Dave Mudgett, April 7, 2002

Two simple versions of Fitt's law (taken from Card, Moran and Newell, 1983, *The Psychology of Human-Computer
Interaction*) compute the time to move to a target as approximately

Formula 1: time_to_target = K1 * log

_{2 }{(distance_to_target / target_size) + K0}Formula 2: time_to_target = K2 * log

_{2 }(2* distance_to_target / target_size)

These formulae are different, but taking the log of the result means they are quite similar in the end. If you look around, you will find that there are other corrections available, but they all use the log function and distance_to_target / target_size.

There are also more complete and thus more accurate versions, but consider these models for now, since they illustrate the basic relationships.

distance_to_target is usually taken to be to the middle of the target, and the target's size is measured in the direction of movement. Clearly, target width orthogonal to movement has some role (or else a 200 item pie menu would be fast indeed), but is not included in this simple equation.

Experiment

Run 100 trials of the Fitts' law demo in the labs/lab8 subdirectory, carefully tabulating distance_to_target, target_size and time_to_target. This should not take long if you stay organized and subdivide responsibilities by having one person make the trials, another read the data off the screen, and a third to tabulate the data as it is read.

Now use any linear regression program to fit your data to these models. There are a number of Java applets and other types of programs on the web.

I like the applet at the West Virginia University Statistics Department: http://www.stat.wvu.edu/SRS/Modules/Applets/Regression/regression.html

- I've put a copy of this program temporarily in the labs/lab9 subdirectory

Also, the following script at the University of Oregon works nicely: http://pmo-sun.uoregon.edu/~dmason/stat/correl.html

- Remember that these programs fit a **linear** equation to your data, so you will need to transform your
data somehow.

Write-up

Write a brief report on your results. It should be no more than 3-4 pages plus one page containing a table of your data. You should include

1) A brief introduction, explaining what you are doing and why.

2) A section explaining how you obtained your data.

3) A section explaining how you fit a model to the data, addressing the questions outlined below.

4) Your conclusions, which should explain very briefly what the result was. You should explain what worked and what didn't work so well.

Questions

In the write-up of your results, answer the following questions:

1) How does your data fit these models? Which model is better? Would a slightly different model fit your data better?

- Read briefly about linear regression. There are lots of resources on the web.

For example, at George Mason University: http://cne.gmu.edu/modules/dau/stat/regression/linregsn/linregsn_frm.html

- Pay particular attention to the idea of **correlation**. The correlation coefficient, r or coefficient
of determination, r^{2}, measure how well your model fits the data. If r^{2} is close to 1, it
means that your fitted equation explains a high percentage of the variations of the in the data.

2) Can you estimate the value of the constants K1 and K0 (for formula 1) and K2 (for formula 2)? Again, remember
that the linear equation you fit needs to be re-transformed back into the logarithmic form.