# How to know which model fits best among Fitts', Walford's and Shannon Model for given data

How to identify on the basis of `regression graph(R^2)` that which model is better among `Fitts', Walford's and Shannon Model`. We have given a task, which we executed using the tapping application and after calculating the `average movement of time(MT)`, and `average distance of cursor from center to target(MD)`, we calculated the values of `Fitts', Walford's and Shannon model`. It can be seen in the below table. Now we have also implemented a graph, which looks like this. Now, I am confused on the basis of what value should I know which model is best. Whether should I see that the lower the `IDe value(Index of difficulty)`, the best the model is. Or the higher the `R^2` value is, the best the model is. Please help me understanding this thing. Thank you.

• What are you comparing in the models to determine which is best? – Kristiyan Lukanov Oct 30 '16 at 10:45
• @KristiyanLukanov we have a demo application which contains few buttons. and we need to click on that, and we get the movement of time and the distance of cursor from center to target. Now we calculate the ID(index of difficulty) for each model and then we plot the graph of regression. Now we need to show which model suits best to the data that we get by using that app and why – Waqar Ahmed Oct 30 '16 at 11:23

It is unclear what you are looking for when you ask "which model is best". All three models are telling you the same thing.

Saying "the lower the IDe value, the best the model is" or "the higher the R^2 value is, the best the model is", is not accurate.

• The IDe within a formulation represents a bias point on the graph for a given subject.
• A higher regression value within a formulation represents the criterion. In the case of Fitts', this is MT. A particular model may be more predictive for your situation. The way to decide that is to run more studies and compare the results to your regression.

You can't just point to one formulation and say "that's best".

Fitts' model is the original and has been shown to apply under a number of conditions.

The Welford model is a 2-factor variation, which takes target distance and target width as influencers, that can not be directly compared to Fitts' 1-factor equation. You can't plot Fitts' and Welford on the same graph and simply compare the two lines. If you really did calculate width as a seperate influence, looking at your data I'm not sure this was done, Welford's model generally provide greater predictive power.

The Shannon model is another variation. It has arguably become more popular when working in human-computer interaction. At least in part that ISO 9241 recommends its use. So, if you're looking for the "offical" internation standard variation, use Shannon's.

• Hello Sir ..thank you for your answer. I mean to ask, according to that graph and the table, which model fits best the data? so that's why i got confused whether we select model by IDe or R^2. – Waqar Ahmed Oct 30 '16 at 8:35
• I'm still not sure I understand. Did you use the same data to create your regressions? – Evil Closet Monkey Oct 30 '16 at 19:32
• Yes. We use the same data for all 3 models and for regressions. – Waqar Ahmed Oct 30 '16 at 20:23