Monday, May 27, 2013

There are 3 laws in Logarithms in Psychology describing human perception: 
1) Fitt's Law- predicts the time required to rapidly move to a target area is a logarithmic function of the distance to and the size of the target 
2) Hick's Law- proposes a logarithmic relation between the time individuals take for choosing an alternative and the number of choices they have 
3) Weber-Fechner Law- proposes a logarithmic relationship between stimulus and sensation 

These laws are used to calculate human reaction time.

Fitt's Law

T = Average time taken to complete the movement
a = Represents the start and stop time of the device (intercept)
b = Represents the inherent speed of the device (slope)
*Note that and b can be determined by fitting a straight line to the measured data
D = The distance from the starting point to the center of the target
W = The width of the target measured along the axis of motion

Hicks Law 
How is the Hick's Law logarithmic? The more choices one is given, the time taken for the person to choose is exponentially proportional to the number of choices he is given. The time taken increases by the factor of 10.

T = b \cdot \log_{2}(n + 1)

T = Time
b = Constant that can be determined empirically by fitting a line to measure data.
+1 = Because there is uncertainty about whether to respond or not, as well as about which response to make
n = The number of choices given

Weber-Fechner Law