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given detracting condition, and since, on the other hand, the absolute detraction effect of a given detractor varies inversely with the degree of attention, we may draw the practically important conclusion, that in the use of a detractor under conditions such as described above, for the purpose of measuring attention, it is the absolute effect which is significant, and not the relative effect. The degree of attention is measured (ranked) by the reciprocal of the absolute detraction effect.

This result is confirmed by other results I have obtained, where I have used other methods of obtaining different degrees of attention, e.g., the use of alcohol, difference in age and having the subject perform simultaneous tasks. These are discussed more in detail in Chapter V, but show that where we presumably are dealing with widely different degrees of attention we still often get very nearly the same relative detraction effect but quite different absolute detraction effects, from given detracting conditions.

So far the data of Tables VIII and IX have been considered as showing the effect of variations in interval on the effect upon reaction time produced by a fixed decrease in intensity. The data acquire additional meaning by studying them as showing the effect of variation in intensity on the effect of prolongation of the preparatory interval. For this purpose I have constructed Table XIII. The first line of the table, headed to the left Intensity gives the intensities used. Line A gives the reaction time for the 2 sec. interval. Line B gives the average of the reaction times for all the longer intervals used with the subject in question, i.e., intervals from 4 to 24 secs. inclusive in the case of subject Vs and from 4 to 20 secs. inclusive in the case of subject Ww. This average is an expression of the effect of the longer intervals all taken together. The difference between the average reaction time for the longer intervals and the reaction time for the 2 sec. interval, given in the line headed B-A, is the absolute amount of the average prolongation produced by the unfavorable intervals. In the line headed A/B, the ratio of the reaction time with a 2 sec. interval to the average reaction time

with the longer intervals is given. These ratios, then, serve to show how the relative prolonging effect of the unfavorable intervals varies with the intensity of the stimulus. All reactions are given in o.

TABLE XIII

(Derived from Tables VIII and IX)

Showing how the Prolongation in Reaction Time Produced by Unfavorable Preparatory Intervals Varies with Variation in the Intensity of the Stimulus.

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Line B-A shows that the absolute prolonging effect of the unfavorable intervals increases very markedly with decrease in intensity. In Figures 7 and 8 this is shown by the fact that the curves representing the results with the weaker intensities show greater increase in height as they extend to the right than the curves representing the higher intensities. It is the rise in the curve, that is, the prolongation produced in the reaction time by the unfavorable intervals, that is numerically represented in Table XIII, column B-A, for each of the four intensities.

The relative prolongation produced by the longer intervals, or the relation of the reaction time with the longer intervals to that with the 2 sec. interval, expressed by the ratio A/B, does not show nearly such marked variation with variation in intensity as does the absolute prolongation. Indeed, with the exception of the weakest intensity, the ratio A/B shows very little variation. The relative prolonging effect of a given unfavorable variation in the preparatory intervals may and does remain constant for a considerable range of variation in intensity (exactly so in the

case of subject Vs, for the two highest intensities), but does not do so throughout. The conclusion is uncertain, except when stated to the effect that the relative prolongation in reaction time produced by unfavorable intervals may not appreciably vary with considerable variation in intensity.

The arrangement of Table XIII as of Table XI, readily brings out the bearing of the data of Tables VIII and IX upon attention. Since the prolongation in interval acts as a condition unfavorable to attention, and solely for this reason produces a prolongation in reaction time, it may be spoken of as a detracting condition, or a detractor. This detractor, used with four different degrees of intensity of stimulus, produces four different amounts of absolute prolongation in the reaction time. Consequently, it has acted on four different degrees of attention, and these different degrees of attention have been conditioned by different degrees of intensity. The detraction effect produced by the prolongation in interval varies greatly with the variation in the intensity of the stimulus. From this fact we may conclude that the degree of attention varies with variation in the intensity of the stimulus and presumably varies greatly. Consequently intensity is not only a condition of attention, but we may further particularize to the extent of saying that the four intensities used in this experiment produced four different, and quite plausibly, four widely different, degrees of attention.

The absolute effect of variations in attention, then, produced in the above instance by variations in interval, is greater the weaker the intensity of the stimulus attended to. This result, merely from the point of view of experimental technique, is important, as it shows the desirability of using rather weak intensities if one wishes to study the effect of attention upon reaction time, as so many investigators have done. If one wished, for instance, to determine whether an "attention wave" were demonstrable by means of reaction time, one should use a weak intensity of stimulus, as variations in attention will then produce a much more marked absolute effect upon the reaction time. Similarly, one could expect that differences in the degree of attention among the members of a class of school children would be more notice

able after a certain amount of fatiguing labor than early in the morning when they are fresh, as fatigue would act as a detractor something after the fashion of weak intensities in the above experiment. And just as weak intensity magnifies, as it were, the differences in attention due to differences in preparatory interval, so would fatigue be likely to magnify the differences in the attentions of different individuals, no matter to what these differences might be due. The weak attentions would be further weakened a great deal by any given detractor while the good attentions would be weakened only slightly, so that the result of the detractor would be greater absolute difference between the weak and the good attentions.

Since the four different degrees of intensity condition four different degrees of attention, and since the prolongation in reaction time produced by the unfavorable intervals may be regarded as a detraction effect, we arrive again at the conclusion that the absolute effect of a given detractor varies inversely as the degree of attention, while the relative effect may or may not remain constant. The practically important point concerning the relative detraction effect is that it certainly may remain constant in spite of variation in the degree of attention; and consequently, as already emphasized, it is the absolute and not the relative prolongation, produced by a given detractor, which is to be taken as an index of the degree of attention.

In conclusion, I wish to argue on theoretical grounds for the plausibility of this result, that it is the absolute detraction effect of a given detractor which is to be taken as a measure of attention, in accordance with the law that the attention varies inversely with the degree of the absolute detraction effect—that the relative effect on the other hand may remain very nearly constant for widely different degrees of attention. A given detractor of attention acts as such on attention only, and on no other factor; but the process in which the decrease in efficiency produced by the detractor becomes noticeable, in the present instance a reaction process, is bound to involve other factors than attention, no matter how important the factor of attention may be. Variation in these other factors may produce great variations in

the efficiency. The efficiency is determined only in part by attention. And if attention may play at one time a relatively small part and at another time a relatively large part, and yet the absolute degree of attention remain the same, evidently the same amount of interference with attention in the two cases, nonattention factors not being disturbed, could not possibly produce the same effect upon the two efficiencies. Theoretically, it might not produce equal absolute effects, but would do so if attention operated as a factor which was variable independently of other factors. Now attention may be varied independently of other factors, as in the case of variation in interval, where factors involved in the reaction process other than the degree of attention remain constant. Evidently, then, it is the absolute detraction effect and not the relative which should be used in the measurement of attention.

SUMMARY

The effect of prolongation of the preparatory interval beyond the most favorable interval, using the regular procedure11 is to produce a marked and regular increase in reaction time, and this increase occurs at first at a more rapid rate than later, as the interval is uniformly increased in duration. If we call the reaction time y and the duration of any interval of 2 secs. or over r, we may write the equation y = A + B. log x, in which A and B are determinable constants. This conclusion is identical with a conclusion stated in the summary to Chapter I and based on the results presented in that chapter on reactions to sound stimuli. The effect of variation in the preparatory interval upon the reaction time, therefore, follows the same general law whether we use auditory or visual stimuli. The same law holds for any degree of intensity of stimulus. Of course the constants A and B will vary with different individuals and with different objective conditions.

As regards the effect of the duration of the preparatory interval on the prolongation produced in reaction time by a given decrease in intensity, the data of this chapter lead to the following law: 11 See Chap. II, p. 40.

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