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2. Weber's Law

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Weber's Law


Understanding human ability of noticing minute differences in shapes, colors, heights etc can help graphic designers in designing better interfaces and interactions. Perceptual ability to make out differences in objects, colors, shapes, texts etc influences the cognition and the interaction efficiency.


Can we perceive the difference between a line of 10cm length against a line of 10.05 cm ? Can  we  perceive  the  difference  in  holding  a   weight  of    10.0 kg  against  a     weight  of  10.05 kg ?  This  incremental threshold for detecting the difference in any observed value is an important human  factor  useful  in  designing  GUIs.


For  an  initial  stimulus  value  I  ( say  10 cm )   let  the   increment  threshold  for  detecting  a difference be ΔI ( say 0.05 cm ). 


Weber's  Law  ( E. H. Weber, in 1834 )  states  that  the  ratio of  ΔI/I  is  constant  for  a  specific  measure.


ΔI  =  Differential  threshold                I =  Initial stimulus intensity                K=  Weber  fraction

Weber’s Law states that the size of the just noticeable difference (jnd) is a constant proportion(K times) of the original stimulus value. It is the minimum amount by which stimulus intensity must be changed in order to produce a noticeable variation in sensory experience.

Thus    there  is  a  linear  relationship  between   differential  threshold  and  the  initial  stimulus  value  as depicted  in  the  figure  below.


The slope of the line is the Weber fraction (aka Fechner fraction). 




Let two circles filled with same color and intensity be displayed side by side. Suppose the initial color intensity is 100 for both circles. Now let  us  keep changing the color intensity of any one circle incrementally till the user perceives noticeable change  or  difference  in  their  intensities. We  will stop at this point and record this new color intensity. Let  this new value be 110. Thus the differential   threshold (jnd)  = 10 (ΔI = 110 – 100 ) and the Weber’s constant in this  case  would  be K = 10/100 = 0.1. If the Weber fraction for discriminating changes in stimulus is a constant proportion equal to 0.1 then the size of the just noticeable difference for a spot having an intensity of 1000 would be 100.


Some interesting human-sense JNDs (Just Noticeable Differences) are tabulated below :


Pitch: 1/333               Brightness: 1/60              Lifted Weights: 1/50

Loudness: 1/10          Pressure on skin: 1/7      Taste: 1/5


( Reference :  http://www.richardbrice.net/webers_law.htm )


Notice how our sensitivity to pitch is 70 times more acute than our sense of taste.


Webers Law as applied to user interfaces


Weber’s Law can be used for  various sensory modalities in GUIs such as brightness, loudness, line length, visual weight of fonts in typography, color matching etc. Many times large amount of information is required to be displayed on a limited size computer screen. Information is displayed in various forms viz. text, pictures, drawings, maps, graphs, videos etc. Poor visual design of user interface lacks the ability of differentiating between two close enough visual stimuli e.g. two lines with different thicknesses in a map (for wide roads and narrow lanes).What is  this  threshold  of  line thickness that  may  lead  to  noticeable difference  is  governed  by Weber’s law.The threshold of noticeable difference between color shades is also governed by Weber’s law.


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