some of the gaps in our existing historical knowledge which are due to the patchiness of firm quantitative data about the past. Similarly, if carried to their logical limits, they allow historians to assess the economic effect of a given policy or innovation by measuring it against what would have happened if the policy had been implemented or the innovation had proved stillborn: the system can be reconstructed to accommodate a different value for one or more variables. That at least is what the most advanced ‘cliometricians’ would claim. In Railroad and Economic Growth (1964), to take the most celebrated case, R.W. Fogel sought to measure the contribution which nineteenth century railway construction made to the U.S. economy by constructing a hypothetical (or ‘counterfactual’) model of what the American economy would have been like in 1890 if no railways had been built. He concluded that, even supposing no additional canals or roads were built, Gross National Product would only have been 3.1 percent lower, and that 76 percent of the land actually farmed in 1890 would still have been farmed. Earlier on most historians-including Fogel himself-had believed that the railways had a much dynamic effect on the American economy. Fogel maintained that counterfactual propositions are implicit in many historical judgments, and that what he had done was to expose this particular assumption as false by subjecting it to rigorous statistical testing.

However, there are several reasons why the work of the ‘cliometricians’ should be used with caution. For want of time and space we shall not dwell on it now. Moreover, to those historians who maintain that research questions should emerge from immersion in the widest possible range of primary sources, ‘cliometric’ history is inadmissible because its point of departure is always a clearly defined problem formulated in theoretical terms. Although there is no reason in principle why historians should not turn to theory in order to expose fresh problems or bring a new perspective to bear on familiar ones. It is important to note that the ‘cliometric’ approach has made a real contribution to our understanding of a number of technical problems in economic history.

Conclusion

Underlying the more modest aspirations of quantitative history is a growing recognition that its contribution to historical explanation-as distinct from the verification of historical facts-is marginal. Yet the generalizations yielded by analyses of numerical data tend to be descriptive rather than explanatory. Accordingly, to plot a trend, or to demonstrate a statistical correlation between this trend and another, does not explain it. Cause and significance remain matters for the interpretative skill of the historian in command of the sources-not merely those which lend themselves to quantification.

During the 1960s quantitative history was a highly contentious issue. Some of the early proponents of the new approach got ‘high’ on figures, becoming ‘statistical junkies’ (to quote Lawrence Stone). The prospects that lies before historians, then, is not the solution of major questions by quantitative means, but new possibilities of synthesis, in which statistical inference is combined with the perceptions of traditional ‘qualitative’ history. Infact on these more restricted terms the place of quantitative methods of historical enquiry seems assured. For a time history’s scientific status was affirmed more unequivocally than at any time since the turn of the century; in 1966 a leading American quantitative historian was rash enough to predict that by 1984 the scientific study of the past would have reached the point when historians could set their sights on the discovery of general laws of human behaviour. Comparable hostages to fortune were given by the ‘cliometricians’. As a result, some of the traditionalists in the profession were provoked into making equally extreme rebuttals: in 1963 the President of the American Historical Association urged his colleagues not to ‘worship at the shrine of that Bitch-goddess QUANTIFICATION’ (sic).

In conclusion, therefore, nearly thirty years later the claims advanced for quantitative history are more modest, other historians fell less threatened, and a more dispassionate assessment led to its breakthrough in historical methods. When all reservations have been made, quantification has still shown itself, as a powerful addition to the historian’s tool-kit in historical analysis.

Endnotes

1. Curtin’s figures are the subject of continuing debate among quantitative historians. See Paul E. Lovejoy, “The Volume of the Atlantic Slave Trade: A Synthesis” Journal of African History, xxiii, 1982; and J. Inikori (ed), Forced Migration, (Hutchinson, 1982).

2. Lee Benson, “Research Problems in American Political Historiography”, in Common Frontiers of the Social Sciences, (ed) Mirra Komarovsky (Glencoe, 111,1957).

3. G.M. Trevelyan, English Social History, (Longman, 1944), p. viii.

4. Emmanuel Le Roy Ladurie, The Peasants of Languedoc, University of Illinois Press, 1974.

5. E.A. Wrigley and R. S. Schofield, The Population History of England, 1541-1871 Arnold, 1981.

6. Peter Laslett (ed), Household and Family in Past Time, (Cambridge University Press, 1972).

7. The Methodological Issues are fully in E.A. Wrigley (ed.), Nineteenth Century Society (Cambridge University Press, 1972).

8. Leo F. Schnore (ed), The New Urban History, (Princeton University Press, 1975).

9. See for example J.R. Vincent, Pollbooks: How Victorians Voted (Cambridge University Press, 1967).

10. The Clearest Statement in English is Emmanuel Le Roy Ladurie, The Territory of the Historian (Harvester, 1979), Ch.2.

11. Lawrence Stone, Letter to Editor, Encounter, XI (July 1958), p.73.

12. On the Use of Models, see the review of the work of Harold Hotelling and others and the further discussion of this problem in Donald E. Stokes, “Spatial Models of Party Competition,” American Political Science Review, LVII (June 1963); on Scaling techniques; See Duncan MacRae, Jr., Dimensions of Congressional Voting: A Statistical Study of the House of Representatives in the Eighty-first Congress (Berkley, Calif., 1958), and “Intraparty Divisions and Cabinet Coalitions in the Fourth French Republic,” Comparative Studies in Society and History, V (Jan. 1963); William O. Aydelotte, “Voting Patterns in the British House of Commons in the 1840s”, pp.134-63.

13. G.N. Clark, Guide to English Commercial Statistics, 1696-1782, Royal Historical Society, 1938.

14. James Cornford, “The Transformation of Conservatism in the Late Nineteenth Century," Victorian Studies, VII (Sept. 1963).

15. B.R. Mitchell and Phyllis Deane, Abstract of British Historical Statistics, Cambridge University Press, 1962, p. 466; for an account of the problems raised by cost-of-living indexes, see Roderick Floud, An Introduction to Quantitative Methods for Historians, 2 edn, Methuen, 1979, pp.125-9.

16. Thomas S. Kuhn, “The Function of Measurement in Modern Physical Science,” in Quantification: A History of the Meaning of Measurement in the Natural and Social Sciences, pp.31,34; remarks by Frank H. Knight in Eleven Twenty-six: A Decade of Social Science Research, (ed). Louis Wirth (Chicago, 1940), p.169; M.B. Abasiattai, (ed), Expanding the Frontiers of African History: The Inter-Disciplinary Methodology, (Calabar: Wusen Press Ltd, 1988), p. 217.

17. W.O. Aydelotte, On the business interests of the gentry in the Parliament of 1841-47, in G. Kitson Clark, The Making of Victorian England, Methuen, 1962, and his Quantification in History, Ch.5.

18. Clarence Crane Brinton, The Jacobins: An Essay in the New History (New York, 1930), pp.70-72.

19. Donald Greer, The Incidence of the Terror During the French Revolution: A Statistical Interpretation (Cambridge, Mass., 1935), pp.97-98.

20. Michael Anderson et al, “The National Sample from the 1851 Census of Great Britain”. Urban History Newsletter 1977, pp.55-9.

21. Roderick Floud, An Introduction to Quantitative Methods for Historians, 2 edn, Methuen, 1979, pp.88-122.

22. Edward Shorter, The Historian and the Computer, (Prentice Hall, 1971), pp.5-8.

23. Peter Burke, Sociology and History (Allen &Unwin, 1980), p.40.

24. For a discussion on this and related issues, See Michael Anderson, Approaches to the History of the Western Family, 1500-1914 (Macmillan, 1980), pp 33-38.

25. W.O. Aydelotte, A.G. Bogue and R.W. Fogel (eds.), The Dimensions of Quantitative Research in History (Princeton University Press, 1972), pp. 10-11.

26. Lawrence Stone, The Past and the Present Revisited (Routledge & Kegan Paul, 1987), p.94.

27. Lawrence Stone, Letter to Editor, Encounter, XI (July 1958).

28. Lee Benson, Toward the Scientific Study of History (Lippincott, 1972), pp. 98-104.

29. Carl Bridgenbaugh, “The Great Mutation,” American Historical Review, LXVIII, 1963, p.236; For a more extended attack, See Jacques Barzun, Clio and the Doctors, (Chicago University Press, 1974)