INSTRUMENTS FOR PRESENTING QUANTITATIVE DATA 



85 



ment has received a great amount of re- 

 search attention in order that its precision 

 might be raised as much as possible and its 

 limitations known more fully. These stud- 

 ies have dealt on the one hand with certain 

 perceptual problems in scale reading, num- 

 ber preferences and the like, and on the other 

 with the details of scale design and scale 

 form. 



Number Preferences and Errors 

 of Interpolation 



A person is said to exhibit a number 

 preference, if in a number or scale reading 

 situation, the frequency of his replies for 

 each digit departs systematically from the 

 distribution of digits presented. Thus, if in 

 the number series read from a "randomizing 

 machine," w^hich over a long time period 

 presents the digits 0, 1 ... 9 with equal 

 frequency, some digits occur considerably 

 more often than others, then the person who 

 recorded those data displays a number pref- 

 erence or bias. Such biases have been ob- 

 served among persons using these machines 

 to set up random number tables (44). They 

 appear also in scale reading tasks where 

 subjects are required to interpolate or round 

 their readings (1, 2, 18, 87). It is the rare 

 subject, for example, who uses all the final 

 digits with equal frequency when reading to 

 tenths of scale intervals. The most common 

 pattern, if one dares to generalize from the 

 not always consistent data, shows a massing 

 of readings at the 0, 2, 5 and 8 positions. 

 Scale reading errors are, of course, least 

 frequent when the pointer or index is at a 

 major division mark, and within divisions, 

 are least frequent when the pointer is at the 

 middle of the division range. The increase 

 in reading errors when the pointer is set to 

 values either side of middle (42, 43, 63, 64, 

 67) is in part a function of the aforemen- 

 tioned preferences or rounding tendencies. 



The implication of these data for scale 

 design is that subjects cannot be expected to 

 read to tenths of divisions with complete 

 accuracy. Their tendency, particularly ap- 

 parent as graduation-mark separation be- 



comes small, is to cluster readings around 

 fourths. Quite probably the improvement 

 of scale reading accuracy in situations w^here 

 high precision is demanded requires the use 

 of scales graduated by twos or units. Ex- 

 actly how much improvement these gradu- 

 ation schemes effect is in need of investiga- 

 gation, for, as will be seen below, good 

 comparative data on reading accuracy are 

 available only for scales graduated by fives 

 and by tens. 



Details of Scale Design 



At least three criteria have been applied 

 in evaluating the scale-design variables to 

 be considered in the following paragraphs. 

 Which design permits the fastest reading? 

 Which design is read with the fewest errors? 

 Which design is read with the fewest large, 

 and generally serious, errors? 



Graduation-Mark Separation, Interval Val- 

 ues, and Scale Length. Research evidence 

 has recently been accumulating w^hich will 

 assist designers in spacing graduation marks 

 and in choosing interval values for scales on 

 instruments which are to be read within 

 stated accuracy limits. Such scale design, 

 based on operator reading characteristics and 

 upon stated performance standards, will 

 mark a real advance over the relatively 

 arbitrary scaling principles employed in the 

 past. 



The primary questions which have been 

 raised by these recent experiments are: (1) 

 What is the relative speed and accuracy of 

 reading scales which are alike in terms of the 

 value assigned to the smallest subdivision 

 but W'hich differ in the scale length devoted 

 to each subdivision? (2) What is the rela- 

 tive speed and accuracy of reading scales 

 which are alike in terms of the scale length 

 devoted to a given number of scale units 

 but which differ in the number of subdivi- 

 sions and hence in the value of the subdivi- 

 sions used? (3) Does over-all scale length 

 or dial size interact with the forego- 

 ing effects? 



For the design of scales which are to be 

 read to the nearest unit, the only graduation 



