Editing Fitts's law (section)

== Adjustment for accuracy: use of the effective target width ==

An important improvement to Fitts's law was proposed by Crossman in 1956 (see Welford, 1968, pp.&nbsp;147–148)<ref name=Welford>{{cite book |last=Welford |first=A. T. |date=1968 |title=Fundamentals of Skill |publisher=Methuen}}</ref> and used by Fitts
in his 1964 paper with Peterson.<ref name=Fitts1964>{{cite journal |last1=Fitts |first1=Paul M. |last2=Peterson |first2=J. R. 
|title=Information capacity of discrete motor responses |journal=Journal of Experimental Psychology |volume=67 |issue=2 |date=1964 |pages=103–112 |doi=10.1037/h0045689|pmid=14114905 }}</ref> With the adjustment, target width (''W'') is replaced by an effective target width (''W''<sub>e</sub>).
''W''<sub>e</sub> is computed from the standard deviation in the selection coordinates gathered over a sequence of trials for a particular ''D-W'' condition. If the selections are logged as ''x'' coordinates along the axis of approach to the target, then

<math display="block">W_e = 4.133 \times SD_x</math>

This yields

<math display="block">\text{ID}_e = \log_2 \Bigg(\frac{D}{W_e}+1\Bigg)</math>

and hence

<math display="block">\text{IP} = \Bigg(\frac{ID_e} {MT}\Bigg)</math>

If the selection coordinates are normally distributed, ''W''<sub>e</sub> spans 96% of the distribution. If the observed error rate was 4% in the sequence of trials, then ''W''<sub>e</sub> = ''W''. If the error rate was greater than 4%, ''W''<sub>e</sub> > ''W'', and if the error rate was less than 4%, ''W''<sub>e</sub> < ''W''. By using ''W''<sub>e</sub>, a Fitts' law model more closely reflects what users actually did, rather than what they were asked to do.

The main advantage in computing ''IP'' as above is that spatial variability, or accuracy, is included in the measurement. With the adjustment for accuracy, Fitts's law more truly encompasses the speed-accuracy tradeoff. The equations above appear in ISO 9241-9 as the recommended method of computing ''throughput''.