The Elements of Scientific Method in Sociology, Summaries of Sociology

Download The Elements of Scientific Method in Sociology and more Summaries Sociology in PDF only on Docsity! THE ELEMENTS OF SCIENTIFIC METHOD IN SOCIOLOGY F. STUART CHAPIN Smith College I At the present time sociology is largely a deductive science, if one can call an extensive and ill-defined body of kinowledge a science. General principles have been deduced from the observations of a few experienced students of human nature and these principles have been elevated into theories without sufficient inductive veri- fication. The individual phenomenon has been explained in the light of these theories. In other sciences, the progress of achieve- ment has been in large measure due to the use of the inductive method. In the inductive method as opposed to the deductive method, the investigator passes from the examination of a consider- able number of observed facts to some theory or generalization with regard to the relations existing between the observed facts. Unfortunately this has not been the procedure in sociology. There has been too much deductive philosophic generalization and far too little inductive verification. The chief difficulty inintroducing the inductive method in the science of sociology inheres in the bewildering complexity of the subject-matter with which it deals. The ultimate unit in social relations is the human individual, the most highly organized thing in organic nature. Each human being has his own individuality and differs from every other human individual. The range of characteristics possessed by the human unit is relatively wide and variation in degree is practically infinite. This diversity of indi- vidual characteristics makes it exceedingly difficult to draw valid generalizations from even the most careful observations. It would seem, therefore, that since each individual is in this sense unique and an end in himself, the only sound method of procedure is to ob- serve each individual separately. But this is obviously impossible. 371 372 THE AMERICAN JOURNAL OF SOCIOLOGY The student is consequently thrown back upon the alternative of making the most of his limited series of observations. This implies the use of some method which will enable him to deter- mine how representative of all individuals is his limited series of observations. The sociologist must obtain some method of recording his observations of the limited series of individuals which will reduce personal bias and individual error to a minimum. The simplest method is to count the frequency with which different degrees of a character occur. This is obviously to use the statistical method. Arthur L. Bowley says: "Statistics are numerical statements of facts in any department of inquiry, placed in relation to each other; statistical methods are devices for abbreviating and classifying the statements and making clear the relations."' In so far as the statistical method involves the collection of a large number of facts and the formulation of generalizations based upon the facts, it is an inductive method. The use of the statistical method ne- cessitates the determination of a standard of measurement. The determination of standards has been of utmost importance in sci- entific advance. As long as standards of measurement are sub- jective, all is confusion. Forces are measured by their effects, not by attributing motives to them. If we try to measure some socializ- ing force by its degree of goodness or badness, since all men differ with respect to what they consider good or bad, we shall get as many standards of measurement aswe have men. Clearly we need some objective standard of measuring social phenomena. Shall we take the richest man in the world as the standard by which poverty is to be measured ? Such a standard is unsatisfactory because the wide range of variation in economic status would make some people quite incapable of appreciating our standard. Evidently we need some standard of more universal acceptability. There is an objective standard of measurement which is uni- versally used in the statistical treatment of social phenomena-the average. The reasons why the average is such a satisfactory stand- ard of measurement will be made clear by considering its properties. The average has, in general, three properties: ' A. L. Bowley, An Elementary Manual of Statistics (London, I9IO), p. I. ELEMENTS OF SCIENTIFIC METHOD IN SOCIOLOGY 375 observed group whose income is $I,500 and over is small, we do not need to bother about the effect hey have made on the mode 80 70 6o 50 0 40 30- 20 IO o o o o o ol ol ol o, o X o ooo ooo 0O~0 C00' 00'0 % OO 0 0~ 0'O, 0 O O0 ~ 'J1 d \ 0 %O H 00H00 OO 0 0 % e 0 0 U i) i %q Income FIG. r.-Incomes of 39I working-men's families 3. "It may be determined with considerable accuracy from well-selected sample data." For example, if Robert C. Chapin 376 THE AMERICAN JOURNAL OF SOCIOLOGY had conducted his investigation by observing the families of Irish in one city block, instead of interviewing families cattered over various parts of the city representing the most important nation- alities, his sample 39I would not have been as well selected' or as representative ofincomes among working-men i New York City. TABLE I* Income No. Families Income No. Families $ 400-$ 499 ............. 8 $I,200-$I,299 ............. 8 500- 599 ............. I7 I,300- I,399 ............. 8 6oo- 699 ............. 72 I,400- I,499 . . . . . . . - - . . . .I 700- 799 . .- 79 1,500- I599. 6 8oo- 899 ............. 73 i,6oo and over. 7 900- 999 .63 I,000- I,099. 3I 39 I,100- I,99. I8 * From R. C. Chapin, Standard of Living among Workingmen's Families in New York City, p. 44. 4. "The mode is a type which, to the ordinary mind, seems best to represent he group." But the mode has several disadvantages which restrict i s use to certain kinds of material. It is not always the best form of the average to use as a standard, because: I. "In many cases, no single, well-defined mode exists." Fig. 2 InfanyOld Age shows the frequency of Infancy deat atdffrngae. FIG. 2.-Frequency of death at different ages death at difherent ages. Here, there are two periods at which death is frequent, in early infancy and at old age. 2. "The mode is not at all useful if it is desirable to give any weight to extreme observations." In Fig. i the existence of 30 families with an income of $i,200 and over has no effect upon the mode. 3. "The mode may be determined by a comparatively small number of items of uniform size in a large group of varying size." I Chapin, op. cit., p. 28. 2 K. Pearson, The Chances of Death, I, 27. ELEMENTS OF SCIENTIFIC METHOD IN SOCIOLOGY 377 It might happen that in a community having great extremes in wealth, the modal value of possessions is $992 simply because three people were listed at that amount while the wealth of all others varied between wide limits. A third convenient form of the average is the median. Bowley regards it as the most useful of averages.' G. U. Yule defines the median "as the middle-most or central value of the variable when the values are ranged in order of magnitude, or as the value such that greater and smaller values occur with equal frequency."2 For 4.0 3. 3 .0 2.5 2.0 I'.5 I.0 III fil fI I T I FIG. 3.-Array of breadths of 47 nuts example, in Fig. 3, the median breadth for an observed group of 47 nuts is 2.7 cm., since this is the value half-way from either end of the ascending series of magnitudes. The median has the follow- ing advantages as an objective standard for the measurement of social phenomena: I. "It may usually be located with greater exactitude than the mode. This is especially true in groups of observations where the mode is ill defined." 2. "It is but slightly affected by items having extreme devia- tions from the normal." The 6 families having an income of from I Bowley, op. cit., pp. I24-25. 2 G. U. Yule, An Introduction to the Theory of Statistics (London, I9I2), p. II6. 380 THE AMERICAN JOURNAL OF SOCIOLOGY recent paper by the writer, "The Variability of the Popular Vote at Presidential Elections."' The thesis of the paper was: increas- ing variability in the popular vote cast at successive presidential elections, as between states, indicates a decreasing degree of control exercised by political tradition over independence in voting. To substantiate this thesis the following method was used. A variable series was obtained by arranging in order of magnitude for any presidential election year the number of votes cast in each state. Series of this sort for Republican and Democratic presidential candidates for each year were obtained. Fourteen series, beginning with the presidential election of I856 and concluding with that of I908, were compared with reference to their respective variabilities around their respective medians. It was found that the fourteen Republican series and the fourteen Democratic series showed con- tinuous and consistent increase in variability such that in the presidential elections of i896, I900, I904, and I908 the variability was over twice the variability of the year I856. After the elimina- tion of several considerations a to the nature of the figures and the causes at work which might lead to spurious results, the conclusion was drawn that the increasing variability in the popular vote was a real indication of increasing independence of vote and decreasing rigidity in political tradition. The hypothesis assumed at the beginning of the investigation was that, just as increasing similarity of response to a stimulus on the part of individuals in a group indicates the slow formation of a usage or a custom of action with reference to that particular stimu- lus, so the increasing dissimilarity (variability) of response to a stimulus on the part of individuals in a group indicates the slow disintegration of the usage or custom. On the basis of this assumption by using a simple statistical method it seems possible to indicate the unraveling of a custom. In this particular study the stimulus was the opportunity to vote for president. It incited individuals geographically grouped by states to respond by voting for the Republican or Democratic candidate. Instead of the popular vote for president as between states becoming standardized as time goes on, it is actually becoming diversified. We have a I American Journal of Sociology, September, IqI2. ELEMENTS OF SCIENTIFIC METHOD IN SOCIOLOGY 38I situation in which the response of large numbers of individuals, geographically grouped, is increasingly variable with reference to a given political stimulus. If the political action of these individuals grouped by states showed increasing numerical agreement, we might say that it was due to the standardizing effect of political tradition. The fact of the matter is that the political action of these individuals grouped by states shows an increasing numerical variability and it becomes important to determine whether this increasing numerical variability is evidence of independent political action.' III We have found that the average is related to the variable series of measurements from which it is obtained in such a way that some of the items in the series are larger while some are smaller than the average. Moreover the deviations are not all of the same size. The question at once arises: Is there any law of the occurrence of these deviations? That is, do the deviations occur in a purely haphazard way with no regularity? Does each group of measure- ments show a series of deviations entirely different from that of preceding groups and subsequent groups ? In answering this question we discover that the deviations of most measures from their averages occur with surprising regularity, that there is a definite law of their occurrence. It has been empirically demonstrated that in dealing with a large number of observations or measurements of most phenomena, when one part of the group is varying in one direction, the probabilities are that another equal part of the same group is varying in the opposite direction. Closer examination of the principle reveals the following law of occurrence of deviations of individual observations from the average of a large series of measure- ments: I. Small deviations tend to occur more often than large deviations. 2. Very great deviations do not occur. 3. Deviations in one direction tend to occur as frequently as deviations in the opposite direction. This principle will be clear by examining the distribution in Fig. 4 and Table II, representing the stature of 8,585 adult males born in the British Isles.2 It will be seen that the average stature I American Journal of Sociology, XVIII (I9I2), 223. 2 Yule, op. cit., pp. 88-89. 382 THE AMERICAN JOURNAL OF SOCIOLOGY (modal) for the group is 67 inches. There are larger numbers of individuals with a stature of 66 and 68 inches than with a stature of 64 or 70 inches, thus fulfilling the first principle of the law. There are no individuals with statures of 24 or I20 inches, thus fulfilling the second principle. There are about as many individuals at the statures of 66 and 64 inches respectively, as at the statures of 68 and 70 inches, thus fulfilling the third principle. When these three prin- ciples are ideally realized in the occurrence of measurements, we call the resulting curve the normal curve. Our illustration is a frequency distribution which approximates omewhat closely to the ideal curve (Fig. 5). Frequency distributions of the type of Fig. 4 and more or less closely approxi- mating the normal curve are true of large series of measurements of many human characters; for example, of the weight of men, the cephalic index, 58 6o 62 64 66 68 70 72 74 76 78 8o the length of infants at Stature in inches birth, the girth of chest of FIG. 4.-Frequency distribution of stature men, the strength of arm- pull of men, the body tem- perature at the mouth in American women, the heart-rate of American students, the reaction time of American college Fresh- men, the memory span for digits in American women students, the efficiency inperception of twelve-and-one-half-year-old boys, etc.' The probable reason why this principle has such general appli- cability to measurements of organic traits is the fact that wide variation from the adapted type of inhabiting species has been strictly limited by natural selection. This can be illustrated by reference to an interesting experiment conducted by Dr. C. B. Davenport. Some 300 chickens were put in an open field; of this number 8o per cent were white or black and conspicuous, 20 per cent I E. L. Thorndike, Theory of Mental and Social Measurements (New York, I904), PP. 46-49. ELEMENTS OF SCIENTIFIC METHOD IN SOCIOLOGY 385 empirical distributions when we have large numbers of items from certain kinds of material. IV In the first part of this paper we saw that because of the com- plexity and individuality of the units of our subject-matter it was desirable to measure each separately, but that this was impossible or at any rate impracticable; we were therefore forced to adopt the alternative of making the most of our limited series of observa- tions and determining how representative of all individuals this limited series was. The elementary method which has been developed in the intervening paragraphs will help us toward a solution of this problem. Clearly any limited series of observations which we have obtained in lieu of measuring all individuals, may be regarded as a sample. It becomes at once important o determine the good- ness of our sample, to determine how representative it is of the larger series composed of all individuals. It is obviously impracti- cable for a few investigators toobserve the conditions in all working- men's families in New York City. Resort is therefore made to the method of investigating a few representative families. Is it possible to determine how fairly the conditions in the sample 391 families represent he conditions in all working-men's families in New York City? Again, the group of 8,585 adult men from the British Isles may be regarded as a sample of all adult men in the British Isles. Is the distribution of stature characteristic of this group representa- tive of the stature of all Englishmen? The average height of this group is 5 ft. 7 in. May we infer from this that the average height of Englishmen is 5 ft. 7 in. ? In these instances as in many others it is practically impossible to measure all individuals, consequently it is of considerable importance to know whether we have a good sample or a poor one, or if we have two samples, which is the better of the two. In the first place we might assume that in the larger group, which includes all the individuals, the measurements are distributed in frequencies which are in accordance with some general aw. Thus the complete series of measurements which we cannot obtain but 386 THE AMERICAN JOURNAL OF SOCIOLOGY which we desire to approximate as closely as possible in our limited series of observations may be regarded as an ideal. This assump- tion of applying the law of error is justified when we have a posteriori reasons for believing that the material we are dealing with is of a certain character. For example, we know by experi- ment, based upon the observation of a large number of group measurements, that biological, physiological, and anthropological measurements show a close correspondence with the law of normal distribution. It is therefore asonable to assume, in dealing with a sample of such material, that we have a good sample when the distribution corresponds with the law of error, that we have a poor sample when the distribution fails to correspond with the law of error. In making the assumption that the distribution of measure- ments in the larger group, including all individuals, is in strict correspondence with the ideal distribution of the law of error, we were justified on certain a posteriori grounds. In the absence of these grounds is it reasonable to base our method upon this assump- tion ? The question is one of considerable importance since many measurements with which the sociologist deals are not of biologi- cal, physiological, or anthropological nature. For example, many economic phenomena show measurements which appear to obey quite different laws. In economic statistics the distribution of wealth in the population at large shows an extremely asymmetrical distribution. The percentage of population in need of relief shows a distribution less markedly asymmetrical but still failing of close correspondence with the law of error.' Bowley says: It may appear that the cases where the agreement is close are so few as to make the whole body of theory useless; but this is an unscientific view to take. The general process of applied science is to frame hypotheses as nearly con- sistent with the facts as is possible without such complications as will prevent their use, and then apply to the idealized case the corrections which the actual cases necessitate. This process has led to the best results in physical science. In the problems dealt with by the law of error, it will be found that many deductions from the idealized cases hold also when applied to the only partially corresponding records of great numbers ... . For instance, . I Yule, op. cit., pp. 92-IOI. ELEMENTS OF SCIENTIFIC METHOD IN SOCIOLOGY 387 the accuracy of an average of random samples of quantities not grouped according to the curve of error varies as the square root of the number of samples taken.' V The validity of our working hypothesis as well as its relativity having been explained, it becomes important o make the practical application. When dealing with certain kinds of material we saw that, in so far as our limited series of observations corresponds to the (unlimited.) ideal series, that is, in so far as the measurements in our sample were distributed in accordance with the law of error, our sample was a good one, a more or less accurate representation of the larger complete series. In many statistical problems, in most sociological problems for that matter, it is unnecessary to resort to the use of higher mathematics in order to determine the goodness of a sample. The reason for this is the fact that one cannot be sure that the statistics are accurate enough to warrant the use of refined mathematical methods. The following tests will usually be found sufficient to determine the goodness of a sample, especially in cases where there is some question of trustworthiness of the statistics: i. The goodness of the sample depends somewhat upon its size. If our limited series of observations are few in number it is clearly improbable that the sample will be as representative of the larger series as it would be if the observations were more numerous, thus including additional numbers from the larger series and redu- cing the probability of any particular item being excluded. More- over, when the sample is small we cannot in general assume that the distribution of errors is approximately normal.2 2. The goodness of the sample depends upon maintaining the condition that every member of the group considered has nearly the same chance of being included in the sample. That is, the sample must be selected at random. "The temptation is always to measure the obvious and easily accessible; but if we do this our sample is of 'the accessible,' not of the whole group. Thus the budgets of working-class expenditure, which are often published, are not I Bowley, op. Cit., p. 298. 2 Yule, op. cit., p. 353. 390 THE AMERICAN JOURNAL OF SOCIOLOGY the discrepancy can hardly be attributed to the fluctuation of sampling and may, therefore, indicate actual differences of con- dition in the group from which the two samples were drawn. Thus we may be really dealing with two different groups instead of one. Consequently the way the probable error is used in practice is that, when the difference between two means exceeds three times the probable error, the difference is significant.' For example, if the difference b tween the mean statures of two sample groups of adult men was in excess of three times the probable error, we should think that our samples represented two different types of men, perhaps dwarfs and giants. The strict application of this method is of Large group whose Large distribution is Group not normal r-"p r -1 Samples of m I I I 1 quantities L_ .2 L Averages of samples Al A2 A3 "As % / An FIG. 6.-Averages of samples of a large group course dependent upon the assumption that the groups we are dealing with are samples of quantities which conform to the law of error; the method is therefore not so well adapted to use in dealing with the samples of quantities which do not satisfy the law of error. In dealing with quantities which do not satisfy the law of error we know that this, at least, is true, "the averages of samples of, say, m quantities, drawn at random from a large group whose distri- bution is not normal, will, if m is large in relation to the fluctuation of the original group, satisfy the law of error. "2 This follows from the law of probabilities which states "that a moderately large I Elderton, op. cit., p. 79. 2 Bowley, Elements, pp. 303, 308. ELEMENTS OF SCIENTIFIC METHOD IN SOCIOLOGY 39I number of items chosen at random from among a very large group are almost sure, on the average, to have the characteristics of the larger group."' Thus our method of testing samples derived from a hypothesis which is consistent with the law of error is found to apply to quantities which do not correspond so closely to the normal distribution, provided only that we fulfil the condition that our samples be large in relation to the variation in the original group. Bowley2 has illustrated this principle by showing that even in dealing with a very unpromising case the theory is confirmed. Although the death-rates per io,ooo in London registration districts, arranged in order of magnitude, reveal a distribution which clearly does not conform to the normal curve, the averages of i8 random samples of 4 death-rates, do fit a curve of error closely. In introducing the statistical method into the investigation of sociological phenomena we have introduced an inductive method. By means of certain assumptions based on the law of error and justi- fied on a posteriori grounds, we have developed a means of dealing with samples of variable quantities which accurately determines, subject to certain limitations, the degree with which any sample represents the material from which it is drawn. The use of this method puts the sociologist in a position to eliminate some of the most serious difficulties arising from the complex nature of the material with which he deals. If the conditions laid down in the course of this paper are followed in applying the principles of this method to the investigation of social phenomena, it is not too much to claim that generalizations based upon the results of such investigation will be fairly comparable as regards validity and accuracy with the generalizations of applied science. X IKing, op. cit., p. 28. 2 Bowley, Elements, pp. 308-I5.