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THE MEASUREMENT OF 
 ATTENTION 
 
 BY 
 
 KARL M. DALLENBAC 
 
 A THESIS 
 
 Presented to the Faculty of the Graduate School of Cornell 
 
 University in partial fulfilment of the requirements 
 
 for the Degree of Doctor of Philosophy 
 
 Reprinted from the^ American Journal of Psychology 
 OctobeE^: igi3. Vol. XXIV, pp. 465-S07 
 
THE MEASUREMENT OF 
 ATTENTION 
 
 BY 
 
 KARL M. DALLENBACH 
 
 A THESIS 
 
 Presented to the Faculty of the Graduate School of Cornell 
 
 University in partial fulfilment of the requirements 
 
 for the Degree of Doctor of Philosophy 
 
 Reprinted from the American Journal of Psychology 
 October, 1913, Vol. XXIV, pp. 465-507 
 
THE MEASUREMENT OF ATTENTION^ 
 
 By Karl M. Dallenbach 
 
 CONTENTS 
 
 I. Introduction : Problem, Observers 465 
 
 II. Methods and Results. 
 
 A. Preliminary Training in Introspection 467 
 
 B. Practice under the Conditions of the Main Experiments 468 
 
 C. Single Task Method: Description of Method 472 
 
 Principal Results 474 
 
 Special Points: l. Reaction-time 483 
 
 2. Mean Variation 485 
 
 3. Reaction-tiine and Objective Change 485 
 
 4. Reaction-time and Accuracy of 
 
 Report 486 
 
 5. Distractort 487 
 
 D. Double Task Method: Description of Method 490 
 
 Principal Results 494 
 
 Special Points: 1. Reaction-time and Mean Variation 501 
 
 2. Reaction-time and Objective 
 
 Change 502 
 
 3. Reaction-time and Accuracy of 
 
 Report S03 
 
 4. Secondary Tasks 503 
 
 5. Attehtion and ' Precision of Work 505 
 
 6. Levels of Attentive Consciousness 506 
 
 III. Summary of Conclusions 507 
 
 I. Introduction 
 
 In his Postulates of a Structural Psychology (1898) Titch- 
 ener expressed the opinion that clearness is to be considered 
 
 'From the Psychological Laboratory of Cornell University. 
 
466 DALLENBACH 
 
 as an intensive attribute of sensation, and that this attributive 
 clearness is the elementary phenomenon of attention." The 
 same view is worked out in detail, and with reference to 
 current theories of attention, in the Feeling and Attention of 
 1908.' In the following year, Geissler published " an attempt 
 at a new measurement of attention in terms of clearness 
 values."* "A very close parallelism was found to exist be- 
 tween introspectively distinguishable variations of attention 
 and corresponding differences in the precision of work per- 
 formed at these levels, under the condition that the estimation 
 of degrees of attention was made in terms of clearness and 
 that the work itself was not influenced by anything else but 
 change in attention."^ The attempt thus yielded a positive 
 result. Geissler, however, worked only with material which 
 was visually presented; and it is clear that the investigation 
 must be carried further into the domains of hearing, touch, 
 and imagery. The present study is an attempt to do for 
 audition what Geissler has done for vision. Since Geissler 
 prefaced his experiments by a fairly full " critical study of 
 previous views and methods,"" we may ourselves dispense 
 with any longer introduction. And since this paper deals 
 only with audition, and experiments upon touch and imagery 
 are still to follow, we have thought it best to offer our results 
 by themselves, without criticism of studies which have ap- 
 peared since Geissler wrote, and without reply to the occa- 
 sional criticisms of Geissler's method which we have met with. 
 The results which we have obtained confirm those of the 
 previous investigation, so that we find no reason to change 
 our fundamental view of the nature of the elementary 
 phenomenon of attention; and the discussion of minor points 
 of controversy may be postponed until the experimental 
 material covers a wider ground.'' 
 
 'Philosophical Review, vii., 1898, 461 f. See also M. W. Calkins, 
 Introduction to Psychology, 1901, 137 ff.; I. M. Bentley, Mind, N. S. 
 xiii., 1904, 242 flf. 
 
 'Lectures on the Elementary Psychology of Feeling and Attention, 
 igo8, Lects. i., v., vii. 
 
 'This Journal, xx., 1909, 502 fl. 
 
 'Ibid., 529. It may be noted that Geissler anticipates an obvious 
 criticism by the statement: "under the same conditions, the intro- 
 spective [we should prefer to say 'subjective'] estimation of the 
 quality of the work was not as reliable as the evaluation of the 
 degrees of attention." 
 
 'Ibid., 473 ff. 
 
 ' The writer takes this opportunity to thank Professor Geissler for 
 important suggestions with regard to the method of the experiments 
 reported below. 
 
THE MEASUREMENT OF ATTENTION 467 
 
 Observers. — Three observers served in all of the experi- 
 ments: Dr. W. S. Foster (F), instructor in Psychology, Miss 
 Mabel E. Goudge (G), graduate student in Psychology, and 
 Mr. J. S. Johnston (J), fellow in Psychology. G and J 
 worked without knowledge of our problem. F was familiar 
 with Geissler's investigation, and knew in general the aim of 
 the present study. 
 
 II. Methods and Results 
 
 A. Preliminary Training in Introspection 
 
 Our first problem was to familiarise our observers with 
 differences of attributive clearness. 
 
 To this end a large number of preliminary experiments was given 
 them. The experiments were of two kinds : with attention directed 
 to the stimulus, and with attention directed away from the stimulus 
 and upon some mental task. In the experiments of the first kind, 
 two metronomes were set going at the rates of 100 and 120 strokes 
 per minute respectively, and the observer, who sat with his back 
 toward them, was instructed to direct his attention to the sounds, 
 and to count the number of sounds between coincident strokes. The 
 observation began with a signal, and ended after a minute and a 
 half, with the word Introspect. The observer was then required to 
 describe, in as great detail as possible, the pattern of consciousness 
 during the period of observation. In the experiments of the second 
 kind, the same stimuli were used, but the observer was required to 
 perform some mental task, such as continuously adding, subtracting, 
 multiplying, dividing, reciting, singing, or repeating the alphabet 
 backwards. At the end of a minute, or a minute and a half, the 
 observer was asked, as before, to give as full and complete an 
 introspection as possible. These two kinds of experiments were 
 alternated throughout the preliminary training; four observations 
 were taken in an hour. The observer F gave in all 62 introspec- 
 tions; G, 60; and J, 128. After relatively few trials, the observers 
 were able not only to compare the clearnesses of the stimuli in the 
 two types of experiments, but also to say that the sounds were not 
 always equally clear or obscure during an observation. Thus, F 
 reports, after an experiment in which the task was to add 7 con- 
 tinuously : " The sounds of the metronomes, as a series of discon- 
 tinuous clicks, were clear in consciousness only four or five times 
 during the experiment, and they were especially bothersome at first. 
 They were accompanied by strain sensations and unpleasantness. 
 The rest of the experiment my attention was on the adding, which 
 was composed of auditory images of the numbers, visual images of 
 the numbers, sometimes on a dark grey scale which was directly 
 ahead and about three feet in front of me. This was accompanied 
 by kinaesthesis of eyes and strains in chest and arms. When these 
 processes were clear in consciousness the sounds of the metronomes 
 were very vague or obscure." Similar reports were made, during 
 the first three weeks of training, by G and J. 
 
 When this degree of proficiency had been reached, the observers 
 were asked to estimate, first the larger, and later the finer differences 
 in the clearness of the sounds. They constructed, independently, a 
 
468 DALLENBACH 
 
 rough scale of five or six steps, from very clear to obscure; but they 
 were presently able to assign a percentage value to the clearnesses. 
 At first this gradation was difficult; and the observers, particularly 
 F, felt uncertain of its correctness. As the preliminary training 
 advanced, however, they grew more confident; and toward the end 
 they were able not only to give an analysis of consciousness during 
 the period of an observation, but also to estimate, without difficulty, 
 the clearness or obscurity of the mental processes experienced. At 
 the end of three months, they had worked out (with some sugges- 
 tion from the experimenter, which, however, bore only upon uni- 
 formity of grades) the following scale: 
 
 1. 100-90% maximally clear. 
 
 2. 90-80% very clear. 
 
 3. 80-70% clear. 
 
 4. 70-60% fairly clear. 
 
 5. 60-50% fair. 
 
 6. So-40% fairly vague. 
 
 7. 40-30% vague. 
 
 8. 30-20% very vague. 
 
 9. 20-00% obscure. 
 
 We give a single illustration. F, after an experiment in which the 
 task was to repeat continuously the alphabet backwards, reports: 
 " Repeated alphabet backwards two and a half times. Practice has 
 made this task much easier than at first, so that it is easier for the 
 distraction (the metronomes) to catch attention. Four times for 
 several seconds the sounds of the metronomes were the clearest 
 processes in consciousness, perhaps 75% clear. The repeating process 
 (i.e., the complex of repeating the alphabet backwards, which was 
 composed of visual images of dark grey lines stretching from right 
 to left, eyes following along on lines sometimes with vague visual 
 images of several letters in a group; accompanied by these visual 
 images, or where visual images were lacking accompanied by the 
 kinaesthetic images of eye movements, sibilant auditory images of 
 letters) was only io-2Q% clear. Aside from these four times the 
 repeating processes were 85% clear, and the sound of the metronome 
 was 10-15% clear.'" 
 
 At this point we turned to the main problem of measuring 
 attention in terms of clearness ; in other words, of discovering 
 how closely the attributive clearness of the processes attended 
 to and of those attended from is correlated with quantitative 
 and qualitative changes of an auditory stimulus of an objec- 
 tively measurable character. 
 
 B. Preliminary Practice in Observation Under the Condi- 
 tions of the Main Experiments 
 
 I. Apparatus. — Our stimulus, the tone of a Stem variator, 
 varied from 300 to 600 vs. in the i sec. The Whipple air- 
 tanks were used to supply the blast. The intensity of the 
 tone was controlled by an air-valve, and the pitch, by the 
 
 'With this account cf. Geissler, op. cit., 510 f. 
 
THE MEASUREMENT OF ATTENTION 469 
 
 crank of the variator. Both valve and crank were fitted 
 with large scales and long moving arms, which permitted us 
 to make gross movements in their adjustment. 
 
 The Whipple tanks" were devised for the purpose of giving a con- 
 stant air-pressure; but further to insure this result we registered the 
 pressure graphically. Between the air-valve and the variator a T- 
 tube was inserted, the one arm of which led to the variator and the 
 other to a large eosin manometer. A delicate Marey tambour was 
 attached to the manometer, and its writing point rested upon the sur- 
 face of a smoked drum. When the air-blast was turned on, the 
 pressure was recorded upon the drum. The tanks as set up by 
 Whipple showed a very slight variation, due perhaps to the small 
 size of the intake valve. We therefore disconnected the tanks, and 
 tried them individually. We found that the pressure was now sen- 
 sibly constant; indeed, between the limits of height 25 and 50 cm., 
 it remained, by our manometer, absolutely the same. During a single 
 experiment the tank was therefore always kept within this central 
 region. Curtains, hung directly over the variator and at other places 
 about the room, eliminated echoes; and thus the constancy of the 
 tone was further insured. 
 
 The observer sat about 2.5 m. from the source of sound, his head 
 secured in position by a biting-board, and his right hand resting upon 
 a silent electrical key. In an adjacent room was placed a kymograph 
 with three writing points. One of these points was connected to 
 the observer's key, another to an electrical push-button in the ex- 
 perimenter's hand. The third point, the lever of a Jacquet chrono- 
 scope, wrote fifths of seconds between the other two. It was added 
 to give an approximate record of the observer's reaction-times. 
 
 2. Instructions. — The following instructions were read to 
 the observer: 
 
 "You are to sit at the table with your back to the stimulus, your 
 head held firmly in position by the mouth-piece and the biting board, 
 your right arm and hand resting upon the table, and your fore- 
 finger, or forefinger and thumb, lightly pressing the electrical key. 
 The experiment will begin upon the signal Ready, Now, and will 
 end when the experimenter says Introspect. 
 
 "The stimulus, which will be the tone of a Stern variator, may 
 vary in intensity or in pitch. The rate of change from one intensity 
 to another, or from one pitch to another, will also vary, the change 
 being made either gradually or very quickly. There are then two 
 points upon which you will report: i. kind of change, whether of 
 pitch or intensity; and 2. rate of change, whether rapid or slow. 
 As soon as a change is perceived, you will press the key. 
 
 " One pressure denotes a change of intensity ; 
 
 " Two a change of pitch ; 
 
 " The rate of change must be given in the introspection. 
 
 " You are to give your attention to the sound of the variator. 
 At the end of 30, 45 or 60 seconds, as the case may be, you will intro- 
 spect, and give a detailed description of your consciousness during 
 the experiment." 
 
 ' G. M. Whipple, this Joitrnal, xiv, 1903, 107 ff. 
 
470 DALLENBACH 
 
 It will be observed that no mention is here made of the word 
 clearness." This omission was made advisedly; for we wished, so 
 far as possible, to keep the observers in ignorance as to the subject 
 of the experiment. It is true that P knew, in a general way, the 
 aim of this study; but neither he nor the other observers knew the 
 particular phase of the problem that we were studying. We ex- 
 pected, however, in view of the long preliminary training, to receive, 
 without requesting them, detailed introspections upon the relative 
 clearness of the processes in consciousness. In this expectation we 
 were not disappointed; for both G and J continued to estimate the 
 rellative clearness of their mental processes in percentage terms, 
 while F, throughout these experiments, used such descriptive terms 
 as very clear, fairly clear, vague, obscure, etc. 
 
 In the experiments of 30 seconds, only one or two changes in 
 pitch or intensity were made, while in the experiments of 45 and 
 of 60 seconds, three and four changes in pitch or intensity were 
 made respectively. A ' change ' means a variation either of pitch 
 or of intensity; not of both together. The rate at which the change 
 was effected was either rapid or slow. The rapid changes were 
 made as quickly as the adjustments allowed, requiring about one- 
 fifth of a second; the slow changes occupied three seconds. 
 
 3. Series. — In the series given to the observers all the pos- 
 sible types of change were represented. In the experiments, 
 e.g., in which only one change was made during an observa- 
 tion, the change was in one case of pitch, in another of in- 
 tensity; in one case it was made rapidly, in another slowly. 
 The standard pitch and intensity were also varied, as was 
 the place of the change within the 30 second interval (near 
 beginning, middle, near end). Again, in the experiments in 
 which four changes were made, the changes of pitch and of 
 intensity occurred an equal number of times in the first, sec- 
 ond, third, and fourth places. The rates of change, rapid 
 and slow, likewise occurred an equal number of times in 
 the first, second, third, and fourth places. The series itself 
 varied from four changes of pitch to four changes of 
 intensity. 
 
 The series in detail were as follows: 
 
 Series I. One change. Duration of experiment 30 seconds. 
 Variation. Change of Pitch. Change of Intensity. Rate. 
 
 1. o (350) I (1-h) r. 
 
 2. o (400) I (h-1) s. 
 3- o (450) I (h-1) r. 
 
 4. o (300) I (1-h) s. 
 
 5. I (350-400) o (low) r. 
 
 6. I (300-400) o (low) s. 
 
 7. I (500-400) o (high) s. 
 
THE MEASUREMENT OF ATTENTION 
 
 471 
 
 Series II. Two changes. Duration of experiment 30 seconds. 
 Variation. Changes of Pitch. Changes of Intensity. Rates. 
 
 (3So) 
 
 (450) 
 
 (Soo) 
 
 (350-450) 
 
 (SOO-400) 
 
 (300-400) 
 
 (300-400-500) 
 
 (400-350-300) 
 
 (1-h-l) 
 
 (h-l-h) 
 
 (1-h-l) 
 
 (h-1) 
 
 (h-1) 
 
 (1-h) 
 
 (high) 
 
 (low) 
 
 s.r. 
 s.r. 
 r.s. 
 s.r. 
 r.s. 
 r.r. 
 r.s. 
 s.s. 
 
 Series III. Three changes. Duration of experiment 45 seconds. 
 
 Variation. Changes of Pitch. Changes of Intensity. 
 
 2. 
 
 3- 
 4- 
 5- 
 6. 
 
 7- 
 8. 
 
 9- 
 10. 
 
 (500) 
 
 (400) 
 
 (300-400) 
 
 (Soo-400) 
 
 (450-350) 
 
 (400-350-450) 
 
 (400-500-450) 
 
 (400-300-450) 
 
 ( 300-400-300-400) 
 
 (400-300-400-300) 
 
 (1-h-l-h) 
 
 (h-l-h-1) 
 
 (1-h-l) 
 
 (h-l-h) 
 
 (h-l-h) 
 
 (1-h) 
 
 (h-1) 
 
 (1-h) 
 
 (high) 
 
 (low) 
 
 Rates, 
 r.r.s. 
 s.r.s. 
 r.r.s. 
 s.s.r. 
 s.s.r. 
 r.s.r. 
 r.r.s. 
 s.r.s. 
 r.s.s. 
 s.r.r. 
 
 Series IV. Four changes. Duration of experiment 60 seconds. 
 
 Variation. Changes of Pitch. 
 
 (350) 
 
 (400) 
 
 1 (350-450) 
 I (450-350) 
 I (soo-400) 
 
 1 (400-450) 
 
 2 (500-400-350) 
 2 (350-450-350) 
 2 (350-450-500) 
 2 (350-400-450) 
 2 (500-400-300) 
 
 2 (400-500-400) 
 
 3 (400-300-400-500) 
 3 (300-400-500-400) 
 3 (400-300-400-300) 
 
 3 (300-400-450-500) 
 
 4 (450-500-450-400-300) 
 4 (400-350-450-500-550) 
 
 I 
 2. 
 3 
 4. 
 5 
 .6, 
 
 7- 
 8. 
 9. 
 10. 
 II 
 12, 
 13 
 14 
 15 
 16. 
 
 17. 
 18, 
 
 Changes of Intensity. 
 
 4 (1-h-l-h-l) 
 
 4 (h-1-h-l-h) 
 
 3 (1-h-l-h) 
 
 3 (h-l-h-1) 
 
 3 (1-h-l-h) 
 
 3 (h-l-h-1) 
 
 2 (1-h-l) 
 
 2 (1-h-l) 
 
 2 (h-l-h) 
 
 2 (h-l-h) 
 
 2 (1-h-l) 
 
 2 (h-l-h) 
 
 I (1-h) 
 
 1 (1-h) 
 
 I (h-1) 
 
 I (h-1) 
 
 o (low) 
 
 o (high) 
 
 Rates, 
 s.r.s.r. 
 r.s.s.r. 
 r.s.r.r. 
 s.s.r.s. 
 s.r.r.s. 
 r.s.s.r. 
 s.s.r.r. 
 r.s.s.r. 
 s.r.r.s. 
 s.r.r.r. 
 s.s.r.r. 
 r.s.r.r. 
 s.r.r.s. 
 r.s.s.r. 
 r.s.s.r. 
 s.s.r.s. 
 r.s.r.r. 
 s.r.s.s. 
 
 The figures in parentheses under Changes of Pitch show the vibra- 
 tion-rates of the tones employed. The letters in parentheses under 
 Changes of Intensity show the direction of change, from lower to 
 higher, or conversely. The letters r and j under Rates of_ Change 
 show the rates at which the changes were effected, r signifying 
 rapid and s, slow. 
 
472 DALLENBACH 
 
 There were thus 125 changes, 61 of pitch, and 64 of intensity. Of 
 these 125 changes, 62 were made slowly and 63 rapidly." 
 
 In the preliminary practice, variations of the above series were 
 chosen at random. For a given experiment, E set the variator and 
 the air-valve at the points required. On the signal Ready, Now, E 
 released a spring-clip that closed the rubber tube between the air- 
 valve and the variator, and at the same time pressed the push-button 
 held in his hand. At every subsequent change, and at the end of 
 the experiment, E again pressed the push-button; so that, by com- 
 parison with the time-line and with O's line, the length of the ex- 
 periment, the times of change, and the time of O's reaction were 
 graphically recorded. 
 
 F gave in all 52 introspections; G, 56; and J, 112. This 
 preliminary practice covered the three months February to 
 April, 1912. At its completion we turned to the main experi- 
 ment, using the Single Task Method. 
 
 C. Single Task Method 
 
 I. Apparatus. — The same apparatus was used as for the 
 preliminary practice; but the room, which before was, light, 
 was now darkened. The observer was, moreover, enclosed 
 in a muslin booth, which was illuminated from above by an 
 electric light, controlled from the experimenter's desk. The 
 experiments were conducted in darkness, unless flicker was 
 used as a distractor; and the light was turned on at the end 
 of the experiment. was thus able to write his introspec- 
 tions, while E marked the record and set the apparatus for 
 the succeeding experiment. 
 
 Distractors. — In the preliminary practice the experiments 
 were performed without distraction. In the present series, 
 eight distractors were employed: 
 
 1. Flicker (9 rhythms and 4 intensities). 
 
 2. Electrical current (3 intensities). 
 
 3. Flicker and current (with above variations). 
 
 4. Clicks of single metronome (3 rates; 60, 100, and iSo). 
 
 5. Clicks of metronome and current (with above variations). 
 
 6. Clicks, flicker, and current (with above variations). 
 
 7. Two metronomes beating at diflferent rates (60, 100, and 150). 
 
 8. Phonograph. 
 
 (i) Flicker. — Behind and somewhat above the observer was placed 
 a second electric light, enclosed within a reflector which directed the 
 light upon a white screen in front of the observer. This light was 
 also controlled from the experimenter's desk; it had four variations 
 in intensity, from very weak to maximally strong. A large card- 
 board disc, from which were cut four sectors of 30°, rotated before 
 
 "The changes are indicated^ under the separate headings: thus. 
 Series I yields 3 changes of pitch and 4 of intensity; and so forth. 
 
THE MEASUREMENT OF ATTENTION 473 
 
 the reflector. Cardboard shields adjustable over the sectors made 
 it possible to obtain nine different rhythms in the flicker. Since 
 there were four variations of intensity, and nine in rhythm of the 
 light, there were altogether 36 variations of the flicker. 
 
 The cardboard disc that served as shutter was driven by a motor, 
 which because of its noise was placed in an adjoining room. The 
 motive power was transmitted by a reduction-system of string belts 
 and gutta-percha pulleys to a large wheel, upon the shaft of which 
 the shutter turned. As the light was controlled from the experi- 
 menter's desk, this part of the flicker apparatus, since it was noise- 
 less, was started at the beginning of the hour and ran throughout the 
 entire period. 
 
 (2) Current. — The faradizing current was also controlled from 
 the experimenter's desk. The induction-coil was placed in an adja- 
 cent room. The strength of the primary current was governed by 
 a three-way switch connected with a rheostat. This gave three 
 intensities of the induced current. The current ran direct from 
 the coil to the electrodes, which were moistened and applied to the 
 observer's left arm, the one a little below the elbow, and the other 
 at the wrist. During the first few experiments, the electrodes were 
 bound one on each wrist; this plan was, however, abandoned because 
 the strongest current caused a violent contraction of the muscles of 
 the arm and hand, which seriously interfered with the observer's 
 reaction. The contraction was none the less severe after the change 
 to the left arm; but the right hand could now operate the key 
 without hindrance. 
 
 (3) Flicker and current. — The third distractor was formed by the 
 combination of the first two, and varied within their limits. There 
 were therefore 108 possible variations of this distractor. 
 
 (4) Metronome. — Two metronomes were placed upon the experi- 
 menter's desk, and were there controlled. In the case of the fourth 
 distractor only one metronome was used. The rate of the beat 
 varied from 60 to 100 and iSo strokes in the minute. 
 
 (5) Metronome and current. — The fifth distractor was formed by 
 the combination of the clicks of a single metronome and the elec- 
 trical current. It was variable within the limits of these two dis- 
 tractors. 
 
 (6) The sixth distractor, formed by the combination of flicker, 
 clicks of a single metronome, and electrical current, varied within 
 the limits of these distractors. In all, 324 variations were possible. 
 
 (7) Two metronomes. — Both metronomes were set going at dif- 
 ferent rates, 60, 100 or 150. There were therefore only three varia- 
 tions within this form of distraction. 
 
 (8) Phonograph. — The phonograph was likwise controlled from 
 the experimenter's desk. Various records were used, including popu- 
 lar and classical pieces, songs, instrumental and band music. 
 
 Previous experimenters have found that distractors very 
 soon lose their power of compelling the attention; the ob- 
 servers become habituated. It was for this reason that we 
 selected eight distractors which were capable of variation 
 and extension. During the first few experiments those forms 
 
474 DALLENBACH 
 
 of distraction were employed which we supposed to be the 
 least disturbing. Habituation was in some measure counter- 
 acted by increase of intensity, or by change in rhythm of the 
 distractor. Thus in the case of the flicker, and also of the 
 electric current, the weaker intensities were used first, the 
 stronger later. 
 
 2. Instruction. — The general instruction remained un- 
 changed. The specific directions were as follows : 
 
 "The stimulus, which will be the tone of a Stern variator, may 
 vary in intensity or in pitch. The rate of change from one intensity 
 to another, and from one pitch to another, will also vary, the change 
 being made either gradually or very quickly. There are then two 
 points upon which you will report: i. kind of change, whether 
 pitch or intensity; and 2. rate of change, whether rapid or slow. 
 As soon as a change is perceived you will press the key. 
 
 " One pressure denotes a change of intensity ; 
 
 " Two a change of pitch ; 
 
 " The rate of change must be given in the introspection. 
 
 " You are to give your attention to the sound of the variator, and 
 to neglect as far as possible any distraction, purposive or acci- 
 dental. At the end of 30, 45, or 60 seconds, as the case may be, you 
 will introspect. In the general description of consciousness, in 
 previous experiments, you have among other things assigned clear- 
 ness values to the various processes reported. You are now to esti- 
 mate clearness values only: that is, you are to report, using a scale 
 of 100, the relative clearness of the processes which you observe 
 in consciousness. For example : ' First change, rapid, clearness of 
 so-and-so x%, of so-and-so 31% ; second change, slow, clearness of 
 so-and-so m%, of so-and-so n%.' " 
 
 3. Number of experiments. — The experiments by this 
 method were conducted in May and June 1912, and in Febru- 
 ary and March 1913. Each observer gave in all 86 intro- 
 spections. 
 
 4. Series. — The series employed were those outlined above. 
 The order of presentation was determined by lot. Each series 
 was employed twice. Five or si'x observations, one of which 
 was taken as a control without distraction, were made during 
 the hour. The experiment without distraction occurred an 
 equal number of times in the first, second, .... and 
 sixth places. The distractions were also so distributed that 
 each kind occurred but once in an hour, and as often in the 
 first as in the other positions. During a single experiment 
 the same distractor persisted without change. 
 
 5. Results. — The Single Task Method was employed, as 
 we have said under 3 above, at two periods. During the in- 
 terval the Double Task Method was employed. The results 
 of G and F for the two periods of the Single Task Method 
 
THE MEASUREMENT OF ATTENTION 
 
 475 
 
 agree throughout, and are therefore grouped together. J, 
 however, gave different results in the two periods; and they 
 are therefore considered separately. Ji denotes the results 
 of the first, and J^ those of the second period. The observer 
 had for some time been depressed by a visual disability which 
 oculists had failed to overcome, and in the first period was 
 anxiously awaiting the outcome of a new treatment; this is 
 probably the ground of the incapacity for high degrees of 
 attention shown under J^ in Tables I and II. In the second 
 period, the reason for depression had been removed. It is 
 possible, also, that the practice in concentration gained during 
 the rather exacting observations of the Double Task Method 
 helped the observer to give the improved results under J^. We 
 cannot offer more than this general explanation of the dis- 
 crepancy. 
 
 In some of the experiments, from the nature of the series, 
 one change was made, in others two, three, and four. In 
 working over the results, each change was considered sep- 
 arately, was judged as a single case and so recorded. Hence 
 in Table I only the number of such cases is given. Under 
 Right are grouped all the right judgments of kind and rate 
 of change, and under Wrong all the wrong judgments. The 
 scale of attention in terms of clearness is arranged above. 
 
 
 
 
 
 
 
 TABLE I 
 
 
 
 
 —^ 
 
 
 Number 
 
 OF Cases 
 
 , Kind and 
 
 Rate 
 
 OP Change 
 
 ^ 
 
 r 
 
 
 
 
 Right 
 
 
 
 
 
 Wrong JI [] 
 
 Q. 
 
 u 
 
 CI 
 
 
 
 
 
 
 
 
 
 oi 
 
 € 
 
 
 to-9 
 
 9-8 
 
 8-7 
 
 7-6 
 
 6-S 
 
 S-4 
 
 10 
 
 -9 
 
 9-8 8-7 7-6 6-s s-4 
 
 
 
 F 
 
 .S3 
 
 14 
 
 2 
 
 
 
 
 
 
 
 
 Ps 
 
 G 
 
 2 
 
 22 
 
 9 
 
 S 
 
 2 
 
 
 
 
 2 
 
 
 
 .'. 
 
 2 
 
 S 
 
 5 
 
 3 
 
 
 I 
 
 
 
 
 
 
 J^ 
 
 9 
 
 9 
 
 I 
 
 I 
 
 
 
 
 I 
 
 2 
 
 I 
 
 Pr 
 
 F 
 G 
 
 32 
 
 3 
 
 5 
 18 
 
 II 
 
 8 
 
 I 
 
 
 
 
 2 I 
 
 Pi 
 
 
 1. 
 
 
 2 
 
 4 
 
 I 
 
 2 
 
 
 
 
 
 a 
 
 
 J. 
 
 18 
 
 S 
 
 4 
 
 2 
 
 I 
 
 
 
 
 
 ■< 
 
 
 F 
 
 13 
 
 II 
 
 
 
 
 
 
 
 
 a 
 
 Is 
 
 G 
 
 2 
 
 IQ 
 
 6 
 
 2 
 
 
 I 
 
 
 
 
 •z 
 
 
 I, 
 
 
 3 
 
 6 
 
 I 
 
 2 
 
 
 
 
 
 3 
 
 
 J. 
 
 4 
 
 s 
 
 3 
 
 2 
 
 I 
 
 
 
 
 
 
 
 F 
 
 27 
 
 10 
 
 
 
 
 
 
 
 
 
 Ir 
 
 G 
 
 2 
 
 13 
 
 IS 
 
 3 
 
 3 
 
 
 
 
 
 
 
 1. 
 
 
 2 
 
 7 
 
 
 2 
 
 I 
 
 
 
 II I 
 
 
 
 J. 
 
 6 
 
 3_ 
 
 I 
 
 
 
 
 
 
 
 I I 
 
476 
 
 DALLENBACH 
 TABLE I — Continued 
 
 Report 
 
 Change 
 
 p 
 
 Right 
 10-9 9-8 8-7 7-6 6-s s-4 
 
 Wrong 
 10-9 9-8 8-7 7-6 6-s s-4 
 
 P 
 Ps G 
 
 Jl 
 J2I 
 
 1 2 
 
 I I 4 I 
 I 22 
 
 2 21 
 
 I 3 4 I 
 2 
 I I 
 
 F 
 Pr G 
 
 ,■1 
 
 4 9 I 
 
 214 
 
 I I 6 2 I 
 I 3 2 I 
 
 I 
 
 I 2 3 I 
 
 I 
 
 3 p 
 
 Is G 
 
 . 2 
 
 241 
 
 2631 
 
 I 212 
 
 2 I 
 
 4 
 
 I 
 
 I 
 
 P 
 Ir G 
 
 J: 
 
 3 6 3 
 
 3732 
 
 I 7 3 
 3 4 3 II 
 
 I 3 I 
 
 I 
 
 I 
 
 P 
 Ps G 
 
 J: 
 
 I 3 4 I 
 2 
 I I 
 
 1 2 
 
 I I 4 I 
 I 22 
 
 2 21 
 
 p 
 
 Pr G 
 
 I 
 
 I 2 3 I 
 
 I 
 
 491 
 2 I 4 
 
 I I 6 2 I 
 I 3 2 I 
 
 Is G 
 
 4 
 
 I 
 I 
 
 2 4 I 
 
 2631 
 
 I 212 
 
 2 I 
 
 P 
 Ir G 
 
 I 3 I 
 
 I 
 
 I 
 
 363 
 
 3732 
 
 I 7 3 
 343 II 
 
THE MEASUREMENT OF ATTENTION 
 TABLE I — Continued 
 
 477 
 
 ^ 
 
 
 
 
 Wrong 
 
 
 
 o, 
 
 O 
 
 
 
 
 
 
 Pi 
 
 g 
 
 
 10-9 9-8 
 
 8-7 
 
 7-6 
 
 6-5 
 
 S-4 
 
 
 
 P 
 
 I 2 
 
 
 
 
 
 
 Ps 
 
 G 
 
 
 
 I 
 
 
 
 § 
 
 
 
 
 
 
 
 I 
 
 N 
 
 
 F 
 
 2 
 
 
 
 
 
 < 
 
 Pr 
 
 G 
 
 
 
 
 
 
 Pi 
 
 
 J: 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 ^ 
 
 
 K 
 
 I 2 
 
 I 
 
 
 
 
 P 
 
 Is 
 
 G 
 
 
 
 2 
 
 I 
 
 I 
 
 o 
 
 
 i: 
 
 
 I 
 
 
 I 
 
 
 
 
 
 
 
 
 
 p 
 
 
 F 
 
 I 8 
 
 I 
 
 
 
 
 t/3 
 
 Ir 
 
 G 
 
 .;, 
 
 J2 
 
 
 3 
 
 
 
 I 
 
 
 
 F 
 
 
 
 
 
 
 
 Ps 
 
 G 
 
 
 
 I 
 
 
 
 
 Pr 
 
 p 
 
 G 
 
 
 
 
 
 2 
 
 s 
 
 
 J. 
 
 
 
 
 
 
 o 
 
 
 . 2 
 
 
 
 
 
 
 P!i 
 
 
 
 
 
 
 
 
 
 P 
 
 I 4 
 
 ■>, 
 
 2 
 
 I 
 
 I 
 
 Is 
 
 G 
 
 
 
 8 
 
 6 
 
 4* 
 
 o 
 
 
 T. 
 
 
 
 I 
 
 2 
 
 I 
 
 iz; 
 
 
 h 
 
 I 
 
 I 
 
 II 
 
 
 I 
 
 
 
 P 
 
 I 
 
 I 
 
 I 
 
 I 
 
 
 
 Ir 
 
 G 
 
 
 
 3 
 6 
 
 4 
 
 I 
 
 3 
 
 I 
 
 * These four cases occurred in the region 4-3 (40-30% of clearness). 
 
 The observers' reports may, however, be grouped under five 
 heads : i. reports in which kind and rate of change are both 
 right or wrong; 2. reports in which kind is judged aright, 
 and rate is wrong; 3. reports in which rate is judged aright 
 and kind is wrong; 4. reports of change in the absence of 
 objective change (subjective reactions) ; and 5. reports which 
 
478 
 
 DALLENBACH 
 
 failed to note an objective change. Under each one of these 
 captions the data are further analysed, according as the ob- 
 jective change is of pitch or intensity, and is made rapidly 
 or slowly. Ps, then, means that the objective change was a 
 slow change of pitch; Pr, a rapid change of pitch; I^, a 
 slow change of intensity ; and Ir, a rapid change of intensity. 
 In the case of the subjective reaction, the analysis depends 
 upon the rate and kind of change reported by the observer. 
 In Table II the right cases, the wrong cases and the failures 
 are grouped according to the kind and rate of the objective 
 change. The subjective reactions are grouped as they were 
 reported by the observer. A summary of the entire number 
 of cases appears at the end of the table. It is clear that the 
 greatest number of right cases occurs with the higher degrees 
 of attention, and that the greatest number of wrong cases 
 occurs from one to two steps lower upon the scale of atten- 
 tion. That this ordering is due to attention, and that it is 
 not the result of any specific reaction to one kind or one 
 rate of change, can be seen by referring to the separate cap- 
 tions of the tables. The relation of the right cases to the 
 wrong cases for all changes, whether of pitch or intensity, 
 whether rapid or slow, is remarkably constant. 
 
 TABLE II 
 
 Number of Cases Grouped According as the Change is op 
 
 Pitch or Intensity, and is Rapid or Slow, with Summary 
 
 u 
 
 
 
 
 
 
 
 
 
 •^^ 
 
 
 
 
 
 Clearness 
 
 
 :^f^ 
 
 Report 
 
 0. 
 
 
 
 
 
 
 
 M 
 
 
 
 100-90 
 
 90-80 
 
 80-70 
 
 70-60 
 
 60-50 
 
 50-40 40-30 
 
 
 
 F 
 
 70 
 
 3° 
 
 3 
 
 
 
 
 
 Right 
 
 G 
 
 s 
 
 43 
 
 22 
 
 21 
 
 4 
 
 
 
 
 J: 
 
 2 
 
 9 
 
 10 
 
 12 
 
 6 
 
 2 
 
 
 
 3° 
 
 17 
 
 9 
 
 S 
 
 I 
 
 
 
 F 
 
 I 
 
 
 
 
 
 
 
 Wrong 
 
 G 
 T, 
 
 
 4 
 
 I 
 
 7 
 
 7 
 2 
 
 2 
 
 I 
 
 
 
 J. 
 
 2 
 
 I 
 
 2 
 
 
 
 
 H 
 
 Subjective 
 
 F 
 G 
 
 1: 
 
 I 
 
 4 
 
 
 
 I 
 
 I 
 
 
 F 
 
 
 
 
 
 
 
 
 No-reaction 
 
 G 
 
 
 
 
 I 
 
 
 2 
 
THE MEASUREMENT OF ATTENTION 
 TABLE II — Continued 
 
 479 
 
 u 
 
 
 
 
 
 
 
 
 
 TJI^ 
 
 
 
 
 
 Clearness 
 
 
 •Srt 
 
 Report 
 
 0. 
 
 
 
 
 
 
 
 M 
 
 
 
 100-90 
 
 go-80 
 
 80-70 
 
 70-60 
 
 60-50 
 
 So-40 40-30 
 
 
 
 F 
 
 45 
 
 31 
 
 4 
 
 
 
 
 
 Right 
 
 G 
 
 4 
 
 37 
 
 34 
 
 II 
 
 6 
 
 I 
 
 
 
 1: 
 
 
 7 
 
 20 
 
 3 
 
 8 
 
 3 
 
 
 
 IS 
 
 13 
 
 7 
 
 2 
 
 2 
 
 I 
 
 
 p 
 
 I 
 
 7 
 
 
 I 
 
 
 
 >H 
 
 Wrong 
 
 G 
 
 
 
 
 2 
 
 
 
 H 
 
 
 1, 
 
 
 I 
 
 I 
 
 
 2 
 
 
 
 
 i 
 
 I 
 
 
 I 
 
 
 I 
 
 
 
 
 
 
 
 
 
 
 
 
 F 
 
 2 
 
 10 
 
 2 
 
 
 
 
 H 
 
 Iz; 
 
 Subjective 
 
 G 
 
 
 
 3 
 
 2 
 
 I 
 
 2 
 
 M 
 
 
 J: 
 
 
 
 I 
 
 
 I 
 
 
 
 F 
 
 1 
 
 5 
 
 4 
 
 3 
 
 2 
 
 I 
 
 
 No-reaction 
 
 G 
 
 
 
 
 II 
 
 I 
 
 10 
 3 
 
 I 4 
 
 I 
 
 
 
 
 I 
 
 I 
 
 17 
 
 3 
 
 I 
 
 
 
 F 
 
 61 
 
 18 
 
 
 I 
 
 
 
 
 
 Right 
 
 G 
 
 4 
 
 42 
 
 18 
 
 12 
 
 3 
 
 I 
 
 
 
 
 .1. 
 
 2 
 
 9 
 
 II 
 
 6 
 
 2 
 
 I 
 
 
 
 
 J2 
 
 14 
 
 15 
 
 4 
 
 3 
 
 I 
 
 
 
 
 F 
 
 7 
 
 IS 
 
 4 
 
 
 
 
 
 
 Wrong 
 
 G 
 
 
 s 
 
 7 
 
 7 
 
 2 
 
 
 
 
 
 ,. 
 
 
 2 
 
 
 4 
 
 3 
 
 2 
 
 
 ts 
 
 
 2 
 
 5 
 
 I 
 
 4 
 
 I 
 
 
 
 
 S 
 
 
 
 
 
 
 
 
 
 
 
 F 
 
 I 
 
 10 
 
 I 
 
 
 
 
 
 
 Subjective 
 
 G 
 
 
 
 I 
 
 2 
 
 2 
 
 I 
 
 I 
 I 
 
 
 
 F 
 
 
 I 
 
 I 
 
 I 
 
 I 
 
 I 
 
 
 
 No-reaction 
 
 G 
 
 
 
 
 8 
 
 I 
 
 6 
 2 
 
 I 
 
 4 
 
 
 
 
 I 
 
 I 
 
 12 
 
 
 I 
 
 
48o 
 
 DALLENBACH 
 TABLE II — Continued 
 
 u 
 
 
 
 
 
 
 
 
 
 ^^ 
 
 
 
 
 
 Clearness 
 
 
 jSc< 
 
 Report 
 
 0. 
 
 
 
 
 
 
 
 
 
 
 100-90 
 
 90-80 
 
 80-70 
 
 70-60 
 
 60-50 
 
 50-40 40-30 
 
 
 
 F 
 
 46 
 
 29 
 
 2 
 
 
 
 
 
 Right 
 
 G 
 
 S 
 
 32 
 
 28 
 
 IS 
 
 S 
 
 
 
 
 J: 
 
 
 4 
 
 II 
 
 I 
 
 S 
 
 I 
 
 
 
 25 
 
 8 
 
 S 
 
 2 
 
 I 
 
 
 
 F 
 
 3 
 
 6 
 
 I 
 
 
 
 
 
 Wrong 
 
 O 
 
 
 S 
 
 10 
 
 7 
 
 2 
 
 I 
 
 P 
 
 
 1. 
 
 
 3 
 
 9 
 
 6 
 
 6 
 
 I 
 
 
 u 
 
 4 
 
 7 
 
 6 
 
 I 
 
 2 
 
 I 
 
 
 
 
 
 
 
 
 
 
 < 
 
 
 F 
 
 2 
 
 4 
 
 I 
 
 
 
 
 Pi 
 
 Subjective 
 
 G 
 
 
 
 3 
 
 
 
 I 
 
 
 F 
 
 I 
 
 4 
 
 3 
 
 2 
 
 I 
 
 I 
 
 
 No-reaction 
 
 G 
 
 
 
 
 3 
 6 
 
 4 
 
 I 
 
 3 
 
 3 
 
 
 
 F 
 
 222 
 
 108 
 
 9 
 
 I 
 
 
 
 
 
 Right 
 
 G 
 
 18 
 
 154 
 
 102 
 
 59 
 
 18 
 
 2 
 
 
 
 
 ,1 
 
 4 
 
 29 
 
 52 
 
 22 
 
 21 
 
 7 
 
 
 
 
 h 
 
 84 
 
 S3 
 
 25 
 
 12 
 
 5 
 
 I 
 
 
 
 P 
 
 12 
 
 28 
 
 S 
 
 I 
 
 
 
 
 
 Wrong 
 
 G 
 
 
 14 
 
 24 
 
 23 
 
 6 
 
 2 
 
 
 
 .' 
 
 
 7 
 
 10 
 
 12 
 
 II 
 
 3 
 
 
 < 
 
 
 J2 
 
 12 
 
 9 
 
 13 
 
 2 
 
 3 
 
 I 
 
 
 
 
 
 
 
 
 
 
 
 ^ 
 
 
 F 
 
 6 
 
 28 
 
 4 
 
 
 
 
 
 s 
 
 Subjective 
 
 G 
 
 
 
 6 
 
 4 
 
 4 
 
 4 
 
 
 m 
 
 
 1: 
 
 
 
 2 
 
 
 2 
 
 2 
 
 
 
 F 
 
 2 
 
 10 
 
 8 
 
 6 
 
 4 
 
 2 
 
 
 
 No-reaction 
 
 G 
 
 
 
 
 22 
 2 
 
 20 
 6 
 
 6 
 2 
 
 8 
 
 
 
 
 2 
 
 2 
 
 36 
 
 6 
 
 2 
 
 
 Inspection shows, further, that the subjective reactions 
 occur for the most part under a relatively high degree of 
 clearness, and conversely that the failures, the no-reactions, 
 occur under a relatively low degree of clearness. We may 
 infer that a subjective reaction is, under our conditions, a 
 less serious error than a no-reaction. Emphasis was laid, 
 throughout the experiment, upon reaction to change of the 
 
THE MEASUREMENT OF ATTENTION 481 
 
 tone of the variator, and the observer was ' set ' for change ; 
 it is consequently but natural that he should sometimes 
 ' imagine ' a change ; whereas failure to notice a change ob- 
 jectively presented argues a definite lapse of attention.^^ In 
 view of these considerations, we have ventured to ' weight ' 
 our results as follows: 
 
 A right or wrong judgment of Kind and Rate counts as. . . . ±2 .0 
 
 A right or wrong judgment of Kind counts as ±1.0 
 
 A right or wrong judgment of Rate counts as ±1.0 
 
 A Subjective reaction counts as — 2 .0 
 
 A No-reaction counts as — 2 . 5 
 
 In Table III the results appear as thus weighted. 
 
 TABLE III 
 
 Weighted Summaries 
 
 0. 
 
 
 
 
 Clearness 
 
 
 
 100-90 
 
 90-80 
 
 80-70 
 
 70-60 
 
 60-50 
 
 50-40 
 
 40-30 
 
 p 
 
 Total right 
 Total wrong 
 
 222 .0 
 
 20 .5 
 
 108.0 
 68. s 
 
 9.0 
 
 19 .u 
 
 I .0 
 
 8.S 
 
 S-o 
 
 ^•S 
 
 
 G 
 
 Total right 
 Total wrong 
 
 18.0 
 
 154.0 
 14 .0 
 
 102 .0 
 30.0 
 
 59 -0 
 54-5 
 
 18.0 
 35-0 
 
 2 .0 
 13-5 
 
 10 .0 
 
 J. 
 
 Total right 
 Total wrong 
 
 4.0 
 
 29 .w 
 
 7.U 
 
 52.0 
 12 .u 
 
 22 .0 
 14. S 
 
 21 .0 
 20 .5 
 
 7.0 
 7-S 
 
 
 J. 
 
 Total right 
 Total wrong 
 
 84.0 
 12 .0 
 
 S3-0 
 
 25 .0 
 IS-S 
 
 12 .0 
 47.0 
 
 5-° 
 10. s 
 
 °-5 
 3-5 
 
 
 The crest of the curve of right judgments now falls, with 
 F, I place; with G, 2 places; and with J, 2 and 2 places 
 respectively to the left, that is, above the crest of the curve 
 of wrong judgments; and we have evidence, once more, that 
 introspectively distinguished variations of clearness are 
 closely paralleled by corresponding differences in the accuracy 
 of the judgments passed. 
 
 The relation of the report to the kind and rate of the 
 objective change appears in Table IV. 
 
 " Of the 1400-odd cases reported in these tables only 61 were sub- 
 jective. We regard this small number (about 4%) as evidence both 
 of the quality of our observers and of the accuracy and reliability of 
 our apparatus and method. 
 
482 
 
 DALLENBACH 
 
 TABLE IV 
 
 Relation Between the Observer's Report and the Kind and 
 Rate of Objective Change, Expressed in Number op Cases 
 
 
 Kind 
 
 Rate 
 
 0. 
 
 Pitch 
 R. W. S. 
 
 N. 
 
 Intensity 
 R. W. S. N. 
 
 Slow 
 R. W. S. 
 
 N. 
 
 Rapid 
 R. W. S. N. 
 
 F 
 G 
 
 }: 
 
 103 I 
 95 21 
 
 62 5 
 
 S 
 
 I 
 I 
 
 2 
 I 
 
 80 9 14 16 
 93 2 8 26 
 
 41 4 2 s 
 40 3 23 
 
 77 1° 7 
 80 21 5 
 
 31 II 3 
 37 II 
 
 12 
 
 18 
 
 4 
 
 IS 
 
 80 26 12 4 
 85 25 4 10 
 22 25 I 
 41 21 9 
 
 Total 
 
 301 30 
 
 7 
 
 3 
 
 254 18 24 70 
 
 225 S3 IS 
 
 49 
 
 228 97 16 24 
 
 R., right report. 
 W., wrong report. 
 
 S., subjective report. 
 N., no report. 
 
 Here we see, in spite of individual differences, first, that 
 a change of pitch, under the conditions of our experiment, is 
 more compelling than a change of intensity; and, secondly, 
 that a rapid change of stimulus is more attractive than a slow 
 change. 
 
 Our observers are more correct as regards changes of pitch 
 than as regards changes of intensity. F, J^, and J2 report 
 more errors for intensity than for pitch. G, on the other 
 hand, reports more errors for pitch than for intensity. This 
 difference, however, is more than offset by the greater num- 
 ber of cases in which she failed to observe a change of in- 
 tensity. A like failure to apprehend changes of intensity is 
 evinced by F, Ji, and Jj. F and Ji noted " change " for every 
 variation in pitch, and J2 for every variation but one; while 
 they failed to observe " change " in 16, 5, and 23 cases, re- 
 spectively, of change in intensity. 
 
 Slow changes are, as Stern has noted, " less likely than 
 rapid to cause a reaction of attention." This rule is borne 
 out, in a measure, by our results. The objective change was 
 neglected 44 times when it was made slowly, and only 24 
 times when it was made rapidly. Moreover, the change when 
 rapidly effected was reported correctly 228 times, and when 
 slowly effected, 225 times. On the other hand, more wrong 
 reactions were made to rapid changes (97 reported as slow) 
 
THE MEASUREMENT OF ATTENTION 483 
 
 than to slow (53 reported as rapid). The law, however, 
 rests upon a fairly large body of experimental results.^^ 
 
 (i) The promptness of voluntary action, i. e., the time of a simple 
 reaction, was first used to express degrees of attention by Obersteiner 
 in 1879." He employed two distractors, an induction current and a 
 musical box, and found that the observer's reaction was slower under 
 distraction. He therefore assumed that "this retardation stands in 
 inverse proportion to the intensity of attention." "The differences in 
 the reaction period," he continues, " which may serve directly as the 
 measure of attention, vary in different individuals, and in the same 
 individual under different conditions."" Many investigators" have 
 used the reaction method to measure the attention. Their results 
 show, for the most part, that reaction-time increases with distraction, 
 though there are those who deny the correlation. Cattell," for exam- 
 ple, found that there is no corresponding lengthening of the reaction- 
 time with reduction of attention ; and Geissler writes that " the final 
 outcome of the reaction experiments, as used for the measurement 
 of attention, has been on the whole negative; it has been impossible 
 to establish a positive correlation between high degrees of attention 
 and short reactions, and between lower degrees and correspondingly 
 lengthened reactions." " In his own experiments, however, Geissler 
 found a remarkably high correlation between " the observers' esti- 
 mates of attentive concentration and the calculated quickness and ac- 
 curacy of their results,"" and remarks that "with all three observers 
 there is a perfect correlation between their best attention and their 
 shortest time, and between correspondingly lesser degrees and longer 
 times." " 
 
 Our apparatus was arranged, as we have said, to measure roughly 
 the reaction-time of our observers. The average and the mean varia- 
 
 ^ G. E. Miiller, Zur Theorie der sinnlichen Aufmerksamkeit, 1873, 
 125 ff. . 
 
 A. Pilzecker, Die Lehre von der sinnlichen Aufmerksamkeit, 1889, 
 
 20 f. 
 W. James, Principles of Psychology, I., 1890, 416 f. 
 L. W. Stern, Psychologie der Verdnderungsauffassung, 1898, 
 
 211 ff. 
 W. B. Pillsbury, Attention, igo8, 30. 
 "H. Obersteiner, Brain, I, 1879, 439-453. 
 "0/>. cit., 444. 
 
 " G. Buccola, Rivista di filos. scientif., I, 2ig ff. 
 G. S. Hall, Mind, VHI, 1883, 170-182. 
 W. Wundt, Grunds, d. physiol. Psychol, I, 1874, 749 f. ; H, 1887, 
 
 293 f. ; in, 1903, 441 ff. 
 E. J. Swift, this Journal, V, 1892, 1-19. 
 W. James, Principles of Psychology, I, 1890, 425, 427-434. 
 S. E. Sharp, this Journal, X, 1899, 356. 
 
 A. Kastner and W. Wirth, Psychol. Stud., Ill, 1907, 361-392; 
 IV, 1908, 139-200. 
 "J. McK. Cattell, Mind, XI, 1886, 242. 
 "Op. cit., 498. 
 "/fcjrf., S08. 
 "Ibid., SM- 
 
484 
 
 DALLENBACH 
 
 tion of the reaction-times in the total number of experiments," irre- 
 spective of the rightness or wrongness of the judgments, appear for 
 each observer in Table V. 
 
 TABLE V 
 
 Average Reaction-time in Seconds at the Different 
 Levels of Attention 
 
 S3 
 
 Clearness 
 
 1 
 
 100-90 
 Av. m.v. 
 
 90—80 
 Av. m.v. 
 
 80-70 
 Av. m.v. 
 
 70-60 
 Av. m.v. 
 
 60-30 
 Av. m.v. 
 
 50-40 
 Av. m.v. 
 
 F 
 G 
 
 .9 -48 
 •5 -3 
 •3 -I 
 
 i-S -7 
 
 i-i -55 
 1-9 -93 
 I.I .4 
 1.8 .8 
 
 2 .0 I.I 
 
 2 .0 1 .03 
 
 1-3 -9 
 1.8 .83 
 
 1 .0 .0 
 1.9 1.05 
 
 1-3 -45 
 2.3 1.2 
 
 2.1 1 .07 
 1.8 .66 
 2.3 1-9 
 
 4 .0 .0 
 1.6 .8 
 2 .6 .0 
 
 Av., average reaction time, m.v., mean variation. 
 Where the mean variation is given as o, only one experiment oc- 
 curred under that rubric. 
 
 There is evidently a positive correlation between attention, intro- 
 spectively estimated in trms of the attributive clearness of mental 
 processes, and rate of reaction. In the whole table there are but four 
 cases in which a lower degree of clearness gives a shorter average 
 time than the next higher degree. Three of these may be summarily 
 dismissed because they are the averages of too few cases : i, S, and i 
 respectively. The fourth case, that under the fourth rubric of G, 
 cannot be so disposed of. Neither can we consider it as an effect of 
 practice, for this was minimized by the long preliminary series, while 
 the several component reactions were also well distributed throughout 
 the experiment. It is, perhaps, worthy of note, that the mean variation 
 is high. In any case the exception is not of sufficient weight to affect 
 seriously the coefficient of correlation as figured by Pearson's familiar 
 " product moments " method."' Calculation yields the following re- 
 sults : 
 
 O Correlation" P.E. 
 
 F 0.9s 0.038 
 
 G 0.76 o .118 
 
 Ji 0.94 0.032 
 
 J2 0.98 0.048 
 
 This correlation is surprisingly high, when it is remembered that 
 no emphasis was laid, in our instructions, upon the observers' reaction. 
 
 ^ The subjective reactions and the failures to react, i. e., the " no- 
 reactions," of course are not considered here; neither case gives a 
 reaction-time. 
 
 " G. M. Whipple, Manual of Mental and Physical Tests, 1910, 27 f. 
 
 " In computing this correlation, the data under the fourth rubric 
 for F, and the sixth rubric for G, Ji, and Jz, were omitted, for the 
 reason that they represent too few cases : i, i, S, and i, respectively. 
 
THE MEASUREMENT OF ATTENTION 485 
 
 Moreover, no one of our observers, so far as we know, was aware 
 that the reactions were being measured." 
 
 (2) The mean variation has frequently been proposed as a measure 
 of attention. A small mean variation would correspond to a high 
 degree, and a large variation to a low degree of attention. Obersteiner 
 was probably the first to suggest this correlation. He showed not 
 only that the reaction-times were longer, but also incidentally that the 
 mean variation was greater, in experiments made under distraction." 
 Later, Friedrich remarks : " It is tempting to fix definitely the some- 
 what unsettled concept of attention by making it proportional to the 
 measure of precision, i. e., to the reciprocal value of the average error, 
 so that a small average error should correspond to a high degree of 
 attention and, conversely, a large average error to a low degree of 
 attention." °° Although his results show close agreement with theory, 
 he nevertheless is careful in his interpretation of them. He thinks 
 that only "in the case of the simplest mental processes, which are as 
 homogeneous as possible and but little subject to practice, may one 
 assume that the average error is essentially dependent upon the degree 
 of attention." Other authors, however, have been less cautious, and 
 have insisted that attention may be measured by mean variation.'" 
 
 Our own results tend to confirm this view. The increase of the 
 m. V. in Table V is not due in any measure to fatigue or practice. 
 It is not due to fatigue, for only five experiments of 30 to 60 seconds 
 were conducted during an hour; and it is not due to practice, for 
 this was raised to a maximum by the long practice series. In the 
 entire table, with the exception of the levels at which only one ex- 
 periment is reported, there are but two cases where a lower degree 
 of attention has a smaller m. v. than the next higher. The mean 
 variations for F and G increase uniformly with decrease of the atten- 
 tive level. Those for Ji and J2 are less regular. Nevertheless, the 
 lower degrees of attention still show a greater m. v. We seem justi- 
 fied then, even on Friedrich's principles, in drawing the conclusion 
 that degree of attention can be introspectively estimated in terms of 
 clearness. 
 
 (3) The relation of the reaction-times to the kind and rate of the 
 objective change appears in Table VI. 
 
 ^'In our case, therefore, the reactions were not known to be re- 
 actions, i. e., were not made under the Aufgahe of reaction. It is 
 possible that a " reaction " of this sort indexes attention, whereas a 
 formal and set reaction, so understood by the reactor, is too complex 
 a matter to serve as an index. 
 ^'Op. cit., 446, 447- 
 
 ^M. Friedrich, Philos. Stud., I, 1883, 73. 
 ^ H. Griffing, this Journal, VII, 1895, 235. 
 A. Oehrn, Psychol. Arbeiten, I, 1895, 92 ff. 
 V. Henri, L'annke psychol, III, 1896, 245. 
 J. J. van Biervliet, Journ. de Psychol, I, 1904, 230. 
 A. Binet, L'annee psychol, XI, 1905, 71. 
 W. Peters, Arch. f. d. ges. Psychol, VIII, 1906, 403 ff. 
 
486 
 
 DALLENBACH 
 
 TABLE VI 
 
 Relation Between the Reaction-time in Seconds and 
 THE Kind and Rate of the Objective Change 
 
 Observer 
 
 Kind 
 
 Rate 
 
 Pitch 
 Av. m.v. 
 
 Intensity 
 Av. m.v. 
 
 Slow 
 Av. m.v. 
 
 Rapid 
 Av. m.v. 
 
 F 
 G 
 
 .80 .28 
 1.70 .79 
 1.18 .37 
 1. 41 .72 
 
 1.27 .76 
 2 .40 2 .14 
 1.50 .58 
 
 i!.4S 1.21 
 
 1.30 .60 
 2.50 1. 13 
 1.60 .63 
 
 n .56 1 .08 
 
 .76 .42 
 
 1-5° -75 
 i-oo .35 
 1.18 .56 
 
 Av., average reaction-time, m.v., mean variation. 
 
 The average reaction-time to a change of pitch is, under the condi- 
 tions of our experiment, much less than that to a change of intensity; 
 snd, further, the average reaction-time to a rapid change is shorter 
 than that to a slow change. This relation is constant for all observers. 
 There is, to be surCj great individual variation, but this tallies in 
 general with the character and quality of the observer's report. F, 
 e. g., gives an exceedingly low reaction-time, but, on the other hand, 
 he makes few errors, and his attention is most frequently judged to 
 be of the highest degree. 
 
 (4) A comparison of Tables IV and VI shows that there is a close 
 relation between reaction-time and accuracy of report; i. e., the 
 shorter the reaction-time, the greater is the probability that the report 
 is correct. Of the kinds of change, pitch has the shorter reaction- 
 time, and also the greater number of right cases and the smaller 
 number of failures. Of the rates of change, the rapid has the shorter 
 reaction-time and also the greater number of right cases and the 
 smaller number of failures. It would seem then that there is a direct 
 relation between the quality and character of the report and the 
 reaction-time. 
 
 This relation becomes apparent at once if the reaction-time is 
 compared directly with the reports. Table VII shows the average 
 
 TABLE VII 
 
 The Reaction-time in Seconds and the Mean Variation 
 OF THE Right and the Wrong Reports 
 
 
 Right 
 
 Wrong 
 
 Observer 
 
 
 
 Av. 
 
 m.v. 
 
 Av. 
 
 m.v. 
 
 F 
 
 ■93 
 
 ■5° 
 
 I .■£ 
 
 ■63 
 
 G 
 
 1 .96 
 
 1 .06 
 
 2.3 
 
 1 .23 
 
 . I 
 
 1.28 
 
 .62 
 
 '■45 
 
 .60 
 
 J3 
 
 1. 71 
 
 .81 
 
 1.80 
 
 I ■OS 
 
 Av., average reaction time, m.v., mean variation. 
 
THE MEASUREMENT OF ATTENTION 
 
 487 
 
 and mean variation of the reaction-times for both the right and the 
 wrong cases. It confirms the conclusions drawn from the comparison 
 of Tables IV and VI. 
 
 The average reaction of the right reports for all of our observers 
 is shorter than that of the wrong reports. While the difference is 
 very small for J2, it is so marked in the cases of Ji, and especially 
 of G and F, that we may conclude with Whipple" that there is a 
 close correlation between rate of judgment and character and quality 
 of report. 
 
 (S) The effect of the distractors is shown in Table VIII. The 
 average clearness of the focal processes (the sounds of the variator), 
 its mean variation, and the number of cases are given for each dis- 
 tractor. 
 
 TABLE VIII 
 
 The Average Clearness op the Auditory Sensation as 
 Affected by the Distractors 
 
 
 
 
 
 
 Distractor 
 
 
 
 
 OhcP"'^" 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 I 
 
 2 
 
 3 
 
 4 
 
 5 
 
 6 
 
 7 
 
 8 
 
 
 Av. 
 
 89-5 
 
 85-7 
 
 88.6 
 
 86.4 
 
 85.8 
 
 87-5 
 
 88.8 
 
 87.0 
 
 77-S 
 
 F 
 
 m.v. 
 
 3-0 
 
 4.4 
 
 3-9 
 
 3 -ft 
 
 7-3 
 
 5-3 
 
 4-1 
 
 3.8 
 
 12 .1 
 
 
 No. 
 
 3» 
 
 22 
 
 21 
 
 IS 
 
 25 
 
 24 
 
 3° 
 
 27 
 
 26 
 
 
 Av. 
 
 85.0 
 
 7.V2 
 
 80.3 
 
 70 .6 
 
 76.0 
 
 65.8 
 
 71.0 
 
 74-5 
 
 57-8 
 
 G 
 
 m.v. 
 
 4.9 
 
 8.3 
 
 3-3 
 
 7.6 
 
 7-4 
 
 7-3 
 
 6-5 
 
 8.9 
 
 8.8 
 
 
 No. 
 
 29 
 
 23 
 
 31 
 
 27 
 
 25 
 
 31 
 
 23 
 
 25 
 
 34 
 
 
 Av. 
 
 73-7 
 
 72 .0 
 
 S8.7 
 
 62 .1 
 
 70 .0 
 
 63.3 
 
 58.0 
 
 67.6 
 
 54-" 
 
 h 
 
 m.v. 
 
 S-i 
 
 4.8 
 
 13 -I 
 
 9.1 
 
 5-1 
 
 9.0 
 
 8.2 
 
 9.0 
 
 8.7 
 
 
 No. 
 
 14 
 
 10 
 
 8 
 
 13 
 
 8 
 
 7 
 
 14 
 
 14 
 
 9 
 
 
 Av. 
 
 94 -o 
 
 84.0 
 
 77-7 
 
 80.0 
 
 74 -o 
 
 79.6 
 
 75-7 
 
 73-° 
 
 60 .0 
 
 .h 
 
 m.v. 
 
 I-.S 
 
 8.0 
 
 II .8 
 
 9.0 
 
 9.0 
 
 i°-5 
 
 8-5 
 
 10. 5 
 
 14 .6 
 
 
 No. 
 
 II 
 
 15 
 
 9 
 
 20 
 
 18 
 
 15 
 
 17 
 
 13 
 
 15 
 
 A v., average clearness of tone, m.v., mean variation. No., number 
 of cases, o, normal conditions, i, flicker. 2, current. 3, flicker and 
 current. 4, single metronome. 5, metronome and current. 6, metro- 
 nome, flicker and current. 7, two metronomes. 8, phonograph. 
 
 '^ G. M. Whipple, this Journal, XII, 1900-01, 433 ff. Whipple gave 
 his observers two successive tones, the second of which varied be- 
 tween the relations equal, greater, or less by eight_ vibrations per 
 second from the first. The second tone was judged in terms of the 
 first. He divided the observers' judgments into three classes accord- 
 ing as the report was imral^iate, slow, or deliberate. He defined 
 the "immediate" as the judgment made without conscious compari- 
 son; the "slow,"' as the judgment made with conscious comparison; 
 and the " deliberate," as the judgment in which the decision was the 
 result of internal debate. He found that a much greater percentage 
 of the immediate judgments was correct than of the slow or the 
 deliberate. 
 
488 
 
 DALLENBACH 
 
 It will be seen that the number of cases under the several dis- 
 tractors varies. This fact appears to confute the statement (made in 
 the discussion of the method) that the distractors were used an equal 
 number of times. But the discrepancy is explained by the 'nature of 
 the series. In some, only one change was made, in others 2, 3, and 4. 
 The distractors were to be employed an equal number of times, as 
 many times first as last, etc., so that their order had to be prearranged. 
 The order of the series, however, was not predetermined. Though 
 every series was used an equal number of times, choice was made at 
 haphazard. The series with the large number of changes thus acci- 
 dentally fell to some distractors more frequently than to others. Still, 
 on the whole, the variation in number of cases is slight and of little 
 consequence. 
 
 There is wide variation in the effect of the distractors both upon 
 the individual observers and upon the same observer at different 
 times. F was little affected by any distractor save the phonograph. 
 This result agrees closely, as we have said, with the general char- 
 acter and quality of his work. His attention during the experiments 
 was higher, he made fewer errors, the reaction-time of his judgments 
 was quicker, the mean variation smaller, than those of either of the 
 other observers. The phonograph served to distract his attention; 
 but even with it atteiition might be as high as under normal condi- 
 tions. He could disregard it provided that unfamiliar pieces were 
 played. When familiar records were played, his attention was " com- 
 pelled " by them, he was " unable to attend from " them. 
 
 The phonograph proved to be the most efficient distractor for all 
 the observers; and attention under normal conditions without dis- 
 traction proved to be highest for all observers. This is shown in 
 Table VIII; and also, perhaps more clearly, in Table IX, 
 in which the effectiveness of the distractors is arranged in ascending 
 order from least effective (normal conditions) to most effective 
 (phonograph). In other respects, however, there is little or no agree- 
 ment. G, Ji, and J2 show, unlike F, a wide distribution of effective- 
 ness; while F's average attention for all distractors, with the excep- 
 tion of the phonograph, lies within four degrees of clearness and is 
 very nearly as high as under normal conditions. 
 
 TABLE IX 
 
 Order op the Effectiveness of the Distractors prom 
 Least to Greatest 
 
 
 
 
 
 
 Order 
 
 
 
 V' 
 
 
 Observer 
 
 
 
 
 
 
 
 
 I 
 
 2 
 
 3 
 
 4 
 
 S 
 
 6 
 
 7 
 
 8 
 
 9 
 
 F 
 
 
 
 6 
 
 2 
 
 5 
 
 7 
 
 3 
 
 4 
 
 I 
 
 8 
 
 G 
 
 
 
 2 
 
 4 
 
 7 
 
 I 
 
 6 
 
 3 
 
 S 
 
 8 
 
 h 
 
 
 
 I 
 
 4 
 
 7 
 
 ,S 
 
 3 
 
 2 
 
 6 
 
 8 
 
 h 
 
 
 
 I 
 
 3 
 
 S 
 
 2 
 
 6 
 
 4 
 
 7 
 
 8 
 
 o, normal, i, flicker. 2, current. 3, flicker and current. 4, single 
 metronome. 5, metronome and current. 6, metronome, flicker and 
 current. 7, two metronomes. 8, phonograph. 
 
THE MEASUREMENT OF ATTENTION 489 
 
 That the effect of the distractors is different for the same observer 
 at different times is shown by J. Though his results for the two 
 periods of the experiment show a gradual change in the effectiveness 
 of the distractors, maximal attention under normal conditions, and 
 minimal attention under the distraction of the phonograph, they can 
 in no other detail be compared. In the first period the degrees of 
 clearness of the focal processes ranged from Ti-7 to S4-o; in the 
 second period they ranged from 94.0 to 60.0. An explanation has been 
 suggested above. 
 
 Table IX shows, further, that there is no uniform gradation of 
 the distractors. Thus the flicker (no. i), which next to the phono- 
 graph proved to be most effective for F, was only moderately effective 
 for G, and had the least effect of all upon J. And so on with the rest. 
 
 It has usually been supposed that attention is best under slight 
 distraction. Titchener says : " It has been shown experimentally that 
 we attend best under a slight distraction," ^ and Geissler finds that 
 "the results of the second group of experiments showed plainly that 
 even the most complex combinations of distractors, after a few days' 
 work, were unable to induce great variations of attention. Instead, 
 toward the end of the whole group, most of the normal series were 
 actually performed at a slower rate than the distraction series." " 
 Hamlin also gives a similar report. She used adding as a distractor, 
 and remarks that "the subjects usually found that it acted as a spur 
 rather than as a check to the attention." °° Our results show, on the 
 contrary, that attention is best under normal conditions; the dis- 
 tractors lower the attention. The advantage of the normal series is, 
 in the case of F, not very great; but it is uniform, and in the cases 
 of the other observers well-marked. Under the conditions of our 
 experiment, therefore, the observers attended best under normal con- 
 ditions. A 
 
 Owing to the precautions that we had taken, the effect of practice 
 and habituation in these experiments was practically negligible. In 
 the first place, the work was divided into two parts, separated by a 
 period of nine months; in the second place, a large number of dis- 
 tractors were employed, and these were capable of wide variation in 
 intensity and in rhythm ; and thirdly, as the experiments advanced, 
 the intensity and rhythm of the distractors were proportionally in- 
 creased and complicated. Habituation was therefore reduced to a 
 minimum. 
 
 In choosing the distractors, our ideal was that of Drew, "to ar- 
 range a series of tasks of increasing degrees of complexity which 
 should from the normal make ever greater demands on the mind until 
 the attention should pass from a fully concentrated to a completely 
 distracted state." " This is the principle laid down by Stumpf in his 
 TonpsychologieJ" and by Titchener in his Psychology of Feeling and 
 Attention." The results show that we were not successful in obtain- 
 ing such a series of graded distractors. There appear to be four 
 main reasons. (l) A change in the stimulus rnay cause the corre- 
 sponding conscious processes to rise involuntarily in clearness. It 
 " catches " the attention. The tone may be comparatively obscure 
 
 '"Psychol, of Feeling and Attention, 1908, 203. 
 
 "Op. cit., S13. 
 
 "A. J. Hamlin, this Journal, VIII, i8g6, 49. 
 
 "F. Drew, this Journal, VII, 1895, 533- 
 
 ''C. Stumpf, op. cit., I, 1883, 73-75- 
 
 "E. B. Titchener, op. cit., 1908, 277, 278. 
 
490 DALLENBACH 
 
 just before the moment of change, but at and during the change it 
 may be maximally clear. (2) There are, in many of the distractors, 
 brief moments of interruption, during which the change may occui 
 and the reaction may be performed as if under norrnal conditions. 
 (3) The distractors vary in effect from individual to individual. What 
 may be a graded series for one observer would affect another very 
 differently. (4) The distractors do not even affect the same observer 
 in the same way from day to day. Factors are here involved which 
 are subjective in nature (mood, general organic tonus, etc.), and 
 which it is therefore extremely difficult to bring under objective 
 control. 
 
 D. Double Task Method 
 
 I. Apparatus. — ^The Single Task Method involved only the 
 higher degrees of attention. Under the instructions, this 
 could hardly have been otherwise; with attention directed to 
 the sounds of the variator and from the distractors, the tones 
 would necessarily be of the higher degrees of clearness. It 
 was incumbent upon us, therefore, to extend thb work by 
 some method which should induce the lower degrees of at- 
 tention, and thus to discover if the conclusions so far drawn 
 hold when the lower levels of attention are involved. 
 
 Geissler gives four essential requirements for such a 
 method.^* The efficiency of the work performed must de- 
 pend as exclusively as possible upon the degree of attention 
 given to it, and as little as possible upon such factors as 
 practice, fatigue, mood, etc. The performance should never 
 become entirely automatic or habitual. It must require abso- 
 lutely continuous attention, so that a momentary lapse should 
 at once manifest itself in a momentary reduction of the qual- 
 ity of the work. And the execution of the work must easily 
 submit itself to a scale of quantitative gradation. 
 
 The method that seemed best to fulfill these requirements 
 was the Double Task Method. This seems to have been first 
 used by Loeb in 1886,''' but since that time it has been em- 
 ployed successfully by many experimenters.'^ It requires the 
 
 " Op. cit.. SIS- 
 
 "J. Loeb, Arch. f. d. ges. Phys., XXXIX, i886, S92-597. 
 
 "A. Binet Rev. philos., XXIX, 1890, 138-155. 
 
 H. Miinsterberg, Beitr. z. exper. Psychol., IV, 1892, 200 ff. 
 
 W. G. Smith, Mind, N. S., IV, 1895, 50-73. 
 
 F. Drewj this Journal, VII, 1895, 533-S72. 
 
 V. Henri, Annee psychol, III, 1896, 232-278; VII, 1900, 2S0 flf 
 
 J. C. Welch, Am. J. Phys., I, 1898, 283-306. 
 
 W. McDougall, Brit. J. Psychol, I, 1904, 435-445. 
 
 W. Wirth, Psychol. Stud., II, 1906, 30 ff. 
 
 A. Kastner and W. Wirth, Psychol. Stud., Ill, 1907, 361-312; 
 IV, 1908, 139-200. 
 
 S. de Sanctis, Zeits. f. Psychol, XVII, 1898, 205-214. 
 
 L. R. Geissler, op. cit., SiS-529- 
 
THE MEASUREMENT OF ATTENTION 49I 
 
 observer to divide his attention, and to perform simrultane- 
 ously two diiferent mental tasks. 
 
 The first task which we selected was essentially the same 
 as that of the previous experiment, — ^judging and reporting 
 the changes of an auditory stimulus. The recording appa- 
 ratus, the Stern variator, and the apparatus for the control 
 of the tone, were the same as before. The second task con- 
 sisted either of counting discrete objects, or of continuous 
 adding. 
 
 In the counting of discrete objects, no. 12 BB shot were first used. 
 Since the right hand rested upon the electrical key, the counting was 
 done with the left. The shot proved to be too small to be picked up 
 one by one and thus counted; and an apparatus was constructed 
 whereby they rolled, as they were counted, down an inclined plane 
 to a common receptacle. The rolling, however, made a slight noise; 
 this gave rise to a distraction which under the conditions of the 
 Double Task Method was objectionable; and accordingly a felt pad 
 was substituted for the box. But now the observers had trouble in 
 separating the shot, in moving them rapidly over the surface of the 
 felt; so that, even under the best conditions, accurate records were 
 seldom made. We therefore abandoned the shot in favor of small 
 corks. These permitted of gross movements, could be taken up sepa- 
 rately as counted, and were noiseless. They were placed upon a felt 
 pad in front of the observer, and were transferred as counted to a 
 felt-lined box which stood a few cm. to the left. 
 
 In the_ continuous adding, five series of thirty figures were selected 
 to constitute five different degrees of difficulty. The easiest contained 
 all the figures from i to g ; with the exception of figure 3, which 
 occurred six times, each integer appeared three times in the series. 
 In the second series all the figures from 3 to 13, with the exception 
 of 10, occurred three times. In the third series all of the figures 
 from 13 to 23, with the exception of 20, occurred three times. In the 
 fourth series the following figures 23 to 27 were used once; 33 to 
 37, 43 to 47 v/ere used twice; and 53 to 57 once. In the fifth and 
 last series the figures 63 to 67 were used once; 73 to yy and 83 to 
 87 twice ; and 93 to 97 once. By using a different starting-number, 
 the effect of practice and memory of previous results were entirely 
 eliminated. The starting-number varied in regular order from day 
 to day between the odd numbers from 3 to 25." 
 
 The numbers were presented visually by an exposure apparatus 
 which was constructed from a kymograph drum. This was slowly 
 revolved by the motor which, in the Single Task Method, actuated 
 the flicker. The drum was concealed behind a neutral-gray screen 
 which stood in front of the observer at a distance of about 30 cm. 
 A rectangular slit 1x3 cm. was cut in the center of the screeii 
 directly in the observer's line of regard. The apparatus was so ar- 
 ranged that the numbers appeared from above. The rate of presenta- 
 tion was variable as slow, moderate, and rapid. It was controlled 
 from the experimenter's desk by a three-way switch, and was gov- 
 erned by increase or decrease of the strength of the electrical current. 
 The rate of presentation was also controlled by the spacing of the 
 
 "C/. Geissler, op. cit, 504. 
 
492 DALLENBACH 
 
 figures upon the drum, which was constant throughout an entire ex- 
 periment. In Series I the figures were single-spaced; in Series II, 
 doubled-spaced ; and in the other series. III, IV, and V, triple-spaced. 
 The exposure slit was illuminated by an electric light which was 
 fixed just above and somewhat behind the observer. The illumination 
 was constant and uniform, and the observer's head cast no shadow 
 upon the visual field. 
 
 A slight shift of the drum upon its shaft made it possible to expose 
 a number-series of any degree of difficulty in the rectangular window. 
 The easier series were first shown, variation occurring only in the 
 starting-number and in the rate of presentation. As the observers 
 became practised in addition, the more difficult series were gradually 
 introduced. We sought to keep the mental task of such difficulty that 
 a high degree of attention was required, and that a lapse in attention 
 should manifest itself directly in the quality and character of the 
 work. Great care, however, had to be exercised not to increase the 
 difficulty of the series and the rate of presentation beyond the limits 
 of the individual observer. F was the only observer to add success- 
 fully series V, even when presented at the slowest rate. 
 
 2. Instruction. — ^As a control, every third experiment was 
 conducted under the normal conditions of the Single Task 
 Method; i. e., the sole task was observation of, and response 
 to, the changes of the auditory stimulus. Five experiments 
 were usually made during an hour. They began at the signal 
 Ready, Now, and the observer directed his attention as in- 
 structed, either to the tone of the variator, or to the counting 
 of the corks, or to the adding of the figures. The instruction 
 was as follows: 
 
 "In this experiment you are to record all changes of intensity and 
 of pitch as in the previous experiment, by one and two pushes re- 
 spectively upon the key, and are also in the subsequent introspective 
 reports to give the rate of change. 
 
 "You are to direct your attention (to the tone of the variator,) 
 (to the counting of the corks,) (to the adding of the figures). At 
 the end of the experiment, which may run for thirty seconds, you 
 shall (give the number of corks you have counted,) (give the sum 
 of the figures you have added,) answer the following questionary :" 
 
 1. How much attention in terms of clearness was given: 
 
 a. To the auditory stimulus? 
 
 b. To the other required task, — ^if there was one? 
 
 c. To any other sensory or ideational processes which may have 
 
 entered consciousness during the course of the experiment? 
 
 2. What affective mood prevailed during the experiment? 
 
 3. Have you any comment to make ? " 
 
 " Cf. Geissler, op. cit., 519. 
 
THE MEASUREMENT OF ATTENTION 493 
 
 These instructions were read to the observer before each 
 experiment.^" The three kinds of experiment, in which the 
 attention is directed to different tasks, will henceforth be 
 represented by the numerals o, i, and 2. o refers to the 
 normal or check series, in which attention is directed to the 
 sound of the variator; i refers to the Double Task Method, 
 in which it is directed also to the counting of the corks ; and 
 2 refers to the Double Task Method, in which it is directed 
 also to the adding of the figures. These three kinds of 
 experiments are taken an equal number of times, and occur 
 as many times in the first place as the second, third, fourth, 
 and last places. 
 
 3. Number of experiments. — The experiments were made 
 during the autumn of 1912. The same observers who had 
 taken part in the other series were, fortunately, available. 
 F gave in all 152 introspections: G, 150; and J 151. 
 
 4. Series. — The series of the Double Task Method differed 
 from those of the Single Task Method in two respects. First, 
 the time of the experiments was reduced uniformly to 30 
 seconds. This reduction was thought advisable, since the 
 shorter period tended toward accuracy in the introspective 
 reports, and since it tended also to rest the efficiency of the 
 work performed upon degree of attention, and as little as 
 possible upon fatigue. Secondly, the number of changes 
 within a single experiment was reduced to two. The four, 
 and even the three changes which were introduced in the 
 Single Task Method had there proved to be a source of dif- 
 ficulty ; and we could not anticipate their successful use under 
 the new conditions, in which the attention was divided be- 
 tween two tasks. In four of the series but one change was 
 made. This precaution was taken in order that the observer 
 might not become habituated to two changes. In all other 
 respects, the series agreed with those of the Single Task ex- 
 periment. 
 
 "The importance of repeating the directions is not to be over- 
 looked. On one occasion, the observer was merely directed to " count 
 corks " and not as usual to " direct attention to the counting." The 
 effect on the experiment was plainly shown in the report and intro- 
 spection. The report was correct, and the clearness was maximal. 
 The introspection read : " At first attention divided equally between 
 tone and counting, both on upper level. On the whole the tone was 
 slightly clearer. Eyes right; turned toward source of sound. These 
 two processes, tone and counting, on upper level for short time. 
 Later they rapidly fluctuated; now the tone was clearer, now the 
 counting." 
 
494 DALLENBACH 
 
 In detail, the series were as follows: 
 
 Time No. of Pitch No. of Intensity Rate 
 
 of Pitch of intensity of of 
 
 Series change changes tone changes tone change 
 I lo" I 400—450 oh r. 
 
 II is" I 350-45° ° 1 s. 
 
 III 20" o 450 I h-1 r. 
 
 IV 25" o 300 I 1-h s. 
 V 5"-io'' 2 500-400-500 o h r.r. 
 
 VI s"-is" 2 400—500—400 o 1 s.s. 
 
 VII 5"— 20" 2 500—400—300 o h r.s. 
 
 VIII S"~^S" 2 300—400—500 o 1 s.r. 
 
 IX io"-is" I 400-450 I h-1 r.r. 
 
 X io"-2o" I 500-450 I 1-h s.s. 
 
 XI io"-2 5" I 300-400 I 1-h r.s. 
 
 XII io"-2 8" I 500-400 I h-1 s.r. 
 
 XIII 2"-28" o 300 2 1-h-l r.r. 
 
 XIV i5"-2o'' o 500 2 h-l-h s.s. 
 XV i5"-2 5" o 400 2 l-h-l r.s. 
 
 XVI i5"-28" o 450 2 h-l-h s.r. 
 
 SUMMARY 
 
 No. of No. slow No. rapid 
 
 Kind, of change changes changes changes 
 
 Pitch 14 7 7 
 
 Intensity 14 7 7 
 
 Total 28 14 14 
 
 5. Results. — In working over the data, the observers' re- 
 ports were grouped as in the other experiment. It soon 
 became apparent, however, that this classification was not 
 entirely adequate. There were occasions when the observer 
 reported " change " without giving either kind or rate. Such 
 cases did not occur with the Single Task Method. We dis- 
 pose of them by grouping them under a new heading, as 
 Fact of Change. 
 
 The results appear in Table X. The data from the check 
 or normal experiments are not here considered. Only one 
 task was set in those experiments, and the attention was di- 
 rected to the tone of the variator ; consequently, the clearness 
 of the auditory processes was nearly always maximal, and 
 the reports were nearly always correct; the results add noth- 
 ing to those of Tables I and II (Single Task Method), and 
 are therefore omitted here. Our object in giving the normal 
 series was, it will be remembered, not to confirm the results 
 of the Single Task experiment, but merely to afford a means 
 whereby the observer could, from time to time, compare the 
 clearness of the auditory processes in concentrated and di- 
 vided attention. 
 
THE MEASUREMENT OF ATTENTION 
 
 495 
 
 TABLE X 
 NuuBBR OP Cases, Kind and Rate of Change 
 
 Report 
 Change 
 
 Right 
 10-9 9-8 8-7 7-6 6-S S-4 4-3 3-2 a-o 
 
 Wrong 
 10-9 9-8 8-7 7-6 6-5 5-4 4-3 3-a a-o 
 
 F 
 Ps G 
 
 a ^ 
 
 4 13 6 2 
 
 III I 
 
 5 6 S 
 
 I a 
 
 7 7 a I 
 
 I 3 2 
 
 ^ F 
 rt Pr G 
 P J 
 
 4 lo 4 
 
 I I 17 7 2 
 
 lo 15 6 I 
 
 I 
 
 I 
 
 1 
 
 < F 
 p Is G 
 Z J 
 
 13 7 
 
 I II 
 
 5 4 2 1 
 
 II I 
 
 4 5 12 
 
 M F 
 Ir G 
 
 J 
 
 5 11 4 4 
 
 3 1 II 
 
 S 4 2 I 
 
 I I 
 
 223 
 
 F 
 
 Ps G 
 
 J 
 
 3 5 13 
 
 4 8 3 
 
 I 6 7 I 
 
 I I 
 
 I I 
 
 4 4 
 
 F 
 ■ri Pr G 
 Z J 
 
 5871 
 
 III 
 
 3 9 5 
 
 I 
 
 112 
 
 S F 
 
 Is G 
 
 J 
 
 II 4 I I 
 
 3 2 I I 2 
 I 3 7 
 
 I 
 
 F 
 
 Ir G 
 
 J 
 
 6 I 
 
 I I 
 I 3 14 
 
 I 2 
 
 3521 
 
 I 
 
 F* 
 Ps G 
 
 J 
 
 I I 
 
 1 I 
 
 4 4 
 
 3513 
 
 483^ 
 
 I 6 7 I 
 
 F 
 
 I 
 
 112 
 
 5871 
 
 III 
 
 3 9 S 
 
 < IT 
 
 •^ Is G 
 
 J 
 
 I 
 
 iz 4 I I 
 
 3 2X1 3 
 
 F 
 
 r." G 
 J 
 
 I 2 
 
 3 5 2 1 
 
 I 
 
 6 I 
 
 I 1 
 
 I 3 14 
 
 F 
 — Ps G 
 
 I 
 
 III 
 
 I 
 
 
 
 I 
 
 I 
 
 
 5 F 
 ° Is G 
 
 1 
 
 I 2 
 
 I I 
 
 
 * Ir G 
 
 J 
 
 I 
 
 I I 
 
 
496 
 
 DALLENBACH 
 
 TABLE X — Continued 
 
 o 
 
 ^ 
 
 
 
 
 Wrong 
 
 & 
 
 5 
 o 
 
 O. 
 
 lO 
 
 -9 
 
 9-8 8-7 7-6 6-5 S-4 4-3 3-2 a-o 
 
 55 
 
 
 F 
 
 
 
 
 O 
 
 Ps 
 
 Ct 
 
 
 
 
 § 
 
 
 J 
 
 
 
 I 
 
 
 F 
 
 
 
 
 
 Pr 
 
 G 
 T 
 
 
 
 
 w 
 
 
 
 
 
 
 
 
 
 
 
 > 
 
 
 F 
 
 
 
 
 B 
 
 Is 
 
 G 
 
 r 
 
 
 
 I 
 
 I 3 
 
 H 
 
 
 
 
 
 
 1— 1 
 
 
 F 
 
 
 I 
 
 z z 
 
 
 
 Ir 
 
 G 
 
 
 
 
 to 
 
 
 J 
 
 
 
 I 
 
 ll Ps G 
 
 S 
 
 I 3 I 7 
 
 4 
 
 § F 
 a Pr G 
 
 3 
 
 I 3 5 
 
 3 3 
 
 W p 
 (^ Is G 
 
 O J 
 
 I I 4 l6 
 3 4 7 13 
 
 3 I6 
 
 ^ F 
 
 Ir G 
 
 J 
 
 I 13 
 
 I 5 lo 
 3 II 
 
 Table X gives only the number of cases. A comparison 
 of the right and wrong cases, the subjective reactions and 
 the failures is more clearly presented in Table XI. This table 
 shows that a lower degree and a greater scope of attention 
 were uniformly, in the case of all observers, induced by the 
 Double Task Method. F's introspective estimations cover 
 nearly the entire attentive scale, though there is nevertheless 
 a marked tendency toward the higher degrees. This dis- 
 tribution agrees closely with his introspections, for he reports 
 that the clearness of the auditory processes rises when a 
 change is perceived; as a change is perceived, the processes 
 immediately become clearer, the judgment of kind and rate 
 is made, and then the auditory stimulus again lapses into 
 obscurity. 
 
 G likewise covers the entire scale. Her results ar^ very 
 regular, and show a tendency towards the central part of the 
 scale. J's estimations, unlike those of the other observers, 
 are limited to the lower degrees of clearness. His attention 
 upon the secondary tasks was maximal; and his work in 
 them was, throughout, of the highest order. 
 
THE MEASUREMENT OF ATTENTION 
 TABLE XI 
 
 497 
 
 Number op Cases Grouped According as the Change is of 
 Pitch or Intensity and is Rapid or Slow, with Summary 
 
 Kind 
 
 
 
 
 
 
 Clearness 
 
 
 
 
 or 
 
 Report 
 
 0. 
 
 
 
 
 
 
 
 
 
 
 Rate 
 
 
 
 10-9 
 
 9-8 
 
 8-7 
 
 7-6 
 
 6-S 
 
 S-4 
 
 4-3 
 
 3-2 
 
 2-0 
 
 
 
 F 
 
 8 
 
 ^i 
 
 2S 
 
 10 
 
 4 
 
 
 
 
 
 
 Right 
 
 G 
 J 
 
 
 2 
 
 2 
 
 23 
 
 16 
 
 6 
 19 
 
 I 
 36 
 
 23 
 
 2 
 
 
 
 F 
 
 
 I 
 
 4 
 
 
 
 
 
 2 
 
 
 
 Wrong 
 
 G 
 
 T 
 
 
 
 
 2 
 
 8 
 
 10 
 
 3 
 
 I 
 
 8 
 
 2 
 
 PTTPTT 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 F 
 
 
 
 
 
 
 
 
 
 
 
 Sub- 
 
 G 
 
 
 
 
 
 
 
 
 
 
 
 jective 
 
 J 
 
 
 
 
 
 
 
 
 
 I 
 
 
 
 F 
 
 
 
 
 
 
 
 
 
 7 
 
 
 No- 
 
 G 
 
 
 
 
 
 
 I 
 
 1 
 
 S 
 
 12 
 
 
 reaction 
 
 J 
 
 
 
 
 
 
 
 
 2 
 
 6 
 
 
 F 
 
 6 
 
 2S 
 
 21 
 
 6 
 
 I 
 
 
 
 
 
 Right 
 
 G 
 J 
 
 
 I 
 
 7 
 
 3 
 
 2 
 
 3 
 II 
 
 I 
 18 
 
 28 
 
 I 
 
 
 F 
 
 I 
 
 ^ 
 
 3 
 
 I 
 
 I 
 
 
 
 
 
 Wrong 
 
 G 
 T 
 
 
 
 
 3 
 
 II 
 
 9 
 
 S 
 
 I 
 
 2 
 
 I 
 
 I 
 
 T'NTT'PMCiTTV 
 
 
 
 
 
 
 
 
 
 
 
 
 F 
 
 I 
 
 I 
 
 I 
 
 2 
 
 
 
 
 
 
 Sub- 
 
 G 
 
 
 
 
 
 
 
 
 
 I 
 
 jective 
 
 J 
 
 
 
 
 
 
 
 I 
 
 3 
 
 
 
 F 
 
 
 
 
 I 
 
 
 
 I 
 
 S 
 
 28 
 
 No- 
 
 G 
 
 
 
 
 
 
 3 
 
 4 
 
 12 
 
 23 
 
 reaction 
 
 J 
 
 
 
 
 
 
 
 
 s 
 
 27 
 
 
 F 
 
 S 
 
 17 
 
 IS 
 
 2 
 
 
 
 
 
 
 Right 
 
 G 
 J 
 
 
 2 
 
 I 
 
 2 
 
 I 
 
 2 
 9 
 
 I 
 18 
 
 14 
 
 
 
 F 
 
 I 
 
 1=; 
 
 10 
 
 •? 
 
 4 
 
 
 
 2 
 
 
 Wrong 
 
 G 
 
 T 
 
 
 
 3 
 
 6 
 
 20 
 
 16 
 2 
 
 3 
 II 
 
 s 
 17 
 
 4 
 
 PT n\7[T 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 F 
 
 
 I 
 
 
 I 
 
 
 
 
 
 
 Sub- 
 
 G 
 
 
 
 
 
 
 
 
 
 I 
 
 jective 
 
 J 
 
 
 
 
 
 
 
 I 
 
 2 
 
 I 
 
 
 F 
 
 
 
 
 I 
 
 
 
 I 
 
 4 
 
 21 
 
 No- 
 
 G 
 
 
 
 
 
 
 ^ 
 
 6 
 
 8 
 
 20 
 
 reaction 
 
 J 
 
 
 
 
 
 
 
 
 2 
 
 20 
 
498 
 
 DALLENBACH 
 TABLE Xl—Contintied 
 
 Kind 
 
 
 
 
 
 
 Clearness 
 
 
 
 
 or 
 
 Report 
 
 0. 
 
 
 
 
 
 
 
 
 
 
 Rate 
 
 
 
 10-9 
 
 9-8 
 
 8-7 
 
 7-6 
 
 6-S 
 
 S-4 
 
 4-3 
 
 3-2 
 
 2-0 
 
 
 
 F 
 
 9 
 
 22 
 
 II 
 
 4 
 
 
 
 
 
 
 
 Right 
 
 G 
 
 J 
 
 
 I 
 
 4 
 
 22 
 
 13 
 
 7 
 IS 
 
 2 
 19 
 
 9 
 
 2 
 
 
 
 P 
 
 
 6 
 
 !■; 
 
 8 
 
 2 
 
 
 
 
 
 
 Wrong 
 
 G 
 
 T 
 
 
 
 I 
 
 I 
 
 3 
 
 3 
 
 4 
 
 4 
 12 
 
 I 
 20 
 
 
 RAPID 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 F 
 
 I 
 
 
 I 
 
 I 
 
 
 
 
 
 
 
 Sub- 
 
 G 
 
 
 
 
 
 
 
 
 
 
 
 jective 
 
 J 
 
 
 
 
 
 
 
 
 I 
 
 
 
 
 F 
 
 
 
 
 
 
 
 
 I 
 
 14 
 
 
 No- 
 
 G 
 
 
 
 
 
 
 I 
 
 I 
 
 7 
 
 IS 
 
 
 reaction 
 
 J 
 
 
 
 
 
 
 
 
 S 
 
 13 
 
 
 
 F 
 
 28 
 
 OS 
 
 70 
 
 22 
 
 S 
 
 
 
 
 
 
 Right 
 
 G 
 J 
 
 
 6 
 
 14 
 
 S° 
 
 32 
 
 18 
 
 S4 
 
 S 
 91 
 
 3 
 
 74 
 
 S 
 
 
 
 F 
 
 2 
 
 2'! 
 
 S2 
 
 12 
 
 7 
 
 
 
 4 
 
 
 
 Wrong 
 
 G 
 T 
 
 
 
 4 
 
 12 
 
 42 
 
 38 
 6 
 
 IS 
 11 
 
 9 
 46 
 
 7 
 
 SUMMARY 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 F 
 
 2 
 
 2 
 
 2 
 
 4 
 
 
 
 
 
 
 
 Sub- 
 
 G 
 
 
 
 
 
 
 
 
 
 2 
 
 
 jective 
 
 J 
 
 
 
 
 
 
 
 2 
 
 6 
 
 2 
 
 
 
 F 
 
 
 
 
 2 
 
 
 
 2 
 
 10 
 
 70 
 
 
 No- 
 
 G 
 
 
 
 
 
 
 8 
 
 14 
 
 7,0 
 
 70 
 
 
 reaction 
 
 J 
 
 
 
 
 
 
 
 
 14 
 
 66 
 
 Table XI shows further that the greatest number of right 
 cases occurs in the higher degrees, and conversely that the 
 greatest number of wrong cases occurs in the lower degrees 
 of clearness. This relation between the right and wrong 
 reports is more clearly shown in Table XII, in which the 
 reports are weighted.*" The same system of weights is here 
 employed as in the Single Task Method. A single addition 
 is, however, made: half a point is added to the right cases 
 for all reports grouped under Fact of Change. 
 
 "We again call attention to the '"subjective" reactions. Out of 
 1160 cases reported under this method only 22 (about 2%) were 
 " subjective." 
 
THE MEASUREMENT OF ATTENTION 
 
 499 
 
 TABLE XII 
 
 Weighted Summaries 
 
 Q 
 
 Report 
 
 Clearness 
 
 
 10—9 
 
 9-8 
 
 8-7 
 
 7-6 
 
 6-5 
 
 5-4 
 
 4-3 
 
 3-2 
 
 2-0 
 
 P 
 
 Right 
 Wrong 
 
 28. s 
 4.0 
 
 95-5 
 
 27 .0 
 
 71.0 
 35 -o 
 
 22 .0 
 18.5 
 
 5-0 
 7.0 
 
 
 ^•5 
 
 16. 5 
 
 87-5 
 
 G 
 
 Right 
 Wrong 
 
 
 6.0 
 
 14 .0 
 4.0 
 
 SO -5 
 12 .0 
 
 33-° 
 42 .0 
 
 20 .0 
 48.0 
 
 6.0 
 32-5 
 
 3-0 
 46.5 
 
 89-5 
 
 J 
 
 Right 
 Wrong 
 
 
 
 
 
 
 54 .0 
 6.0 
 
 92 .0 
 33-° 
 
 74-5 
 69-5 
 
 5-0 
 91-5 
 
 The crests of the curves of right judgments now fall with 
 F, 7 places; with G, S places; and with J, 3 places, respec- 
 tively, to the left of the crests of the curves of wrong judg- 
 ments. The crests of the latter curves lie uniformly, for 
 all observers, in the lowest degree of clearness, from o to 20. 
 This result, as is shown by the preceding tables, is due to 
 the great number of changes which were unobserved and 
 during which the tone of the variator was very obscure. 
 The general relation holds, however, even if the no-reactions 
 are not considered: in that case, the crests of the curves of 
 wrong reactions still fall i, 2, and i place for F, G, and J 
 respectively below the crests of the curves of right reactions. 
 The results thus substantiate those of the Single Task Method, 
 and confirm our conclusion that a close parallelism exists be- 
 tween the introspectively distinguished variations of atten- 
 tion and the accuracy of the work done, — ^provided, first, 
 that the estimation of the degrees of attention is made in 
 terms of the attributive clearness of the processes attended 
 to; and, secondly, that the work itself is not influenced by 
 anything other than a change in the attention. That this 
 second requirement is fulfilled under the conditions of our 
 experiment, and that our results are due to attention and 
 not to any other influence, such as a specific reaction to a 
 particular kind and rate of change, is not to be doubted. It 
 is clearly shown in Table XI that the relation holds irre- 
 spectively of the kind and rate of the change. The crests 
 of the " right " curves lie from one to two, three and four 
 steps above the crests of the " wrong " curves. 
 
SOO DALLENBACH 
 
 It might be objected that the precision of the work is no more 
 dependent upon degree of attention than upon duration of attention. 
 That the moment of change is significant, an objector might say, can- 
 not be questioned. Sometimes a change will occur when the addition 
 is easy, or a cork has just been deposited within the box. Under 
 such conditions a change may be freely attended to, and consequently 
 both the degree and the duration of attention will be increased. If, 
 on the other hand, a change occurs at some critical point in the 
 counting or adding, though it may be perceived as clearly as in the 
 former case, yet the duration of attention will necessarily be shorter; 
 and consequently the precision of the work (judgment of kind and 
 rate of change) will be decreased. In other words, the accuracy of 
 the report will vary directly with duration of attention. This, indeed, 
 might be a formidable criticism if the facts vvere found to justify it; 
 but they are not. We might, in any event, raise the question whether 
 attentiouj under the unfavorable conditions of the second case given 
 above, could be as high as under the favorable conditions of the first. 
 We might also point out that our observers were instructed to esti- 
 mate the clearness-values only, that a long preliminary and practice 
 period was allowed in order that they might accurately estimate the 
 attributive clearness of mental processes attended to and attended 
 from, and lastly that their introspective estimation of clearness-values 
 was entirely independent of duration of attention. But we need only 
 refer to the results of the Single Task Method. There, the observers 
 were directed to attend to the tone, and from the distractors. They 
 were not instructed to react as quickly as possible, but only to respond 
 " as soon as a change is perceived ;" there was no pressure upon 
 them to hasten their report." If the duration of attention varied at 
 all, it varied quite independently of, and apart from, the clearness 
 of the mental processes during the change, and the accuracy of the 
 reports made after the change. As now the results of the two methods 
 agree very closely, we may conclude without hesitation that degree 
 and not duration of attention is responsible in our experiments for 
 precision of work done. 
 
 It is apparent, however, from the preceding tables, that 
 there is a difference in the accuracy of reaction to the various 
 changes. The relation between report and objective change 
 in the Double Task Method is shown in Table XIII. 
 
 This table shows, first, that a change of pitch is more 
 compelling than a change of intensity; and, secondly, that a 
 rapid change is more attractive than a slow. The results are 
 uniform for all observers. With changes of pitch, more 
 reports were correct, fewer were wrong, fewer subjective 
 errors were made, and fewer objective changes were unob- 
 served, than in the case of intensity; and likewise, though 
 not so markedly, more rapid changes were reported correctly, 
 fewer wrongly, fewer subjective errors were made, and fewer 
 
 " The phrase " as soon as " was not felt as a temporal pressure ; 
 for, as we have said, no one of the observers knew that the 
 " reactions " were being measured. Had they possessed this knowl- 
 edge, the instructions might have received a temporal interpretation. 
 In fact, their only concern was to report correctly. 
 
THE MEASUREMENT OF ATTENTION 
 
 SOI 
 
 rapid changes were passed over unobserved, than was the 
 case with slow changes. 
 
 TABLE XIII 
 
 Relation Between the Observer's Report and the Kind and 
 Rate of Objective Change, Expressed in Number of Cases 
 
 0. 
 
 Kind 
 
 Rate 
 
 Pitch 
 R. W. S. N. 
 
 Intensity 
 R. W. S. N. 
 
 Slow 
 R. W. S. N. 
 
 Rapid 
 R. W. S. N. 
 
 F 
 G 
 J 
 
 76 7 7 
 50 24 19 
 80 IS I 8 
 
 59 9 5 35 
 20 30 I 42 
 
 58 3 4 32 
 
 39 35 2 27 
 
 9 53 I 37 
 
 41 34 4 22 
 
 46 31 3 IS 
 49 13 24 
 45 36 I 18 
 
 Total 
 
 206 46 I 34 
 
 137 42 10 109 
 
 89122 7 86 
 
 140 80 4 57 
 
 R., right report. 
 W., wrong report. 
 
 S., subjective report. 
 N., no report. 
 
 (i) The interval between the moment of change and the observer's 
 reaction was measured, as before, in fifths of a second. The average 
 reaction-time was computed for each degree of attention as estimated 
 by the clearness of mental processes. This time, together with the 
 m. V. and the number of cases at each level, appears in Table XIV. 
 
 TABLE XIV 
 
 Average Reaction-time in Seconds, Mean Variation, and 
 Number op Cases at the Different Levels op Attention 
 
 
 
 
 
 Clearness 
 
 
 
 
 0. 
 
 
 
 
 
 
 
 
 
 10-9 
 
 9-8 
 
 8-7 
 
 7-6 
 
 6-5 
 
 5-4 
 
 4-3 
 
 3-2 
 
 2-0 
 
 
 Av. 
 
 1-13 
 
 I .22 
 
 1 .46 
 
 1.30 
 
 2 .10 
 
 
 
 2.30 
 
 
 F 
 
 m.v. 
 
 .48 
 
 •5° 
 
 .66 
 
 .45 
 
 1.36 
 
 
 
 ■30 
 
 
 
 No. 
 
 13 
 
 54 
 
 44 
 
 13 
 
 6 
 
 
 
 2 
 
 
 
 Av. 
 
 
 1.30 
 
 ■95 
 
 1.83 
 
 ■^.17 
 
 4 .00 
 
 4.00 
 
 5.80 
 
 
 G 
 
 m.v. 
 
 
 •3° 
 
 .27 
 
 ■73 
 
 •77 
 
 1.30 
 
 .60 
 
 •13 
 
 
 
 No. 
 
 
 3 
 
 7 
 
 23 
 
 18 
 
 3 
 
 2 
 
 3 
 
 
 
 Av. 
 
 
 
 
 
 
 1 .10 
 
 i.32 
 
 1. 61 
 
 I .10 
 
 J 
 
 m.v. 
 No. 
 
 
 
 
 
 
 ■52 
 24 
 
 ■63 
 46 
 
 .87 
 48 
 
 .20 
 4 
 
 Av., average reaction-time, m.v., mean variation. No., number 
 of cases under rubric. 
 
 The number of cases in this table does not agree with that shown 
 in Tables X and XI, although the table includes every reaction-time 
 
S02 
 
 DALLENBACH 
 
 at our disposal. The difference is due to three causes. First, the 
 subjective reactions and the failures gave no reaction-times. Secondly, 
 the delicate writing-point of the Jacquet chronometer not infrequently 
 bound on the smoked drum. Since the apparatus was in another 
 room, we had no intimation of this defect until the experiment was 
 ended. Though such cases could be (and were) used when we were 
 concerned only with a correlation between the introspective varia- 
 tion of attention and the accuracy of the reports, they were useless 
 for the correlation between introspective variation of attention and 
 rate of report. And thirdly, the observers under the Double Task 
 Method did not always react as soon as the change was perceived 
 and judgment made. They were not instructed to react immediately; 
 and if a change occurred at a critical point, they might voluntarily 
 delay their reaction until a more favorable opportunity to react pre- 
 sented itself. Such delayed reactions were noted in the observer's 
 introspections, and are naturally omitted from the table. 
 
 The table itself corroborates Table V; there is a positive correla- 
 tion between variation of attention and rate of reaction. The reaction- 
 times in the higher degrees of clearness are shorter, and the mean 
 variations are smaller, than in the lower degrees. The numerical 
 expression of this correlation (for length of reaction-time) and of its 
 probable error is as follows: 
 
 0. 
 
 Correlation " 
 
 P.E. • 
 
 p 
 
 0.88 
 
 0.068 
 
 G 
 
 0-S9 
 
 °-253 
 
 J 
 
 o .60 
 
 .248 
 
 (2) Table XI shows that there is a positive correlation between 
 variation in attention and accuracy of work performed irrespectively 
 of the kind and rate of the objective change. Nevertheless, we have 
 seen that changes of pitch, and rapid changes, are more compelling 
 
 TABLE XV 
 
 Relation Between the Reaction-time in Seconds and 
 
 THE Kind and Rate op the Objective Change 
 
 0. 
 
 Kind 
 
 Rate 
 
 Pitch 
 Av. m.v. No. 
 
 Intensity 
 Av. m.v. No. 
 
 Slow 
 Av. m.v. No. 
 
 Rapid 
 Av. m.v. No. 
 
 p 
 
 G 
 J 
 
 1 .29 .61 71 
 1. 91 .75 42 
 1-24 .53 73 
 
 1.52 .65 48 
 2.28 1 . 40 15 
 1.54 .85 48 
 
 1.78 .98 58 
 
 2.73 i.OI 18 
 
 1.93 .82 49 
 
 •99 -34 61 
 
 1.68 .76 39 
 
 .96 .28 72 
 
 Av., average reaction-time, m.v., mean variation. No., number 
 of cases. 
 
 " In computing this correlation we omitted the data for F under 
 the 8th rubric, for G under the 2d, 6th, 7th, and 8th rubrics, and for J 
 under the last rubric. If these data had been considered in the com- 
 putation the correlation would have been much greater. They are, 
 however, the averages of too few cases: 2, 3, 3, 2, 3, and 4, respec- 
 tively. 
 
THE MEASUREMENT OF ATTENTION 
 
 503 
 
 then changes of intensity or slow changes (see Table XIII). In 
 Table XV, in which the relation between the average reaction-time 
 of the observers' reports and the kind and rate of the objective change 
 appears, this result is further confirmed. 
 
 The average reaction-times and the mean variations are uniformly, 
 for all observers, smaller for pitch than for intensity, and smaller 
 for rapid changes than for slow. These results agree with those of 
 the Single Task Method. 
 
 (3) Table XIII shows the greatest number of right cases under 
 the rubrics pitch and rapid, and conversely the greatest number of 
 wrong cases under the rubrics intensity and slow. Since Table XV 
 shows that the former rubrics have a more rapid reaction than the 
 latter, it would appear that the reaction-time for the right answers 
 was faster than that for the wrong. This inference is borne out by 
 Table XVI. 
 
 TABLE XVI 
 
 The Reaction-time in Seconds and the Mean Variation 
 OF the Right and the Wrong Reports 
 
 Observer 
 
 P 
 G 
 J 
 
 Wrong 
 Av. No. m.v. 
 
 !.45 
 .46 
 
 56 0.79 
 28 I .46 
 62 0.73 
 
 Av., average reaction-time, m.v., mean variation. No., number 
 of cases. 
 
 (4) The effect of the secondary tasks upon attention is shown in 
 Table XVII. The average clearness of the sounds of the variator, 
 the mean variation, and the number of cases for each task are given. 
 
 This table shows the eflfect of the division of attention. The fact 
 that F and J have less changes under o than under i and 2 is due 
 to the nature of our procedure. In some series, only one change oc- 
 curred during the period of observation; and since the order was 
 haphazard, these series might fall to one kind of experiment more 
 frequently than to another. The diflference, however, is small. 
 
 The average clearness of the auditory processes in the normal ex- 
 periments is, for all observers, uniformly higher, and the mean varia- 
 tion is correspondingly lower than in the Double Task experiments. 
 The secondary tasks are, on the average, very eflfective, though the 
 large mean variation shows that there were cases_ in which the audi- 
 tory processes were normally clear. This result is borne out by the 
 introspective reports of the observers. There were many cases in 
 which the change compelled the attention, so that the auditory process 
 momentarily became maximally clear, and the task of counting or 
 adding became obscure. The table shows, further, that the task of 
 adding was uniformly more_ efficient than the task of counting. The 
 larger size of the mean variation may be ascribed in the light of the 
 introspective reports to the more frequent occurrence of " critical 
 points " in the adding. It will be remembered that the rate at which 
 the corks were counted was governed entirely by the observer, while 
 the adding was objectively controlled. 
 
504 
 
 DALLENBACH 
 
 TABLE XVII 
 
 The Average Clearness op the Auditory Stimulus as Affected 
 
 BY Direction of Attention on the Primary 
 
 OR Secondary Task 
 
 Observer 
 
 
 Attention directed to 
 
 o 
 
 [ 
 
 2 
 
 P 
 
 Av. 
 m.v. 
 No. 
 
 88-5 
 87 
 
 7° -3 
 98 
 
 S3 -4 
 
 29-S 
 
 100 
 
 G 
 
 Av. 
 m.v. 
 No. 
 
 85.0 
 93 
 
 48.4 
 
 12 -S 
 
 92 
 
 3S-I 
 17.7 
 
 94 
 
 J 
 
 Av. 
 m.v. 
 No. 
 
 92 .1 
 
 2.8 
 
 82 
 
 2S-S 
 
 7-3 
 100 
 
 21.8 
 8.9 
 
 lOI 
 
 Av., average clearness of tone, m.v., mean variation. No., num- 
 ber of cases under rubric, o, attention directed to tone of variator. 
 I, attention directed to counting of corks. 2, attention directed to 
 adding of figures. 
 
 TABLE XVIII 
 
 Comparison Between the Average Clearness op the Mental 
 
 Processes Involved in Counting Corks and the Degree 
 
 AND Accuracy of the Work Performed 
 
 
 Clearness op Mental Processes 
 
 Observer 
 
 Involved in Counting Corks 
 
 
 100-90 
 
 90—80 
 
 80-70 
 
 70—60 
 
 
 Av. 
 
 44.0 
 
 36.0 
 
 34-2 
 
 27 .0 
 
 
 m.v. 
 
 S-i 
 
 3-2 
 
 2 .2 
 
 .0 
 
 F 
 
 W. 
 
 4 
 
 8 
 
 3 
 
 I 
 
 
 No. 
 
 16 
 
 21 
 
 8 
 
 I 
 
 
 Av. 
 
 32.6 
 
 28.6 
 
 23-S 
 
 21 .0 
 
 
 m.v. 
 
 1-7 
 
 2.7 
 
 2.8 
 
 .0 
 
 G 
 
 "W. 
 
 
 6 
 
 2 
 
 I 
 
 
 No. 
 
 9 
 
 33 
 
 4 
 
 I 
 
 
 Av. 
 
 65.0 
 
 61.3 
 
 58.4 
 
 
 
 m.v. 
 
 3-5 
 
 3-S 
 
 2.8 
 
 
 J 
 
 W. 
 
 6 
 
 9 
 
 2 
 
 
 
 No. 
 
 17 
 
 29 
 
 S 
 
 
 Av., average number of corks counted. m.v., mean variation. 
 W., number of experiments in which the corks were incorrectly- 
 counted. No., number of experiments. 
 
THE MEASUREMENT OF ATTENTION 
 
 505 
 
 (5) Tables XVIII and XIX show the relation between the character 
 and quality of the work performed, and the attention as estimated in 
 terms of attributive clearness. Since the tasks occupied the entire 
 period of observation, the clearness of the processes involved in them 
 was obtained as the average of the period." 
 
 F and G it should be remarked, counted the corks singly; J counted 
 them in pairs. 
 
 The results under Av. and W. confirm our previous conclusions. 
 When the mean variation is considered, however, a discrepancy ap- 
 pears. F and J show a greater m. v. for the higher degrees of atten- 
 tion than for the lower; G alone follows the rule. We can only sug- 
 gest that the irregularity is due to the small number of cases. 
 
 TABLE XIX 
 
 Comparison Between the Averaoe Clearness of the Mental 
 
 Processes Involved in Continuous Adding and the 
 
 Accuracy of the Work Performed 
 
 
 
 Clearness op Mental Processes 
 
 Observer 
 
 Report 
 
 Involved in Continuous Adding 
 
 
 100-90 
 
 90-80 
 
 80-70 
 
 70-60 
 
 
 Correct 
 
 20 
 
 6 
 
 I 
 
 
 
 Nearly correct 
 
 14 
 
 3 
 
 I 
 
 
 P 
 
 Failures 
 
 
 4 
 
 2 
 
 
 
 No. cases 
 
 34 
 
 13 
 
 4 
 
 
 
 Correct 
 
 9 
 
 12 
 
 
 
 
 Nearly correct 
 
 
 18 
 
 2 
 
 
 G 
 
 Failures 
 
 
 4 
 
 4 
 
 I 
 
 
 No. cases 
 
 9 
 
 34 
 
 6 
 
 I 
 
 
 Correct 
 
 13 
 
 S 
 
 2 
 
 
 
 Nearly correct 
 
 S 
 
 6 
 
 
 
 J 
 
 Failures 
 
 6 
 
 II 
 
 4 
 
 
 
 No. cases 
 
 24 
 
 22 
 
 6 
 
 
 In Table XIX the correct additions are grouped under the heading 
 Correct. Those in which there was a mistake of one digit, as 164 
 for 16s, or 2ig for 229, are classified as Nearly correct. And lastly 
 those cases in which the error was greater, or in which the observer 
 lost count of the numbers, are brought together as Failures. The 
 degree of attention is determined, as in the previous table, as the 
 average clearness of the mental processes involved in the adding dur- 
 ing the entire period of observation. 
 
 F and J give the results that we have learned to expect : G's showing 
 
 " This average, though not asked for in the instruction, was volun- 
 tarily estimated introspectively by both F and G, and the value was 
 taken that they ascribed. J gave no such estimation. His average 
 was computed from his estimations prior to and between the moments 
 of change. We may add that the same data were at hand (or the 
 same plan was followed) for estimating the clearness of the mental 
 processes at times when No Reaction was made to an objective change 
 (see Tables I and X). 
 
506 DALLENBACH 
 
 is less regular. During maximal attention, however, all of her addi- 
 tions were reported correctly. In absolute number, it is true, more 
 correct answers were returned in the next lower degree of attention; 
 but at this level we also find not only i8 cases in which the answer 
 contained a slight error, but also 4 cases of failure. In view of the 
 small number of cases, we may be fully satisfied with the general 
 confirmation of our earlier experiments. 
 
 (6) The large number of introspective reports obtained during 
 these experiments, nearly 1400 in all, should yield information con- 
 cerning the number of levels of attention. Titchener, in his Psychol- 
 ogy of Feeling and Attention^ reviews and discusses the literature, 
 and concludes that " a diagram of consciousness would show . . a 
 two-level formation. The surfaces are not smooth; the upper cer- 
 tainly, the lower probably, is creased or wrinkled." These creases or 
 wrinkles correspond to the finer differences of attributive clearness 
 at the two main levels of consciousness. Since this review, two im- 
 portant contributions to the subject have been made. Wirth*" finds, 
 under certain conditions, that there are more than two levels of clear- 
 ness in his own consciousness, and maintains that at any moment of 
 attention all possible degrees of apperception may be represented. 
 Geissler suggests that there are two more or less distinct types of 
 observers: those for whom the dual division is the most natural and 
 most common; and those who as a rule experience several levels of 
 clearness.* Only two of his observers reported a multi-level forma- 
 tion, and he was therefore very cautious in drawing his conclusions. 
 " There seem," he says, " to be two types of the attentive conscious- 
 ness, the dual division and the multi-level formation." Later, in a 
 review and criticism of Wirth's results, he expresses the opinion that 
 Wirth, and probably also Wundt, belong to the latter type." 
 
 Our own results throughout corroborate Titchener's original con- 
 clusions." All of our observers reported, without exception, the dual 
 division : a clear focus and a vague background, which varied recipro- 
 cally." In not a single instance was the multi-level formation even 
 hinted. The distinction of the two types is, then, apparently, a true 
 individual difference, and is not dependent upon external conditions. 
 
 The records thus show to date three observers of the multi-level 
 type: Prof. W. Wirth,°° Prof. M. Bentley," and Dr. H. M. Clark;" 
 
 " Op', cit., 220-242. 
 
 « W. Wirth, Phil. Stud., XX, 1902, 493 f . 
 
 "Of. cit., 528 f.; cf. Titchener, Text-Book, 1911, 302. 
 
 "This Journal, XXI, 1910, 155. 
 
 " Op. cit.,_ 220-242 ; also Text-Book, 276 ff ., 290. 
 
 "The values of the upper and lower levels of attention did not 
 in every case total 100. The discrepancy, however, was never very 
 great, varying only about 5 degrees on the one side or the other 
 There was some individual variation among the observers. F was 
 ordinarily about 5 per cent, short in the total; he never, however, 
 made an error greater than this. G's totals were on the average 5 
 per cent, too large; frequently they were correct; at times they were 
 10 per cent, too large; the value never fell below 100. J's results 
 almost always totaled 100. 
 
 " Cf. op. cit., IV, 1908, 139 f . ; Phil. Stud., XX, 1902, 493 ; and L. R. 
 Geissler, this Journal, XX, 1909, 120-130. 
 
 "Geissler, op. cit., 527 f. 
 
 "Ihid., 528. 
 
THE MEASUREMENT OF ATTENTION 507 
 
 and eight observers of the dual type: Prof. E. B. Titchener,'® Prof. 
 W. H. Pyle," Dr. T. Okabe" Dr. A. de Vries,'" Prof. L. R. Geissler," 
 and our observers. Dr. W. S. Foster, Miss M. E. Goudge, and Mr. J. 
 S. Johnston. 
 
 III. Summary. 
 
 The general results of our study may be summarized as 
 follows : 
 
 (i) Attention may be measured introspectively in terms of 
 attributive clearness. For introspectively distinguished varia- 
 tions of attention (i. e., clearness) are closely paralleled by 
 corresponding differences at the same level in accuracy of 
 work performed, in rate of reaction, and in degree of pre- 
 cision as expressed by the m. v. 
 
 (2) Under our conditions, the time of reaction, as is shown 
 throughout by the high coefficients of correlation, serves ac- 
 curately to measure the attention. 
 
 (3) Changes of pitch and rapid changes are more com- 
 pelling than either changes of intensity or slow changes. 
 The accuracy of judgment for change of pitch and for rapid 
 change is greater than that for change of intensity or for 
 slow change; and, furthermore, the reaction-time to the for- 
 mer changes is smaller than that to the latter. 
 
 (4) A close correlation exists between accuracy and rate 
 of report. 
 
 (5) Under our conditions, distraction, no matter how 
 slight, tends to lessen the degree of attention. 
 
 (6) The difficulty of obtaining a graded series of dis- 
 tractors is very great. In our experience, the action of the 
 distractors is not constant, but varies from day to day, and 
 from observer to observer. 
 
 (7) There are two types of the attentive consciousness: 
 the dual division, and the multi-level formation. These 
 types represent true individual differences, and do not depend 
 upon external conditions of observation. 
 
 (8) In the dual-division type of attention, the levels vary 
 reciprocally. 
 
 °* E. B. Titchener, Lectures on the Experimental Psychology of the 
 Thought-processes, igog, Lect. I. ; also Psychology of Feeling and At- 
 tention, 220. 
 
 "Geissler, op. cit., 527. 
 
 "Ibid., 527. 
 
 "Ibid., 527. 
 
 "Cf. this Journal, XXI, 1910, 154 f. 
 
Cornell University Library 
 BF321 .D14 
 
 Measurement o attention l?X,„!f,9r!,,M-,„''^' 
 
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 3 1924 029 037 426 
 
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