Class L 3 /<> f° Book— / 4s» CopyrightN . COPYRIGHT DKPOBm HANDWRITING By EDWARD L. THORNDIKE tl Professor of Educational Psychology, Teachers College Columbia University Reprinted from Teachers College Record, Vol. It, No. 2, March 1910. PUBLISHED BY Gfeartpra (&o\U$t, (Mmtttoa Itttiwrutti} NEW YORK CITY 1912 Copyright 1910 Copyright 1912 CCI.A314733 ^0 I CONTENTS SECTION PAGE i. Introduction i Part I. The Measurement of the Quality of Handwriting 2. The Construction of a Scale for Quality of Handwritings by Children in Grades 5 to 8 4 3. The Nature of the Scale, including Qualities or Degrees of Merit from that of Copy-Book Models down 7 4. Criticisms of the Scale 8 5. The Uses of the Scale 17 6. A Scale for Quality in Adult Women's Writing 19 7. The Derivation of the Scale 24 Part II. The Speed and Quality of Handwriting in Seven School Systems 8. Differences between Systems 29 9. The Relation of Differences in Results to Differences in Means and Methods of Teaching Handwriting 32 10. Differences between Individuals within the Same School System.. 33 11. The Relation Amongst Individuals between Speed and Quality. . 35 12. The Relation of the Quality of Slow Writing to the Quality of Rapid Writing by the Same Individual 36 13. Miscellaneous Comments 36 14. A Scale Based on Equally Often Noted Differences in Quality. . . 40 Scale A between pp. 10 and 11 Scale B " " 24 and 25 Scale C " " 40 and 41 HANDWRITING OF CHILDREN IN GRADES S a&oumA tLaZ tfu. aLh, c^-uJ, {
< cxxjxcL', Wvv-^ v/T^^/^n^u^-^r-ULoX X>t^^yy^l -»-£/ya- t ~' J ? ' 1 ""*- pupil, teacher, or superintendent of schools knows how well any child, class, or group of children writes in anything approaching the sense in which we know how hot any liquid is or how long a wire is. The main purposes of this monograph are to describe the means by which a graphometer or scale for handwriting may be made, to present such a scale for the handwriting of children in grades 5, 6, 7, and 8, to explain how such a scale is to be used, to present a similar scale for adult women's handwriting, and to mention some of the facts and questions of importance to which the discovery and use of these scales have led. Many circumstances have combined to prevent me from giving at this time anything like a perfect scale. The individual differ- ences amongst competent judges in rating any example are so great that to get for it a measure accurate within one per cent of the difference in merit between the best and the worst of gram- mar-school (i.e., grades 5 to 8) writing requires that at least 200 judges rate it. I have not been able to command the services of so many. For the greatest practical convenience a scale should have for any quality samples of all the common styles of children's writings, and should include about ten qualities differing each from the next by equal steps — equal, that is, within, say, four per cent of a step or one half of one per cent of the difference between the worst and the best grammar- school writing. But to get such samples one would need to have several thousand samples of each style of writing, and to have about half a million ratings made. This means roughly four thousand hours of labor. The final selections of samples for the scale should properly be made from very many printed reproductions such as will form the scale itself. The cost has prohibited me from making many of these. Tke" v scaie is presented now, in spite of its imperfections, for these reasons : It is the result of some twenty thousand ratings Introduction 3 and ensures measurements far more accurate than anyone could make without it. For the present needs of school practice and educational research, a very precise instrument for measur- ing handwriting is not required. The best way to get a more perfect scale is by the use of this one as a starting point. , This scale is then offered as a preliminary scale whose imper- fections the maker is, perhaps, more conscious of than any critic will be. I beg the reader to bear this in mind, since, for the sake of simplicity in description in what follows, I shall not in each case state the fact that a quality or point on the scale is determined only to a certain approximation, and the fact that the differences between successive qualities are only approximately equal. PART I The Measurement of the Quality of Handwriting Section 2. The Construction of a Scale for Quality of Hand- writings of Children in Grades 5 to 8 If one selects from children's written work 1000 samples rang- ing from the best to the worst handwriting found in grades 5 to 8 and tries to rank these 1000 samples in order of merit for handwriting, one finds that he cannot make 1000 such ranks. Some of the handwritings will be indistinguishable in " good- ness " or " quality " or " merit." Nor can one make 100 such ranks. Nor can one make 40. One can make about 20, but if he so ranks the samples a number of times he gets substantially the same average result as he gets when he ranks them a number of times in 10 or 11 groups. To get an individual's judgment of the relative merits of the 1000 samples it is sufficient to have him rank them in 10 or 11 groups three or four times. If he grades in 10 groups and tries to make the difference in " goodness " or " quality " or " merit " all equal, — to make, that is, the sample he puts in the highest group (call it 11) as much superior to those in the next highest group (call it 10) as the latter are to those he puts in the second from the highest group (call it 9), etc., etc., — we have in the average 1 result of his groupings his judgment of the relative merits of the samples in a specially convenient form. For instance, if he grades sample 217 as in group 5 three times, as in group 4 once, and as in group 6 once, and grades sample 218 as in group 6 three times, in group 5 once, and in group 7 once, he judges 218 to be " 1 " better than 217, " 1 " being, in the individual's judgment, one tenth of the difference between group 1 and group 1 1. If thirty or forty individuals chosen from competent judges of handwriting thus judge the 1000 samples, the average 1 of all 1 Except for certain factors which will be described in section 7. 4 The Measurement of the Quality of Handwriting 5 their gradings give approximately the relative merit of each sample in the judgment of competent judges in general. If they grade sample 317 in group 3 two times, in group 4 five times, in group 5 thirteen times, in group 6 thirteen times, in group 7 five times, and in group 8 two times, their average or median grade for it is 5.5. If their average or median grade for sample 318 is 6.4, they esteem 318 as .9 better than 317. The .9 means, in their judgment, nine tenths of one tenth of the difference between grade one and grade eleven. If now from all the 1000 samples we could find some which were graded exactly 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, and 11 by the average or median 1 judgment of 30 or 40 competent judges, each grading the set into groups 1 to 11 by what he thinks are equal steps in merit, we would have a very useful scale of merit in handwriting. It would include all grades from the worst to the best and would proceed by what were, by the average com- petent opinion, equal steps. Or if we could find some graded 1.5, 2.4, 3.3, 4.2, 5.1, 6.0, 6.9, 7.8, 8.7, 9.6, and 10.5 we would have a scale nearly as useful. It would not be so likely to in- clude the very worst and very best samples, but would proceed by equal steps, as before. The scale which I shall proceed to describe was obtained by a method in principle the same as the above. Such a scale could be got in a different way, as follows : Sup- pose competent judges to compare each sample with every other, stating in each case which was better. If then we picked out samples a, b, c, d, etc., such that a was judged better than b, just as often as b was judged better than c, and just as often as c was judged better than d, and so on, we could have, in samples a, b, c, d, etc., a scale by equal steps, if two other conditions were fulfilled by them. The first of these conditions would be that a should not be judged better than b and worse than b equally often. For if it were, a would be equal to b, b to c, c to d, and so on, and we would have no extent to our scale. The second of these conditions would be that a should not always be judged better than b. For, if it were, it might be just enough better to barely be so judged, or it might be very, very much better. 1 Except for certain factors which will he described in section 7. 6 Handwriting Only if differences are not always noticed can we say that dif- ferences equally often noticed are equal. But if we had, as a result of the judgments, facts like those below, we could say that a, b, c, d, etc., represented samples of writing progressing by equal steps of difference in quality. iooo comparisons of a, b, c, d, etc., being made : a was judged better than b in 73 per cent., equal to & in 11 per cent., and worse than b in 16 per cent, of the judgments. b was judged better than c in 73 per cent., equal to c in 11 per cent., and worse than c in 16 per cent, of the judgments. c was judged better than d in 73 per cent., equal to b in 11 per cent., and worse than b in 16 per cent, of the judgments, and so on for d-e, e-j, n. The scale which I shall describe was tested throughout by this second method. The two methods do not give results that corre- spond exactly. The variations follow this rule: Judges will notice differences between poor samples when they compare them directly one with another which they would not count in rating them by a mental scale. For example, suppose samples a, b, c, and d to be rated 10, 9, 3, and 2 by comparison with a mental scale of eleven grades by equal steps. The percentage of judges regarding 10 as better than 9 will be smaller than that regarding 3 as better than 2. Since we get two different scales by the two methods, there are four alternatives. We may adopt one or the other or com- bine them, or give the results by both methods. I shall take the latter alternative, but shall at this point present only the scale as derived by the first method. In a later section (Section 12) the scale is derived by the second method will be presented. The scale given here is then a scale in which the steps of dif- ference are equal in the sense of being called equal by competent judges. Equal will mean just this in the next three sections. They are not equal in the sense of being equally often noticed when the single question " better or worse," is answered for each sample in connection with every other sample. The dif- ferences in the upper part of the scale would be less often so noticed than those in its lowest third. The Measurement of the Quality of Handwriting 7 Section 3. The Nature of the Scale Scale A is the scale for merit of the handwriting of children of grades 5 to 8. It is not a scale of merit of the writings of children of grades 1 to 4 or of the writings of boys and girls of high-school age. It can, however, be more or less well used for such cases until we get more appropriate scales. Each set of samples represents a point on this scale. The use of 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, and 17 for these qualities of handwriting means, first of all, that 14 is as much better than 13, as 13 is than 12; that 13 is as much better than 12, as 12 is than 11, and so on. In the second place it means that quality 14 is two times as far above o merit in handwriting as quality 7 is; that quality 16 is twice as far above o merit in hand- writing as quality 8 is, and so on. Zero merit is defined roughly as writing as bad as sample 140 (see page 16), as a hand- writing, recognizable as such, but of absolutely no merit as hand- writing. The use of several samples under one quality means that those samples are of equal merit. The scale includes sam- ples of as many different styles as could be obtained, so that in using the scale the merit of any sample of any style of writing can be quickly ascertained by comparison with the scale. The scale extends in actual samples by children from nearly the worst writing 1 of fourth-grade children (quality 5) to nearly the best writing of eighth-grade children (quality 17). Quality 7 is nearly the worst writing of fifth-grade children. The scale includes a sample of a copy-book model which is rated by competent judges as of approximately quality 18, two samples of fourth-grade writing which are judged to be approxi- mately of qualities 6 and 5, and a very bad writing, arti- ficially produced, which is rated by competent judges as of ap- proximately quality 4. The scale thus extends from a quality better than which no pupil is expected to produce, down to a quality so bad as to be intolerable, and probably almost never found, in school practice in the grammar grades. If one had a finer scale, its use would give but slightly more accurate results, and would require more practice and more time. 1 In a formal exercise in writing at their " natural " rate. 8 Handwriting Any specimen of handwriting is measured by this scale by put- ting it alongside the scale, as it were, and seeing to what point on the scale it is nearest. Thus, the sample on page 9 (sample 9) is measured by comparing it with those of Scale A. I judge it to be between quality 15 and quality 14 and assign it the measure 14 rather than any other unit measure of the scale. If one wishes to measure more finely than to units, he can add or subtract a frac- tion according as the sample to be measured seems better or worse than the quality of the scale to which it is nearest. The sample to be measured should, for convenience, be exam- ined with the entire scale in view. If the scale's samples are arranged in order on a table or against a wall, the examined sample is easily compared with them. The measurer then de- cides what quality of the scale the sample possesses and records the measure. The measurer should be, of course, careful not to decide its grade because of its likeness in style, but only because of its likeness in quality to some sample of the scale. If, for instance, one has a pronounced vertical that is really of quality 7, one must not call it quality 8, because it is in style more like sam- ple 14 than like the sample of quality 7. The measure may be made more and more accurate by having other judges also measure, each always in ignorance of the ratings given by the others. In default of other judges, the measure may be made more accurate by rating the sample two or more times, each time in ignorance of the ratings previously given. An individual may be measured more accurately by using several samples of his writing, each being rated in ignorance of the ratings given to the other sample. Section 4. Criticisms of the Scale The scale has, as previously noted, some defects. First of all, not all styles of writing are represented on the scale, much less at each point of quality on it. For example, we have no pronounced backhand writings of certain qualities and no very pronounced forward slant of certain qualities. There are hardly any mark- edly angular writings on the scale. This defect can be at any time remedied by securing enough samples of children's writing of the missing sorts at approximately the qualities in question, The Measurement of the Quality of Handwriting g 1 •^ -^ 3- ^^=P io Handwriting selecting, with the aid of thirty or forty competent judges, sam- ples whose merit is exactly 8 or io or 12 or 14 as the case may be, and adding these to the scale. I shall be grateful to any one who sends me collections of children's handwritings of styles not represented in the scale. Each such sample should be accompanied by a statement of all the grades assigned to it on our scale by at least ten or twelve competent observers, each of whom measures it with the scale and rates it in complete ignorance of the ratings given by all the other judges. It is desirable, though not necessary, that the writings be on unruled paper. In the second place, the qualities below 5 and above 17 should perhaps be represented in the scale by actual children's writings. This defect could be remedied by collecting children's handwrit- ings that were superlatively bad and superlatively good. I shall be grateful to anyone who sends me samples of children's writing which are notably better than quality 17 or notably worse than quality 5. In the third place, although I have so far spoken of the quali- ties 5, 6, 7, 8, 9, 10, etc., as if they might be absolutely these amounts — as if the 13's might be all absolutely equal in merit and all absolutely halfway between any one of the 12's and any one of the 14's — this is not exactly the case. As was noted on page 3, the scale is only approximate. 16 on the scale does not pretend to mean 16.00000, but between 15.9 and 16.1. 8 does not pretend to mean 8.0, but between 7.9 and 8.1. And as a matter of fact, although I have had a thousand samples graded and have chosen as wisely as I could, some of the samples do vary in merit from 7, 8, 9, 10, etc., by more than .1 plus or minus. Even after one has picked samples that vary only that much, the relations may be altered in the process of making the electrotypes from which the scale is printed or in the process of printing itself. This defect can be remedied by the expenditure of enough time and money in getting more samples, having them graded by more judges, reproducing more of them in electrotypes, and having these reproductions graded again by more judges. In this work I am now engaged. The defect is, however, of little consequence to any use to which any of my readers is likely to put the scale. as 11 I * 3 11 n 4h 4 m u '.it- is. hXJ u ift 3 , 1 li*r i ft 1 i i^ 5 i- j 4 3 'I J - -£. H'i m SI I M m tin f r < Hit 4 I J i KM lli The Measurement of the Quality of Handwriting n For the variations in the scale are trivial compared to the vari- ations in individual judgment. I have measured the quality of each sample in the scale to tenths of a step, subject to slight changes had more judges been available, and apart from varia- tions in the printing. For example, the quality of sample 49 in the scale is 15.1, not exactly 15.0. Similar figures for each sample in the scale are given below. If any one wishes to have the values of each sample as precise as possible he may substitute these values. In scientific studies of handwriting in schools this should be done, but in practical grading by teachers the 5, 6, 7, 8, etc., of the scale may be kept without the decimal alterations. What changes might be made in the qualities, if the consensus of thousands of judges were to replace the consensus of from twenty to seventy, is shown in the figures in the third column, which give the probable average divergences of the former con- sensus from the latter. They show that the scale is not nearly so precise as, say, a 25 cent scale for weight. But, on the other hand, the superiority of the scale to the personal opinion of any one teacher or investigator is enormous. The latter would have a probable average divergence of from 1.0 to 1.6 from the con- sensus of a thousand competent judges. Table I im -le Quality 32 16. 1 • 14 84 l6.2 • 43 47 I5.0 .19 49 15. 1 .18 89 I5.0 • 39 90 15. 1 •35 19 I4.O .20 54 14.0 .19 4 12.9 .20 24 13. 1 .18 26 12. Q .18 55 13. 1 .21 30 11. 9 .19 7 12.0 .20 52 12.0 .20 23 ir.o .20 Probable average divergence of the estimated quality from an estimate by an infinite number of judges 12 Handwriting Probable average divergence of the estimated quality from an estimate by an infinite number of judges Sample Quality 45 II. o .19 106 11. o .28 17 10.2 .18 21 9.1 .15 28 8.9 .15 31 8.9 .14 48 8.0 .14 14 8.1 .19 126 7.0 .40 The reader, in examining the scale, may think that some of the samples called equal are really unequal. If he objects to vertical writing, he may, for instance, think that sample 55 in Scale A is at least one step worse than sample 24. Such criticisms of the scale are, however, really strong arguments in its favor. For such a critic is surely wrong. That he denies the correctness of the average opinion of forty competent judges me s simply that his own judgment is partial or crude, and the act that each individual's judgments of handwriting are thus partial and crude proves that he needs a scale representing the general judgment of competent people to help him to judge and to teach him to eliminate the unfairness in his own future judgments. If no one felt any disagreement with this scale, it would not be so valuable as it is under the condition that many individuals will think it wrong. For those who are unfair to any style of handwriting or who overemphasize beauty in com- parison with legibility, or evenness in comparison with " char- acter," or the reverse, can be proved by the scale to be unfair — that is, to diverge from the average judgment of competent people in general. If they are intelligent, they can learn from the scale to correct their bias. It is possible, however, that some critic may deny the value of the average judgment of competent people in general and declare that though that judgment pronounces two handwritings equal in merit, he knows that they are not equal. Now conceivably he might be right. But the chances are enormously against his being right, and science naturally cannot count his assurance as of more weight than that of any other judge of equal competence. The Measurement of the Quality of Handwriting 13 Some more sophisticated critic may object, not that he knows that this scale is wrong and prefers his own supposed competence to that of forty of his peers, but that no one can know whether this or any such scale is right. For, he will add, any such scale is subjective, 1 representing only what certain individuals think about the merit or value of samples of handwriting. In this there is some truth. There is no value in average opinion as such. The world was as round, when the most competent judges thought it flat, as it is today. If it should some time be proved that evenness of width of line was the sole criterion of real merit in handwriting, the scale would be wrong. But in the case of handwriting the only available criterion of real " merit " or " quality " or " goodness " is the average judgment of competent people. A hundred years from now merit in handwriting may mean something different from what it now means and a new scale may be required. But what it then means will then be determined by the average judgment of competent men and shown in a scale derived just as this one has been derived. Wnat merit does now mean is precisely the thing measured by is scale. Merit in handwriting in the judgment of competent people today is the composite of qualities, each duly weighted, wherein the samples marked 12 are as much better than the samples marked 10 as the latter are than those marked 8, etc. The scale measures not only some absolute merit, but merit as now defined in the average judgment of forty or more persons chosen at random from the competent. And no other sort of merit is so well fitted to be the basis of a scale. A far more sagacious criticism than either of these would be that a scale like this for merit in general is less useful than a scale for legibility alone, or for beauty alone, or for "character" alone, or for ease alone. Of course, I admit that such specialized scales are highly desirable, and I hope that this scale for general 1 If this report were addressed to students specially interested in logic and scientific methods applied to the social sciences, it would be worth while to show here that the objectivity of a scale for length as compared with the subjectivity of a scale for merit of handwritings, Or moral worth of acts, or beauty of poems, means only a closer likeness amongst men in their judgments, not a radically different sort of judgment. Being far, far more alike in sense-organs and muscles than in the central eon nections of neurones, we agree far better in comparing lines and weights than in comparing handwritings or poems. 14 Handwriting merit will stimulate others to the labor of making similar scales for legibility alone, beauty alone, and so on. But it seems sure that the scale of most importance and usefulness is that for gen- eral merit. General merit is that for which school grades are oftenest given, in respect to which school systems or classes are oftenest compared, and with which other features of a pupil's achievements are oftenest related. Moreover, only after a scale for general merit has been made can one measure the extent to which legibility, beauty, etc., respectively determine general merit. So much for criticism of the general method of constructing the scale. I turn now to possible criticisms of the scaling itself. Some one may ask why 4, 5, 6, 7, 8, etc., are used as the values of the samples of Scale A instead of some other equal-step series of numbers such as 1, 2, 3, 4, 5, 6, etc., or 65, 67^2, 75, 77%, 80, etc. The step is made 1 rather than 2% because one cannot judge samples precisely enough to profit by more than 18 divisions in a scale. Hence the time spent in deciding whether to call a sample measured by the scale 78 or 76 or jy and in later computing with the large numbers would be largely wasted. The ratio of the highest to the lowest children's writing in the scale is made 17 to 5 (or roughly 3^2 to 1), instead of 6 to 1 or 13 to 9 (97% to &7%) because, from the average opinion of competent judges and the facts of individual differences in motor ability, zeal for handwriting, and other factors determining the quality of a pupil's writing, the best writing from children in these grades seems likely to possess less than six times as much merit as the worst, but more than one and a third times as much — in other words, to be less than six times as far, but more than twice as far, beyond zero merit. That is, the scale was arranged so that the numbers represent- ing the distances beyond zero of the best and worst samples of children's writing in our scale should stand in the ratio of ap- proximately 3^2 to 1, and also so that the numbers on the scale should be the smallest compatible with as accurate measure- ment of handwritings as educational theory and practice need. If any one prefers as a scaling 15, 17, 19, 21 43, or 3, 4, 5, 6 .... 17, or 7, 8, 9, 10. . . .21, it would be hard to prove to him that his choice was inferior to the 4, 5, 6, 7, 8. ... 18 used. The The Measurement of the Quality of Handwriting 15 essential thing is that the steps be equal, and that the ratio which the amount attached to the best children's writing bears to the amount attached to the worst be a reasonable one. Having defined what was meant by o merit (see sample 140 on page 16, I judged as best I could the distance of sample 141 1 therefrom in terms of the distance of sample 2 2 therefrom. The judgment of 3 2/5 times is by no means final. Indeed I am now engaged in an investigation aiming to revise it. I could argue plausibly for a ratio as low as 2^ to 1 or for one as high as 5 to 1. But a ratio somewhere between 3 to 1 and 3^2 to 1 seems the most reasonable. The whole matter of the choice of an absolute o for merit in handwriting, and of the consequent absolute values of the points on the scale, is one involving many intricate considerations out of place in this discussion. I fear that in touching upon it at all I may have perplexed some readers. Such may rest confident that in using the 4, 5, 6, 7, 8, 9, 10, 11, 12, etc., of the scale in measur- ing a sample of handwriting as they would use 4, 5, 6, 7, 8, 9, 10, 11, 12, etc., dollars in measuring the value of a book or a jewel or a trunk, they will commit no error of much consequence or, at least, no error so great as they would be likely to commit by measuring it in any other one way. Another criticism may be that the scale does not guarantee agreement among the observers using it to measure a sample of handwriting. The same sample may, it will be said, be measured by one person as equal in merit to 8, by another as equal to 10, and by still another as equal to 9. This is true, but it is not the fault of the scale. Observers will disagree in their measure- ments made with the scale, but not nearly so much as in meas- urements made without it. No scale guarantees absolute agree- ment. Observers measuring the length of this line to tenths of a millimeter will not agree. But they will agree better than they would if they had no scale and judged its length as a savage might. 1 Nearly the best sample from children in grades 7 and 8. 2 Nearly the worst sample from children in grades 4 and 5. i6 Handwriting .t: cj ha O fl.8 The Measurement of the Quality of Handwriting ly * Section 5. The Uses of the Scale The topic of this section is fitly treated in the one statement: Any measurement of the quality of handwriting may be made more accurately and conveniently with the scale, either actually present or held in memory, than without it. The reader may apply this statement to whatever cases his interests suggest. I shall mention a few of the commoner uses and explain the func- tion of the scale as a standard held in memory. The class-room teacher has to measure the quality of a single pupil's handwriting in order to assign him a rating in comparison with his fellows and, better still, in comparison with his own past performances. If she uses the scale either by giving its numeri- cal measures outright or by letting her A, B, C's, or 75, 80, 82, etc., per cents, or excellents, goods, fairs, etc., mean certain points on the scale, her ratings will have a definite meaning to the pupil, can have the same meanings that similar ratings by other teachers in the school have, and may be used to measure the actual improvement of the pupil month by month and year by year. She can more easily and more accurately measure the relative values of the different methods of teaching which she may from time to time employ, of different lengths of periods for drill, and the like. A principal or supervisor or superintendent of schools needs to measure the quality of the handwriting of individuals, of classes, and of all classes of the same grade, in a school or system. If he has such measures honestly made by the scale, he can compare the work of one teacher with that of another, the work within his own school or city with that of other schools or cities and with that of his own city five years later, the work of schools using one system of writing with that of schools using other systems, and the like. If he tried without the scale to esti- mate the superiority or inferiority in handwriting of twelve-year- olds in city A to twelve-year-olds in city B, he would have to collect many samples in both cities and have them graded alike. He could define the amount of difference found only by actually exhibiting it in samples or by making out a scale like ours, defin- ing it as I have done, and expressing the difference as such a distance on the scale. With the scale in use in both cities, on the 1 8 Handwriting contrary, if marks are honestly given by the teachers, the superiority or inferiority of any group will be measured by the difference in the scale-values of the marks themselves. The scientific student of education will use the scale to mea- sure the quality of samples of handwriting from individuals, classes, cities, groups chosen for grade, age, sex, method of teaching, or length of time devoted to writing, and from any other sources. He will also be able to use any marks or ratings honestly given by teachers or others. Whoever has any occasion to define a standard of quality in handwriting can define it unmistakably and conveniently by the scale. Business men can decide what quality they wish the schools to secure in the boy fourteen years old who is to apply for clerical positions. A supervisor can inform all the teachers of, say, grade 7 that the minimum requirement is, say, quality 11, at a rate of 50 letters per minute, that the average pupil must be made to write at quality 13 at a rate of 60 letters per minute, and so on. Whatever standard is set will be absolutely defined by those who set it and will be clear to all those who are to follow it. The pupil himself may profitably know and use the scale. He may see by it what is expected of him and may tell how nearly he reaches the standard and how much he has gained. Even if precision is not desired in the estimate of the quality of handwriting, — even if good and bad or satisfactory and un- satisfactory are the only ratings to be given, — the scale is none the less useful. For if good and bad, or satisfactory and unsatis- factory are to mean anything, they must mean handwritings above and below some point on some scale of merit. They can be properly defined only by locating that point. And until some better scale is available that point can be located only by ex- hibiting samples or by stating the numerical value these samples would have on our scale. To put the whole matter in a word, any measurement of the quality of handwriting should be made by the scale and reported in terms of the scale, for substantially the same reasons that any measurement of the length of an object should be made with a linear scale and reported in meters or feet. The Measurement of the Quality of Handwriting 19 Measurements may be made by the scale without the com- parison of the sample with the actual scale itself. Just as one uses his experience of feet and inches as a mental standard whereby he estimates more or less accurately the length of pencils, tables, windows, and the like, without an actual ruler or tape, so one may come to estimate that this sample of writing is about quality 16, that one about quality 9, and the like, from the mental standard left from examination and use of the actual scale. The scale should always be present for reference in any measurement which requires exactitude, but it will do its greatest amount of service, not by actually serving as a foot-rule for quality in handwriting, but by creating in the minds of teach- ers mental standards to be used in even the most casual ratings of everyday school-room life. To one who uses the scale quality 18 or quality 15 or quality 7 comes to be a definite agent in de- termining all judgments, just as 18 inches or 15 pounds or 7 dollars is. Just as a child learns to think about length correctly and with fair precision without a ruler in his hand, by having measured off lengths with it, so teachers may come to think about handwriting correctly and with fair precision without the scale before their eyes by having measured handwritings with it. Just as the thermometer teaches us to supplant the vague " very cold," " cold/' " moderate," " warm," " hot," and " very hot " by " about o," " about freezing," " about 60 degrees," " about 70 degrees," " about 80 degrees," " nearly 100," and the like, so the graphometer can teach us to supplant the vague " illegible," " very hard to read," " a good plain hand," and the like, by judg- ments which mean something definite and constant to those who make and those who hear them. Section 6. A Scale for Quality in Adult Women's Hand- writing The scale for adult women's handwriting consists of only six points, each represented by only one sample. Let us call these samples a, b, c, d, e, and /. They represent the best selection that I could make of writings ranging from nearly the best to nearly the worst of the ordinary writings of some five hundred women teachers and students and differing progressively by 20 Handwriting equal degrees of merit. The derivation of the scale was as follows : Thirty judges rated samples a, b, c, d, e, and /, together with from 37 to 456 other samples. The ratings given were from 1 (the lowest grade) to n (the highest), grades 1 to n being roughly shown by samples and the requirements being made that the grades 2, 3, 4, 5, etc., should represent grades of merit dif- fering by equal steps. The number of the samples was reduced from 456 to 37 by gradually dropping samples which seemed unlikely to be near the points 1 to 1 1. The result of the thirty ratings is shown in Table II. Table II The Quality of Samples a, b, c, etc., as Measured by 30 Judges from the Original Writings Quality Frequencies of Each Quality for Each Sample a b » c d e f 1 20 I I 2 7 12 3 I 6 2 I 4 267I 5 2 10 6 I 6 1532 7 3862 8 1 1 3 4 9 1563 10 166 11 3 5 19 Bearing in mind that a rating of quality 1 means 1 or worse than 1 and that a rating of quality 11 means 11 or better than 11, it is clear that in the combined judgment of all 30 judges a, b, c, d, e, and / represent qualities progressing by approxi- mately equal steps. Thus 10 of the judges ranked a as better than 1, 10 ranked b as better than 3, and 10 ranked c as better than 5, 12 ranked d as better than 7, and 11 ranked e as better than 9. Of the 20 judgments of a as 1, it is probable that about 10 would have been " worse than 1 " had the series included a lower range. Of the 18 judgments of /as 11, it is probable that about 10 would have been "better than 11 " had the series in- cluded a higher range. The median values of a, b, c, etc., with this interpretation of the grades 1 and 11, are: 1.0, 2.833, 5-°> The Measurement of the Quality of Handwriting 21 7.125, 8.833 an d 10.94, tne differences in quality being respec- tively 1.833, 2-167, 2.125, 1.708, and 2.107. These six samples were then printed and were graded in their printed form, together with seven other samples of approxi- mately the qualities 1, 3, 5, 5, 7, 9 and n, by thirty-eight judges. The ratings in this case were in 6 grades, to progress by equal steps. These were called by the judges 1, 2, 3, 4, 5 and 6, but represent respectively 1, 3, 5, 7, 9 and 11 of the gradings just presented in Table II. Hence in Table III, which gives the re- sults of the gradings by these thirty-eight judges, I shall use 1, 3, 5, etc., for 1, 2, 3, etc. Table III The Qualities of Samples a, b, c, etc., as Measured by 38 Judges from the Printed Reproductions Quality Frequencies of Each Quality for Each Sample a b* c d e f 1 32 7 3 5 21 8 3 5 1 9 19 12 1 7 9 19 6 3 9 2 3 22 13 11 1 9 22 * Only 2>7 judges rated this sample. The median ratings for a, b, c, etc., are .8, 3.1, 5.1, 6.4, 9.1, 10.7. These thirteen printed samples were then rated together with from 58 to 104 samples of children's handwriting, including samples much better than the best of the adults', by 26 judges. The ratings were from 1 to 11, but the meanings of these num- bers were unlike those attached to them in Tables II and III, except in the case of the 1. The 3, 5, 7, 9, and 11 of Tables II and III have approximately the values 2.4, 3.8, 5.2, 6.6, and 8. Finally, the thirteen samples were rated, together with 120 sam- ples of children's writings, including some still better and some still worse, by 9 judges. The ratings were o to 12 but the values of the 1, 3, 5, 7, 9, and 11 of Tables II and III were, as before, approximately 1, 2.4, 3.8, 5.2, 6.6 and 8. The median values attached by the 35 judges were, for a, b, c, d, e, and /, in order, 1, 2.4, 3.83, 5.3, 6.5, and 7.9. We have then as a result of the three series of judgments, numbering 103 in all, the following: 22 Handwriting Differences between a and b, b and c, c and d, etc. : I. Using the median ratings of 30 judges (ink samples) : 1.83, 2.17, 2.13, 1.71, 2.11. II. Using the median ratings of 38 judges (print) : 2.3, 2.0, 1.3, 2^, 1.6. III. Using the median ratings of 35 judges (print, long series) reduced to equivalences with (I) and (II) : 2.0, 2.04, 2.1, 1.7, 2.0. Average differences: a-b, 2.04; b-c, 2.07; c-d, 1.84; d-e, 2.04; e-f, 1.9 1. The approximate equality of the steps may be verified by as- certaining how often b is rated higher than a, how often c is rated higher than b, etc., that is, by an adaptation of the so-called method of right and wrong cases. The facts are as follows : Comparisons of a, b Table IV b, c, d, e, AND f BY 102 Judges Long series, written samples Series of i printed samples 3 Series of 71 to 133 printed samples All series together 30 37 35 102 25* 26* 23 23 23 * 26 25* 25* 29 24 23 27* 25* 19 26 74 78 73 7i 73 No. of comparisons b rated as better than a c rated as better than b d rated as better than c e rated as better than d f rated as better than e In the starred cases the obtained figure was 1 less than that printed, but the number of comparisons it was from was also 1 less than that printed at the top of the column. Samples a, b, c, d, e, and / thus represent points on a scale of quality differing each from the next by approximately equal steps. We can properly call their values in order x, x + 2, x + 4, x + 6, x-\-S, and #+10 where 1.0 equals a difference roughly equal to one-tenth of the difference between the best ten and the worst ten of a thousand samples each from an adult woman student and x equals the average quality of the worst ten of the thousand. To be more precise we should call them, in order, x, x + 2.0, x + 4.1, x + 6.0, x -V 8.0, and x + 9.9. The Measurement of the Quality of Handwriting 23 To turn these values into numbers referring to zero merit as a starting point we must define zero merit for adult handwriting and measure the distance of x from it. This I have not attempted to do at all adequately since the need of an elaborate scale is not nearly so great in the case of adult handwriting as in the case of children's writing. Quality x of the adult scale is judged by the average of some forty indi- viduals to be approximately equal to quality 8 of the children's scale. A difference of 1.0 along the adult scale is judged to be approximately equal to a difference of .7 along the children's scale. If we take the zero point for adults as approximately the same as for children of grades 5, 6, 7, and 8, the qualities of a, b, c, etc., may be taken as approximately equal, in order, to 8, 9.4, 10.8, 12.3, 13.6, and 14.9 or 15 on an absolute scale whose zero is a writing recognizable as an attempt to write, but of zero merit. Such a numbering would not be far wrong. This adult scale very much needs samples of other styles at each point. Perhaps I should have delayed printing it until such had been obtained, but the labor and expense of collecting and selecting, by grading and gradual elimination, samples to fit ex- actly certain places on the scale is very great. The present scale has required thousands of gradings. It will be of great value in economizing the time and money of any one who wishes to make a better scale, if in no other way. As a matter of fact, in spite of its lack of samples of all styles at each point, it will also be of service in every case where the quality of a woman's handwriting is to be definitely known. For example, (1) the authorities of a college or a normal school wish to set a clear standard as to how good handwriting must be in order to make an examination paper, or a composi- tion, or other written work, acceptable. If they set this standard as " at least as good as quality c of the Thorndike scale " every student, every member of the teaching staff, the faculties of other colleges, and the public can tell just what the standard is. There can be real as well as " paper " uniformity in the standard. (2) In civil service examinations, examinations for teacher's licenses and the like, the standard of a certain quality by the scale at a certain minimum speed can be set and the candidates 24 Handwriting can be exactly, impartially, and uniformly (all over the country, if desired) rated. (3) The relation between (a) ability in handwriting under the pressure of school drill to (b) ability in handwriting in later life requires for study some adult scale. So also with any other relation of the quality of adult handwriting to anything. I shall be indebted to any one who will send me samples of adult women's handwriting, especially of vertical writing of qualities d, c, b, a, and worse, of pronounced slant writing of qualities d, e, f, and better, and of pronounced backhand writing of all qualities. Each such sample should be accompanied by a statements of all the grades assigned to it on our scale by ten or twelve competent observers, each of whom judges in entire ignorance of the judgments made by all the others. It is de- sirable, though not necessary, that the writings be on unruled paper. Section 7. The Derivation of the Scales 1 Certain partial descriptions of the means and methods by which the children's scale and adult women's scale were derived have been given in sections 2 and 6. A full account of the deri- vation of either is inadvisable both because it would necessarily be extremely long and because much of the work done was such as I now know, from the very experience of doing it and seeing its results, to have been unnecessary. I shall therefore give only such notes as are likely to be helpful to any one who is stimulated by this scale to construct similar scales for other educational products. To construct a scale by which to measure various qualities (that is, amounts of merit) in handwriting ranging from, say, x to x -f y, it is desirable to have samples of qualities, not only of every degree from x to x + y, but also of qualities worse than jf and of qualities better than x + y. The reason is that otherwise the exact values of samples at x or x plus a slight amount and of samples at x + y or x + y minus a slight amount cannot be di- rectly measured, but only inferred. 1 The reader uninterested in educational measurements is advised to skip this section, and to turn at once to the more immediately practical discussion of differences amongst school systems with respect to speed and quality of handwriting. §1 3 i 4 X Hi i-tiT j< ; U' £ cS y it HI' H * | 5 4 J * 1 t* ^-M - i hit 1=5= i f|H The Measurement of the Quality of Handwriting 25 For example, call x 1 and y 10. X + y then being n, x or 1 is nearly the worst and x + y or 11 is nearly the best of a series of samples, ranging continuously from x to x -\- y. If now any one is required to fix in mind 11 points including x (or 1) and x + y (or 11) differing each from the next by equal amounts, and to rate each of the samples as 1, 2, 3, 9, 10, or 11, according to which of these mentally fixed points it seems most like, he can err by rating a sample as 2 or 3 when it is really 1, but cannot err by rating it o or minus 1 when it is really I. Similarly he can err by rating it 9 or 10 when it is really 11, but cannot err by rating it 12 or 13. For a sample really close to point 11, rated in the way just described by 33 judges, the results were: Rated as 11 by 21 judges Rated as 12 by 7 judges Rated as 9 by 3 judges Rated as 8 by 1 judge Rated as 7 by 1 judge The apparent average rating would then be 10.4 and the apparent median rating 10.7. When, however, the samples are increased by some of the real quality x + y+i (or 12) and the ratings are to be made at twelve points including x-\-y+i (or 12), a certain proportion of the judges rank the sample in question 12 and the average and median are raised to nearly 11. Unless the set of samples to be rated includes some samples one, two, three, and even four grades better than the best quality (x + y) to be represented in the final scale and also some sam- ples one, two, and three grades worse than the worst quality (x) to be represented in the final scale, one cannot get the values of x + y and x themselves save by inference. Hence, to make a scale for the handwritings of, say, 10-year- old school children conveniently, it is necessary to have a collec- tion of samples varying in quality from much below the worst to much above the best of their writings. This involves the use of " unnatural " samples, which may seem very objectionable, but which as a matter of fact does little or no harm. In the case of a scale for the merit of English compositions by high-school pupils one should start from a collection of com- 26 Handwriting positions ranging by small gradations from compositions much worse than the worse point on the final scale is to be, to composi- tions much better than the best point on the final scale is to be. Here the extremely bad ones may be obtained by artificial con- struction, from the feeble-minded, or from very old and stupid grammar-school children. The extremely good ones may be obtained from the printed or manuscript compositions in youth by gifted authors. To get samples exactly situated at points differing progres- sively by equal steps requires that the original set range from one extreme to the other by very slight gradations. This means for practical purposes that one must have at the start a very large number of samples. After these have been graded by enough judges to rate each roughly, only those which are near the points to be represented by the scale need be graded further. As the value of each sample of this narrower selection is deter- mined more exactly by further judgments, only those very near the points to be represented on the final scale need be preserved for still further judgments ; and so on till the values of enough samples are determined to the degree of precision required for the scale itself. Points on the scale exactly determined, but not at progres- sively equal steps, can be got with far less labor. If, for example, after a single rating I had picked samples at intervals from the best to the worst and then had only these few samples rated by the twenty to seventy judges, the value of each could have been stated nearly as exactly as is the case in the samples of the scale. But they would form a series like 17.33, x 6.65, 16.28, 15.82, 15.40, 15.47, 15.23, 14.95, J 4-7> etc -> instead of the approximate 17, 16, 15. 15. I 5, 15, 15, I4» I3» 13, 13, etc., of the scale. They would have served the purpose of a scale as well so far as aiding an observer to make exact measurements which any other observer could verify, and to report them unambiguously, but the labor of allowing for the decimal values or of computing measures ex- pressed in awkwardly long numbers would burden each person using the scale. If the scale were designed for use only by scien- tific investigators of education, I should have economized in re- spect to the number of samples rated, had far more ratings of each sample, and presented a scale of very exactly determined The Measurement of the Quality of Handwriting 27 qualities but at irregular intervals. For the common use of pupils, teachers, and supervisory officers a less precise scale by approximately equal steps seemed far more valuable. Also the precise evaluation of each sample can be determined by many students each spending independently a little effort in getting the samples which I print rated ; whereas the selection of samples varying by equal steps can be managed best under one indi- vidual's supervision. It is possible that the determination of the amount of dif- ference between two samples by the percentage of judges notic- ing the difference is preferable to the determination by the amount of difference between their median values as given by judges attempting to apply to each a scale of mentally equal dif- ferences. I used both methods. Experience of their use provides many facts of importance to methods of quantitative work in both psychology and education, but the facts would be of interest to only the small proportion of readers to whom surfaces of fre- quency of errors in judgment are familiar and esteemed friends. In general, the experience in constructing this scale gives great encouragement to the hope that for many educational facts, units and scales may be invented that shall enable us to think quanti- tatively in somewhat the same way that we can about facts of physics, chemistry, or economics. It has been commonly sup- posed that the great complexity of such facts as examination papers in spelling, manifestations of interest in history, acts of moral significance, habits of industry, essays, poems, inventions, replies to questions demanding logical inferences, and other like results of education, prevents the samples composing any one such group from being measured by any one linear scale at all comparable to a foot rule or thermometer or galvanometer. It is true that some judges find it hard to judge handwriting for the complex of legibility, beauty, ease, " character," etc., into which " quality " or " goodness " or " merit " resolves itself. But none of them found it impossible to do so, and most of them rated the writing for the complex, — " merit or goodness in your opinion," — as readily as an appraiser would rank articles of sale by money price, or as a little child would arrange pieces of paper in the order of their size regardless of the fact that some were squares, some circles and some triangles. 28 Handwriting The entire history of the judgments of the merit of handwrit- ings supports the claim that if a number of facts are known to vary in the amount of any thing which can be thought of, they can be measured in respect to it. Otherwise, I may add, we would not know that they varied in it. Wherever we now properly use any comparative, we can by ingenuity learn to use defined points on a scale. PART II The Speed and Quality of Handwriting in Seven School Systems The conclusions to be reported in sections 8 to 13 are based upon about 3000 samples of handwriting made in a formal test conducted by Dr. C. W. Stone 1 in seven school systems, five public and two private. These samples were scored in about 700 cases by six judges using no scale, and in the remaining cases by two judges using an early form of the scale. The two judges differed by more than one step of the scale in only three samples out of ten. Thus the combined opinion of the two judges, though giving only a rough estimate for any single sample, is sufficiently precise for estimating the average quality of the writ- ing of a group of thirty or more pupils, such as a school class. Section 8. Differences between Systems It is known that school systems differ greatly one from another in arithmetic (Stone, '07) and much less in spelling (Rice, '97, Cornman, '02). They differ markedly in handwriting if we compare them for its quality, but six of the seven differ hardly any when they are compared for quality of writing done at the same speed. Thus in the case of the eighth grade the median quality (for the whole grade) of writing done " as well as you can " varies from 1 1.4 of the Thorndike scale in system A to 14.5 in system F (see Table V) ; the median quality for the whole grade of writing done " at your usual rate " varies from 10.3 in system A to 14.0 in system G (see Table V). In average speed of the eighth-grade writings, there is a range from system G with 37 letters a minute to system B with 67 1 To whom I am greatly indebted for permission to use this material. The ratings by the six judges were also obtained by him. 29 30 Handwriting letters per minute in the careful writing, and, in the writing at one's usual rate, a range from system G with 50 letters per minute to system C with 80. (See Table V.) Table V Speed Irrespective of Quality and Quality Irrespective of Speed in the Case of the Handwriting of Seven School Systems. Median Results for Eighth-Grade Pupils (Upper Figure) and Seventh- Grade Pupils (Lower Figure). School system Letters per minute in careful writing A 61 46 B 67 48 C 66 62 D 51 46 E 48 43 F 47 48 G 37 26 Letters per minute in " natural " writing 79 68 75 63 80 75 60 61 63 56 63 64 50 36 Quality (by T. scale) in careful writing 11. 4 11. 4 11. 8 11. 7 11. 7 11. 4 12.0 11. 7 12.3 13.0 14.5 14.0 14. 1 13. 1 Quality (by T. scale) in natural writing 10.3 10.3 11. 2 11. 1 11. 10.6 11. 7 11. 3 11. 6 12.7 13.7 13-0 14.0 13.0 If we compare the eighth-grade pupils of the different schools who wrote at roughly the same rates, they range as shown in Table VI. Table VI Quality of Handwriting at Roughly the Same Rate in Seven School Systems Median Results for Eighth-Grade Pupils System A B C D E F G At 20-29 words in 4 minutes 14.5 13.0 15 At 30-39 words 11. 5 11. 3 11. 6 12.3 12.3 14 At 40-49 words 11. 5 12.0 12.0 11. 8 12.3 14 At 50-59 words 11. 5 11. 6 11. 1 11. 1 11. 6 13 At 60-69 words 10.3 11. 8 11. 5 11. 3 11. 6 13 At 70-79 words 10. o 10.8 1 1. 3 4 14.8 5 14.2 4 15.3 o 11. 7 6 Median Results for Seventh-Grade Pupils System A B C D E F G At 10-19 words 13.3 14-5 13-5 At 20-29 words 12.3 13.3 13.0 13.6 14.2 13.0 At 30-39 words 11. o 11. 8 12.3 13.3 14.2 13.0 At 40-49 words 11. 11. 8 11. 3 11. 7 11. o 13.3 11. 8 At 50-59 words 10.3 11. 4 11. 1 11. o 11. 8 13.0 At 60-69 words 10. o 11. 3 10.5 10. o 11. 4 11. 8 At 70-79 words 9.8 9.8 9.9 That these likenesses and differences between systems are not due to chance but are true characteristics of the school systems, is proved by the fact that the measurements come from so many cases as to be subject to only very slight chance or accidental The Speed and Quality of Handwriting 31 errors, and also by the slight differences found between buildings or classes within one system. For instance, of three schools of system F, the seventh grades of the two most unlike differ in quality at the same rate by only three tenths of a step, the best one being about 3 per cent better than the worst. Of three schools of system G, the seventh grades of the two most unlike differ in quality at the same rate by only four tenths of a step, or 4 per cent. The average difference of one school from another within the same system is little if any over two tenths of a step or 2 per cent. The comparison of systems by the quality of the handwriting at the same rates is not, however, perfectly just. For in so doing we are comparing the more rapid writers of some systems (especially G) with the slower writers of other systems (especi- ally A, B, and C). Now in general the more rapid writers of a system would write a little better at the average rate for that system than would the slower writers of the same system. If, for instance, all the seventh-grade pupils of any systems were made to write at different speeds until for each one a record at the rate of 64 letters per second was secured, we should find that the pupils whose undirected rates were higher than 64 would at the 64 rate do better than those whose undirected rates were below 64. Also, within the 10-19 or 20-29 or 30-39 word group, there are prejudicial differences between the schools. In grade 8 of school G, for example, the 20-29 word group will contain a larger per- centage of pupils writing at rate 20-25 than it will in grade 8 of school F. In comparing a slow-writing school with a fast- writing school, by the quality of groups roughly equal in speed, we thus give an unfair advantage to the slower writing school. To make the comparison just we would have to find equiva- lents in quality for each degree of superiority in speed, so as to be able to combine the two into a score for general efficiency in handwriting for each individual. Such an investigation of the exact relative values of certain increases in speed and in quality should some time be made. I have not had time or means to make it as yet. As our data are, in the case of the 8th grade pupils, systems A, B, and C can be compared inter se for they are substantially alike in speed. So also can systems D, F, and 32 Handwriting F. A, B, and C can be compared with D, E, and F with only- slight chance of error by taking the " careful " work of A, B, and C and the " natural" work of D, E, and F. But the selection of cases at equal rates slightly favors D, E, and F at the expense of A, B, and C and favors G at the expense of all the other six systems. Of systems A, B, and C in the eighth-grade writing, A is the worst by about 5 per cent. Of systems D, E, and F, F is the best by about 25 per cent, D and E being alike. F is equal to G in quality and nearly 30 per cent superior in speed. Roughly estimating the equivalence of A's greater speed and F's superior quality, F seems to be about 30 per cent better than A. A, B, C, D, and E are of about equal merit. The data to support these comparisons were given in Tables V and VI. The records from the seventh-grade pupils give substantially the same result as those from the eighth-grade pupils just stated. A, B, C, D, and E differ little, A being about nine tenths as good as the others. F is about 25 per cent better than B, C, and D. E is a little better than B, C, and D. F shows writing as good as G's at a speed nearly six sevenths greater. These facts are derived from the data of Table VI, an allowance being made for the two constant sources of injustice in such data, and from the data of Table V, G seems, speed and quality both being taken into account, to be little or no better than B, C, D, and E. Section p. The Relation of Differences in Results to Differ- ences in Means and Methods of Teaching Handwriting Not much can be proved by relating these differences to dif- ferences in means and methods of teaching handwriting, since the number of school systems studied is so few. F, which is so markedly superior, uses vertical writing of a special system arranged by the supervisor of handwriting, uses writing books, devotes 75 minutes weekly to specific instruction and practice in writing in grades 5, 6, and 7 (of what is done up to grade 5, I have no report), and 30 minutes weekly in grade 8. The teachers in general follow the same system in writing on the blackboard. The other systems are about alike in general merit in hand- writing, A, B, and C gaining speed at a reasonable cost in The Speed and Quality of Handwriting 33 quality. A and B teach no fixed system, devote no time to pen- manship as such, and permit the teachers to write according to any or no system. C uses a medium slant or intermediate or business system, uses copy books, devotes 50 to 60 minutes weekly to penmanship as such, and has the teachers use the system taught to the pupils. D uses a modified Spencerian with copy books, devotes 50 to 75 minutes weekly in grades 5 and 6, and 75 to 100 in grades 7 and 8, to penmanship as such, and has the teachers follow the system in their own writing. E uses a forward slant, and devotes 100 minutes in grade 6, 60 to 90 in grade 7, and 60 in grade 8, to penmanship as such. System G uses an intermedial writing, devoting from 60 to 90 minutes weekly to special instruction and practice in grades 7 and 8. The teachers use the same system in their own writing on the blackboard. What these facts do prove is : First, that at least three systems (C, D, and E) get little or no better results at a time cost of about 75 minutes a week than two systems (A and B) do at zero time-cost; second, that one system (F) at no greater time- cost than C, D, and E gets results about 25 per cent better than they do; and third, that practice for quality may secure it only at the cost of speed. The teachers in A and B are better paid than those in the other cities, so that the success of these schools at no time-cost might not be generally attainable. Leaving F out of account, the differences of these school sys- tems in the method of teaching handwriting, in the time devoted to it, and in the ideals of the system in respect to it are of incon- siderable influence upon efficiency. One makes its pupils write very well at very slow rates, the others vary a little in quality with small inverse variations in speed. On the whole, in spite of the achievement of system F, efficiency in handwriting seems, like spelling, and unlike arithmetic, to be under present condi- tions not very much influenced by the management of the schools. Section 10. Differences between Individuals within the Same School System We have seen that the school systems, with the exception of F, differ little among themselves in the efficiency of the hand- writing which they secure. Individual pupils on the contrary 34 Handwriting do differ greatly. Excluding system F, we still find amongst eighth-grade pupils a range from a pupil writing only 55 letters per minute, at quality 7.5 up to a pupil writing 79 letters per minute at quality 15.2. Of the 15 eighth-grade pupils writing at the same rate (53 words in 4 minutes) the scores for quality (excluding system F) run from 9.1 to 14.6. The variation among pupils of the same grade in the rate of writing of the same quality is also large. In the seventh grade of system F, for instance, of the writings of the pupil's usual rate there were 74 samples of from quality 12.7 to 13.3. The number of words written in four minutes ranged from 19 to 87. The 87 may possibly be due to overtime writing. The next highest case was yy, and the next 70. After the two cases at 19 Table VII Relative Frequencies of Different Speeds of Writing at Natural Rate, the Same Quality of Writing Being Secured Number Frequencies of words F, 7th grade G, 7th grade IS 2 17 19 2 21 2 3 I 5 2 2 7 12 9 4 2 31 2 2 3 4 5 3 7 5 9 3 1 41 3 3 5 5 5 7 2 9 4 1 5i o 3 4 5 5 7 6