4 BELL SYSTEM TECHNICAL JOURNAL 



a large number of votes will show a plurality for the wider band, the margin 

 of choice increasing as the difference in band width is made greater. A 

 significant measure of the detectable difference in band width will be taken 

 to be that difference such that 75% of the observers correctly select the 

 wider band and 25% wrongly select the narrower band. This difference in 

 band widths will be designated one "difference limen." The sensory effect 

 of a change of one difference limen will be called one "liminal unit". 



The significance of the vote of 75 to 25% is assumed to be as follows: On 

 a particular test some of the observers can detect the difference between the 

 conditions while the remainder will guess. Of the latter, half are likely to 

 guess right and half wrong. When 25% vote wrongly they are assumed to 

 be guessing and must be paired with another 25% who also guessed but 

 happened to guess right. Therefore a vote of 75 to 25% is taken to indicate 

 that 50% of the observers were guessing and the remainder could actually 

 detect the difference. The difference limen may now be more specifically 

 defined as that difference in band widths which is detectable to half the ob- 

 servers. 



It may be commented that this attempt to explain the definition of ''lim- 

 inal unit" is perhaps over-simple. The observers themselves are frequently 

 uncertain whether they are guessing or are influenced in their choice by some 

 minute difference. The test could be done with a single observer, repeated 

 many times to obtain the same number of observations as with a group. 

 When the conditions are nearly equal he will vote about as often one way as 

 the other, but as the difference between the conditions is increased he will 

 vote a larger per cent of the time correctly for the wider band, just as did 

 the group. When the two conditions are separated by one difference limen 

 he will vote correctly 75% of the time and wrongly 25% of the time, which 

 may be said, in line with the argument given earlier, to indicate that he is 

 guessing half the time and can discern the difference half the time. The 

 difference limen could therefore be defined as that threshold difference for 

 which there is an even chance of its discernment by a listener. 



Having chosen a method of expressing the results, the analysis can now 

 be attacked. The first step is to group together all tests on similar types of 

 program material, and to determine for each band width comparison the 

 per cent of votes for the wider and narrower band, respectively. The data 

 thus obtained for music and speech are shown by the solid curves of Figs. 

 2 and 3. A curve labeled 8 kc, for example, shows the per cent of the total 

 votes which selected as the wider each of the other band widths to which 8 

 kc. was compared. The points, although somewhat irregular, fell syste- 

 matically enough to permit drawing the smooth curves with the application 

 of some judgment and having due regard to the necessary symmetry be- 

 tween them. (For example, the 8 kc. curve at an abscissa of 5 kc. must 



