Graphic methods for presenting facts

Front matter

GRAPHIC METTOS

FOR

I^RESENTiNG FACTS t ■%ILLARD C. BRINTON

Preface

IN the preparation of this book there has been a constant effort to present the subject to suit the point of view of the business man, the social worker, and the legislator. Mathematics have been entirely eliminated. Technical terms are used practically not at all. Since the readers whom it is most desired to reach are those who have never had any statistical training, consistent effort has been made to keep the whole book on such a plane that it may be found readable and useful by anyone dealing with the complex facts of business or government. Though written primarily for the non-technical man, it is hoped that this book may, nevertheless, prove convenient to the engineer, the biologist, and the statistician.

A definite effort has been made to produce a work which can serve as a hand book for anyone who may have occasional charts to prepare for reports, for magazine illustration, or for advertising. Unfortunately, there are extremely few draftsmen who know how to plot a curve or prepare any kind of a chart from data presented to them in the form of tabulated figures. Most draftsmen can plot a curve if they are given the data and an example showing the general type of chart desired. The executive who desires a chart is usually too busy to stand by a draftsman and explain in detail just how the chart should be prepared as concerns those all important details of proportion, scale, width of line, etc. It is believed that the owner of this book wiU find it feasible to run through the various chapters and pages until he finds a chart most nearly like that which he desires to have made from his own data. A sample chart placed before any draftsman of average ability should give the draftsman practically all the instruction needed for the preparation of a similar chart from other data.

Much careful labor has been expended in so arranging the book that a busy reader may get the gist of the matter by looking at the illustrations and reading only the titles and the sub-titles. The main title under each illustration is intended to show exactly what the chart represents, just as if it were used in some publication relating to the particular subject matter of the chart. The sub-titles relate to method and give criticism of each chart as a whole. Though the text gives much more detailed information concerning method than can possibly be put into any sub-titles, the reader who examines only the illustrations and the titles, without any reference to the text, will undoubtedly get a major portion of the vital material in the book. It is believed that an average reader may go through the illustrations and the titles in about one hour.

V

VI GRAPHIC METHODS

Many of the illustrations which have been borrowed for use in this book are criticized ad\'ersely. It is the hope that all such criticisms will be accepted as an honest attempt toward an advance in the art of showing data in graphic form. In fairness to the authors of those charts which are criticized, it must be said that there has been a very rapid advance in the art of graphic presentation within the last few years and that many of these men would not present the material to-day by the methods which may have been used some years ago in the preparation of certain charts shown here. Where charts are used and criticized adversely, the charts have been included only because it is felt that they show a practice which is rather common but is nevertheless of questionable desirability.

Many of the suggestions for standard practice contained in this book should be taken as tentative only. The American Society of Mechanical Engineers has invited about fifteen of the chief American societies of national scope to co-operate by sending one member each to a Joint Committee on Standards for Graphic Presentation. Though this committee is not yet completely organized, and it will be some time before any report is available, the reader who desires further information regarding standard practice should be on the lookout for any reports which the joint committee may publish in the future.

This volume may arouse in the minds of many readers a desire for more detailed information than can possibly be given here. The following books are suggested for the person who wishes to take up the study of statistics as related to the collection and interpretation of data without special reference to the methods of graphic presentation. The present work is necessarily limited to the consideration of graphic presentation, and those who wish to go further in the general subject of statistics should by all means consult books of the type exemplified by "The Elements of Statistical Method," by Willford I. King, The Macmillan Company, New York; "An Introduction to the Theory of Statistics," by G. Udny Yule, Grifiin and Company, London; '"Elements of Statistics," by Arthur L. Bowley, Charles Scribner's Sons, New York; "Primer of Statistics," by W. Palin Elderton and Ethel M. Elderton, Adam and Charles Black, London; "Statistical Averages," by Franz Zizek, Henry Holt and Company, New York; "Statistical Methods with Special Reference to Biological Variation," by C. B. Davenport, John Wiley and Sons, New York. Any list of this sort is, of course, incomplete and these books are mentioned as only a few of those which may be found useful to supplement the study of the subject considered in this volume.

Part of the matter here presented was given in lectures delivered at the Graduate School of Business Administration of Harvard University, the Amos Tuck School of Administration and Finance of Dartmouth College, the Northwestern University School of Commerce, and the College of Commerce and Administration of the University of Chicago. Some of the material was presented before the American Society of Mechanical Engineers in New York. The advance presentation of matter in course of preparation for the press was made with the cordial assent and approval of the publishers of this work.

I am greatly indebted to Mr. Edward Scott Swazey, Mr. Curtis Prout, and Miss Katherine Tyng, for valuable assistance and suggestions received during the preparation of this book. Chapter XV is largely based on an article prepared at the

PREFACE Vll

suggestion of the author by Mr. Pierpont V. Davis of New York City and pubUshed by Mr. Davis in Moody's Magazine. I wish also to express my thanks to numerous friends who have given excellent suggestions and criticisms during the time the manuscript was in preparation.

If this book should receive any commendation, much of that commendation will be the result of good fortune in securing an unusually high grade of drafting skill on those charts which are original.

The author cannot be responsible for the accuracy of the data presented in many of the charts shown. The illustrations have been selected partly on account of the educational value of the facts, but chiefly because of the methods used in presentation. Though great care has been exercised to make the titles complete, the elaboration of titles beyond their wording in the original source may have resulted in some inaccuracies.

As far as the author is aware, there is no book published in any language covering the field which it has been attempted to cover here. If the presentation of the subject appears to be crude and incomplete, it is hoped that any critic will keep in mind that there is httle precedent for guidance in a territory so unexplored.

It is impossible entirely to avoid errors in any book containing as much detail as results here from the numerous complex illustrations and the necessity of carefully worded language to give condensed information. Any corrections, criticisms or suggestions will be appreciated by the author.

WiLLARD C. BrINTON

New York, June, 1914

Contents

PAGE

Chapter I. Component Parts 1

The need for graphic methods in presenting facts. The method of presentation as important as the data. PossibiKty for standard methods of presentation. Tabulated figures versus graphic methods. A total shown with its component parts. The horizontal bar. The circle and sectors. Subdivision of components. Separate bars totalling 100 per cent. Charts giving numerous subdivisions. Organization charts. Routing charts for manufacturing plants and offices.

Chapter II. Simple Comparisons 20

Errors due to comparing by areas or by volumes instead of by one dimension only. The use of graphic methods in geography books. The data should be shown on the face of each chart if possible. Good and bad methods of including the data. "Eye-catchers" to attract the attention of the reader. Criticisms of methods commonly used. Certain bars made especially prominent. Increases and decreases. Lines connecting different bars. Examples of various good methods.

Chapter III. Simple Comparisons Involving Time 36

Impossibility of accurate interpretation when circles of different size are compared. Errors when pictures of the human figure in different size are compared. Methods which are popular and accurate as well. Examples of bad practice in arrangement and the same data correctly represented. Vertical bars giving the general effect of a simple curve. Curve plotting.

Chapter IV. Time Charts 53

Horizontal bars drawn to a scale of time. Complex time charts by which the relations of numerous horizontal bars may be studied. Time charts showing bars combined with a curve expressing totals. Curves to study whether time schedules are maintained. Rank charts to portray the rank of different individuals at various times. Rank charts showing actual relative rank at any time and also changes in rank at various times. Train-dispatching charts. Time-distance curves.

ix ■

Chapter V. Curve Plotting 69

The desirability of using only well-known methods of presentation. Curves permit a more rapid and more accurate interpretation than possible by other methods. Studies of the causes of crests and valleys of curves. Curves especially needed for complex data. The use of curves in advertising. Polar co-ordinates objectionable for presenting statistical data. Examples of good practice in curve plotting.

Chapter VI. Curve Plotting Continued 84

Independent and dependent variables. Confusion caused if the independent variable is not used for the horizontal scale. Examples showing correct arrangement of scales. Curves to advertise newspaper circulation. Curve charts combining much complex information. The use of two sets of co-ordinate ruling for the vertical scale. Moving averages. Smoothing curves. Index numbers. Weighted averages. Curve studies of national prosperity. . .

Chapter VII. Comparison of Curves 107

Similarity and contrast of curves plotted in the same field. The zero of the vertical scale should be shown on the chart. Advantages of plotting curves for different years one above the other for comparison. Contrast in shape of curves plotted in separate fields. Advantage from shading the space under a curve. Numerous dissimilar but related curves on the same sheet. Errors resulting if curves not having the same zero line are compared. A total curve plotted from several other curves. Inverse relations, one curve trending downward when another trends upward. Study of correlation by plotting a curve from the data of two other curves. The angle of a curve on ordinary rectangular co-ordinates tells nothing about the percentage rate of growth. Disadvantages of the arithmetical scale ruling for curve plotting. Advantages obtained by plotting curves on logarithmically ruled paper.

Chapter VIII. Component Parts Shown by Curves 138

Use of vertical bars with components totalling 100 per cent. Shaded area under a curve when the height of the total field represents 100 per cent. The use of several areas in a curve field which totals 100 per cent, in height. A contrasting method of showing all curves plotted separately but from the same zero line. Universal co-ordinate paper for convenience in curve plotting. Total curves with component areas so that any point on a curve totals 100 per cent for the height of the areas beneath.

Chapter IX. Cumulative or Mass Curves 149

Factory production schedules and actual outputs plotted on a cumulative basis. Curves for income and expense on a cumulative basis. Various uses for cumulative curves. Cumulative curves with lines drawn to show rate

CONTENTS XI of change. A grand total cumulative curve plotted from several other cumulative curves. Cumulative curves for the determination of storage requirements for water supplies.

Chapter X. Frequency Curves. Correlation 164

The arrangement of objects so that their position shows a crude frequency curve. Vertical bars to represent frequency. Frequency curves. The "mode." Frequency curves much easier to interpret than charts using bars or areas. Cumulative frequency curves. The use of cumulative frequency curves for business problems. Cumulative frequency curves preferably plotted on a "more than" basis instead of on a "less than" basis. Necessity for making the independent variable the horizontal scale. Wage comparisons for industrial work. Studies of the percentage of clerical work and percentage of revenue from orders of various sizes. Pin boards to record costs of doing work on orders of different size. Theoretical curves for percentage of clerical work and percentage of revenue from orders of different size. The Lorenz curve. Correlation curves. "Shot-gun" diagrams. Plotting curves to represent numerous points. Shaded areas to represent numerous dots. Correlation charts for two independent variables. Isometrically ruled paper for chart work.

Chapter XI. Map Presentations 208

Map presentation of prime importance. Shading of different areas. The Ben Day method of mechanical shading. Lines of equality. Profiles. Maps with circles or dots representing quantities. Shaded areas with a key to represent quantity. Miscellaneous methods. Map charts showing traffic. Map models with built up strips to show quantities.

Chapter XII. Maps and Pins 227

Map tacks projecting above the map. Map pins pushed in till the heads touch the map. Photographing pin maps. Mounting maps for use with map pins. Wall maps for use with pins. Map cabinet systems. Pin maps for advertising work. Pins bearing identifying numbers. Spot maps to a scale with each dot representing some large quantity. Routing systems. Various types of pins and beads available. Bead maps and their great advantages.

Chapter XIII. Curves for the Executive 254

Peak-top curves versus flat tops. Methods for combining curves with figure^ recording the data. Cards for plotting curves for operating records. Advantages of the card method for instantaneous comparison of different curves. Typical operating curves for a manufacturing business. Typical records for a selling organization. Arrangement of the card system for extension with increase of business. Moving average curves for operating records. Record cards for preserving all information regarding each curve.

Xll GRAPHIC METHODS

Chapter XIV. Records for the Executive 288

Need for complete records in curve form relating to all main features of a business. Curve-card filing methods. Blueprints from the curve cards allow a cross-index of all important operating curves. A complete record department for a business. Methods for keeping records as used by various large corporations. The need for education in the interpretation of curves. Curves in conference meetings by using a reflecting lantern and the curve-record cards without lantern slides. Curves on swinging-leaf display fixtures.

Chapter XV. Corporation Financial Reports 307

The annual report of corporations not usually put in form to permit intelligent comparison by the stockholders. Records of previous years not usually given. The number of stockholders constantly increasing. Best policy is to give complete and clear information. Recent examples showing bad practice. Curves for the United States Steel Corporation as a suggestion for the type of chart to be included in a corporation annual report. Charts should be a feature of the annual report of every large corporation.

Chapter XVI. General Methods 321

Methods for collecting and tabulating data. Punched-card sorting and tabulating machines. Use of tabulating machines for manufacturing records and for analyses of selling results. The slide rule as a great convenience. The use and abuse of significant figures. Photographic copying of charts. Use of the reducing glass. Preparation of copy for the engraver. The Ben Day process. Charts for two independent variables. Card-board models. Solid models. The desirability of curves and charts in political campaigns. The projecting lantern with charts for campaign purposes. Methods for presenting election returns to large numbers of people. Charts in parades.

Chapter XVII. A Few Cautions 344

The importance of clear and accurate titles. Symbols which are easily remembered. No necessity for plotting curves vertically. Errors resulting in interpretation of curves if the zero of the vertical scale is not shown on the chart. The selection of scales for curve plotting. Different impressions from curves from the same data but with various scales. Optical illusions which may afl^ect graphic work. A checking list for final inspection of graphic presentations. Need for standard rules of grammar for the graphic language. A few suggested rules for graphic presentation. Great advantages may result if graphic methods are more widely used for portraying quantitive facts.

FOR PRESENTING FACTS

GRAPHIC METHODS FOR PRESENTING FACTS

Chapter I COMPONENT PARTS

AFTER a person has collected data and studied a proposition with great care so that his own mind is made up as to the best solution for the problem, he is apt to feel that his work is about completed. Usually, however, when his own mind is made up, his task is only half done. The larger and more difficult part of the work is to convince the minds of others that the proposed solution is the best one — that all the recommendations are really necessary. Time after time it happens that some ignorant or presumptuous member of a committee or a board of directors will upset the carefully -thought-out plan of a man who knows the facts, simply because the man with the facts cannot present his facts readily enough to overcome the opposition. It is often with impotent exasperation that a person having the knowledge sees some fallacious conclusion accepted, or some wrong policy adopted, just because known facts cannot be marshalled and presented in such manner as to be effective.

Millions of dollars yearly are spent in the collection of data, with the fond expectation that the data will automatically cause the correction of the conditions studied. Though accurate data and real facts are valuable, when it comes to getting results the manner of presentation is ordinarily more important than the facts themselves. The foundation of an edifice is of vast importance. Still, it is not the foundation but the structure built upon the foundation which gives the result for which the whole work was planned. As the cathedral is to its foundation so is an effective presentation of facts to the data.

We daily see facts presented in the hope of creating interest and action for some really worthy piece of work to benefit the people as a whole. In many of these cases the attitude of the person presenting the matter seems to be that the facts will speak for themselves and that they need little or no assistance. Ordinarily, facts do not speak for themselves. "When they do speak for themselves, the wrong conclusions are often drawn from them. Unless the facts are presented in a clear and interesting manner, they are about as effective as a phonograph record with the phonograph missing.

If it were more generally realized how much depends upon the method of presenting facts, as compared with the facts themselves, there would be a great increase in the use of the graphic methods of presentation. Unlimited numbers of reports, magazines, and newspapers are now giving us reams of quantitative facts. If the facts were put in graphic form, not only would there be a great saving in the time of the readers but there would be infinite gain to society, because more facts could be absorbed and with less danger of misinterpretation. Graphic methods usually require no more space than is needed if the facts are presented in the form of words. In many cases, the graphic method requires less space than is required for words and there is, besides, the great advantage that with graphic methods facts are presented so that the reader may make deductions of his own, while when words are used the reader must usually accept the ready-made conclusions handed to him.

In many presentations it is not a question of saving time to the reader but a question of placing the arguments in such form that results may surely be obtained. For matters affecting public welfare, it is hard to estimate the benefits which may accrue if a little care be used in presenting data so that they will be convincing to the reader. If the average citizen, and especially the business man, knew how to uiterpret charts and curves, it would be feasible to convey to him in effective form those facts relating to broad public improvements, public-service operation, and national, State, or municipal management, which might affect the whole fabric of our civilization. Archimedes wanted only a fulcrum for his lever and he would move the world. If the world is ever moved it will probably be by facts properly presented. The method of presentation is the fulcrum without which facts, as a lever, are useless.

The preparation and interpretation of simple charts and curves should be taught in the public schools as a part of arithmetic. The work of kindergarten nature now done in the lower grades of the public schools could very readily be extended so that the pupils would be making charts and curves without realizing that the work (or play) had any relation to mathematics. Text-books for geography are already making effective use of charts. In the public schools of Newark and of Trenton, New Jersey, grammar-school pupils are preparing charts and plotting curves relating to records which show the present condition and recent development of their home city. The principles of charting and curve plotting are not at all complex, and it is surprising that many business men dodge the simplest charts as though they involved higher mathematics or contained some sort of black magic.

If an editor should print bad English he would lose his position. Many editors are using and printing bad methods of graphic presentation, but they hold their jobs just the same. The trouble at present is that there are no standards by which graphic presentations can be prepared in accordance with definite rules so that their interpretation by the reader may be both rapid and accurate. It is certain that there will evolve for methods of graphic presentation a few useful and definite rules which will correspond with the rules of grammar for the spoken and written language. The rules of grammar for the English language are numerous as well as complex, and there are about as many exceptions as there are rules. Yet we all try to follow the rules in spite of their intricacies. The principles for a grammar of graphic presentation are so simple that a remarkably small number of rules would be sufficient to give a universal language. It is interesting to note, also, that there are possibilities of the graphic presentation becoming an international language, like music, which is now written by such standard methods that sheet music may be played in any country.

With oral and written language and with tabulated figures also the reader sometimes draws conclusions regarding the relative importance of different things from the comparative length of time or amount of space used in presentation. Graphic methods overcome this difficulty by showing quantitative facts in true proportions which give instantly the correct interpretation. In tabulations like that on page 4 it is only the highly skilled reader who can refrain from regarding the five different items listed as of somewhere nearly equal numerical importance, simply because the five different items are given exactly the same space and prominence when written down on the page.

Percentage op Each Race in the Population of the World

Yellow 45

White 41

Black 11

Brown 2

Red 1

It requires mental concentration in interpreting even these simple figures to get the correct impression of the very large percentage of the two chief races and the numerical insignificance of the one last named. If these data were shown in a simple horizontal bar, somewhat like that seen in Fig. 1, the relative proportions of the different races o

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Fig. I. Disposition of a s-cent Fare Paid to the Boston Elevated Railroad in the Year

Ending September 30, 1909

The horizontal bar gives an especially good method for showing component parts would instantly be seen without any mental effort on the part of the reader.

Fig. 1 is a very satisfactory form of chart to bring out the component parts of any group total. The horizontal bar need be made only wide enough to show the various kinds of shading necessary to give a good contrast. Engineering dimension lines above each block in the bar are of great advantage 50%

for convenient reading. The dimension that several of the detail blocks could be included in various sets of dimension lines to show such items as total fixed charges, total operating expenses, etc.

In this type of chart the actual figures representing the value of the components should be given for the use of any reader who may wish to draw his own conclusions or to make new combinations of figures different from those shown in the chart. As a general thing it is always desirable to have full data given on any chart. Fig. 1 gives all the data without in any way detracting from the ease of reading the chart itself.

It would be desirable to have a large number of the illustrations in this book printed in color. Charts which are made in color can readily bring out points which are not easily portrayed when only black ink is used. The reader should keep in mind for his own work that he should use colors in making those charts where colors are economically possible. For the purpose of this book, color printing is prohibitive

Disposition of the Gross Revenue of the Bell Telephone System for the Year 191 1

This chart was taken from the annual report to the stockholders of the American Telephone and Telegraph Company for the year ending December 31, 1911

The circle with sectors is not as desirable an arrangement as the horizontal bar shown in Fig. 1 on account of the cost. In printed reports, in magazine articles, and in magazine advertising, color printing is not at the present time commonly available. The illustrations of this book will accordingly show what can be done in printing complex charts with only one color of ink,

under the same conditions that would be found in the preparation of material for magazine articles, printed reports, and ordinary prospectus or other advertising matter.

Fig. 2 is a form of chart used probably more widely than any other form to show component parts. The circle with sectors is not a desirable form of presentation, however, because it does not have nearly such flexibility as the method shown in Fig. 1. The sector method does not permit of convenient arrangement of names for the different

Fig. 3-

The Survey

Disposition of a Family Income of from $900 to $1000

This cut shows an attempt to put figures in popular form. The eye is likely to judge by the size of the pictures rathei' than by the angles of the sectors components. Note that the direction of the lettering must be reversed as the eye proceeds around the circle. In this case, "Interest and Dividends" reads upward while "Materials, Rents, Traveling Expenses, etc." reads downward. Another disadvantage of the sector method is the impossibility of placing figures in such manner that they can be easily compared or added. The horizontal-bar method permits of placing figures so as to keep the decimal points in line, thus making it possible to add the whole column of figures relating to the various components.

The sector method is probably so widely known through presentation in exhibits, illustrations for popular magazines, etc., that it is more generally understood than any other niethod now in use. The more easy reading of the wedge or sector chart is, however, largely due to habit. If the horizontal-bar method of Fig. 1 were used as frequently as the sector method, it would be found in every way more desirable

UOSTTHROUOH RADIATION, LEAKAGE OF STEAM ETC

LOST THROUGH UNCON5UMEO FUEL IN ASH i.G5TJN THE FORM QF UNCONSUMEI? FUEL IN THE CfNDEfIS AND SPARKS

LOST (N OASES DISCHARGED FROM STACK

LOST IN VAPORIZING MOISTURE IN COAL lOO 3 than the sector method and would, in a very short time, become so well known that it would be read much more quickly and accurately than the method involving sectors.

In Fig. 4 a double scale is used by which the same data can be interpreted from two different standpoints. On the left the scale is given in millions of tons, and on the right in millions of dollars.

The reader can interpret the chart from whichever standpoint he prefers. Though this chart is arranged vertically instead of horizontally, it really makes little difference which way the bars are placed. As a general thing, the horizontal arrangement lends itself more readily to the use of type so that the reader may read type statements without having to turn the book.

In Fig. 5 the whole population of the United States is divided first into native white, foreign white, and colored, then each of these groups is subdivided according to place of birth. This is an excellent type of chart to use if subdivisions in the component parts of any unit have to be shown. If the scale to which the chart is drawn is specified, it is possible for the reader to measure, with an ordinary ruler or with an engineer's scale, the exact percentage size of each of the different components.

OTtLlZED BY BOILER

I

CONStJMeO IN STARTING flBES^

AND LEFT IN FIRE aOJ^ aTCNDOI^ RUN^ESTimATEd)

Adapted from Data, Chicago

Fig. 4. Utilization and Accompanying Wastes of One Year's Coal Supply for Locomotives on Railroads of the United States

The double scale permits reading this chart in tons or in dollars

If the chart is made on co-ordinate paper with ruled squares, the reader can obtain the size of each component direct from the co-ordinate lines. The trouble, however, with using co-ordinate paper for charts of this sort is that the components are likely to begin and end at points not falling upon the co-ordinate lines, thus making it necessary to count fractions of a division at both beginning and end of the component to be measured. The best thing in charts of this kind is to use unruled paper, and specify the scale. The reader, if he wants the exact data, can take his measurements with a ruler. The engineer's scale has its subdivisions in decimals and hence is the most convenient scale for chart work. An engineer's scale should be part of the equipment of every person who has charts to make.