In: Statistics and Probability
Fitt's Law. A robust and highly adopted model of human movement is Fitt's Law. According to Fitt's Law, the time T required to move and select a target of width W that lies at a distance (or amplitude) A is
T = a + b log2(2A/W)
where a and b are constants estimated using simple linear regression. The quantity log2(2A/W) is termed the Index of Difficulty (ID) and represents the independent variable (measured in "bits") in the model. Research reported in the Special Interest Group on Computer-Human Interaction Bulletin (July 1993) used Fitt's Law to model the time (in milliseconds) required to perform a certain task on a computer. Based on data collected for n=160 trials (using different values of A and W), the following least-squares prediction was obtained:
That = 175.4 + 133.2(ID)
a. Interpret the estimates, 175.4 and 133.2.
b. The coefficient of correlation for the analysis is r = .951. Interpret this value.
c. Conduct a test to determine whether the Fitt's Law model is statistically adequate for predicting performance time. Use alpha = .05. (SPECIFICALLY, I WOULD LIKE AN EXPLANATION OF WHAT TO DO WHEN THE CRITICAL VALUE FOR THE STUDENT'S T IS NOT GIVEN IN THE TABLE WHEN THE DEGREES OF FREEDOM (FOR THIS PROBLEM)=n-2=160-2=158. THE t-DISTRIBUTION TABLE STOPS AT 120 FOR DEGREES OF FREEDOM.)
d. Calculate the coefficient of determination, r2. Interpret the result.