THEORY

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.

 

where 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).

Example

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.