Update fitts_law_study.md

Exercices/Fitt's Law/fitts_law_study.md

@@ -31,6 +31,119 @@ I selected the same "default" parameters as Cecile :
 - Number of trials : 6
 
 Then, I plotted my results and Cecile's in the same graph. 
+Here are the results, the blue dots are from my trial and Cecile have red dots :
+
+![Test 1](https://gitlab.ensimag.fr/floresmo/Mosig-SMPE-2021/-/blob/master/Exercices/Fitt's%20Law/result_test_1.png)
+
+We can see the results are very different :
+- first, Cecile doesn't have any value of ID = 6 
+    - maybe she forgot to put it in her results ?
+    - maybe she made a mistake in the parameters she gave us ?
+- the slope of the regression lines are not at all the same 
+    - for my trial (blue), I am faster at the begining but I also take more time at the end 
+    - Cecile takes more time but seems more consistant in her results
+
+From that experiment, I must say that it was really hard for me to do the experiment.
+- I have a terrible vision, then clicking on a 1px line was hell.
+- My screen may have been to bright, so it was very exhausting for my eyes
+
+Because of that, I choose to do an other "witness study" that will be used as a base of comparing parameters... but with different parameters that will be less exhausting to test.
+
+### Test 2 : Witness study 
+The parameters I choose have to be greater than Cecile's (to be less exhausting to experiment), but it also need to give a wild range of IDs. I choose to have a range from 2 to 5, with the following parameters :
+- Width : 5,10,15 px
+- Distance : 50,100,150,200 px
+- Number of trials : 6
+
 Here are the results :
 
-![Test 1](./results_test_1.png)
+![Test 2](https://gitlab.ensimag.fr/floresmo/Mosig-SMPE-2021/-/blob/master/Exercices/Fitt's%20Law/result_test_2.png)
+
+We can see that the task was easier for me to perform, even if the ID are the same. We can already conclude that :
+- different width an distance can make the experiment harder / easier, even with the same IDs. 
+    - The Fitt's Law depends on different parameters than just Width, Distance and number of trials.
+
+I then wanted to test the effect of the distance : do I take more time to perform the experiment if the distance doubles ?
+Hypothesis : I may take a little more time, and that time will the proportionnal to the distance.
+
+
+### Test 3 : Doubling the distance
+I performed the same experiment as the Test 2, except that I double the distance for each trial :
+- Width : 5,10,15 px
+- Distance : 100,200,300,400 px
+- Number of trials : 6
+
+Here are the results (with blue dots : test with double distance and red dots : witness test) :
+
+![Test 3](https://gitlab.ensimag.fr/floresmo/Mosig-SMPE-2021/-/blob/master/Exercices/Fitt's%20Law/result_test_3.png)
+
+Surprisingly, the two experiment give almost the exact same results !
+I then had a look on the data and I noticed that the "test 3" gained one level of difficulty, comparing to "test 2".
+
+Data from test 2 : 
+| MT (mean) | ID |
+| ------ | ------ |
+| 385 | 2 |
+| 595.5 | 3 |
+| 723.75 | 4 |
+| 891 | 5 |
+
+Data from test 3 : 
+| MT (mean) | ID |
+| ------ | ------ |
+| 561.5 | 3 |
+| 704.75 | 4 |
+| 911 | 5 |
+| 1054.5 | 6 |
+
+As I compared only similar IDs (I intentionally dropped ID 2 from "test 2" and ID 6 from "test 3" to really be able to compare the curves), then I have the same results. 
+
+My conclusion to this experiment is that doubling the distance is totally adding a level of difficulty in the task, and that I should be more careful on the data I work on. 
+
+The conclusion of this test is that doubling the distance definitely make the experiment harder, here I gain 1 ID.
+
+Then, I wanted to test the Fitt's Law on a different device. I am used to use the mouse, but what about the tactile pad ?
+Hypothesis : Using the tactile pad will increase a lot the difficulty, I will take more time to do the same task as "test 2".
+
+### Test 4 : mouse vs tactile pad
+I will keep the exact same parameters from the witness experiment, to see if the device have an impact on my results.
+- Width : 5,10,15 px
+- Distance : 50,100,150,200 px
+- Number of trials : 6
+
+Here are the results (blue dots : with tactile pad ; red dots : witness test, with mouse) :
+
+![Test 4](https://gitlab.ensimag.fr/floresmo/Mosig-SMPE-2021/-/blob/master/Exercices/Fitt's%20Law/result_test_4.png)
+
+We can very easily see that the slopes of the two tests is are very different. 
+I took more time with the tactile pad, and the more the difficulty increases, the more I take time comparing to the mouse.
+
+I can conclure from this that using a different device can increase the "starting" difficulty, and difficult tasks will be even more difficult.
+
+Finally, I wanted to see if the bihavior of the tester has an impact on the results. 
+During the witness test, I wasn't trying to be particularly fast, or precise. What if I try to be very precise ?
+Hypothesis : I will take more time to archieve the same results as before, and the more the difficulty increase, the more I will take time.
+
+### Test 5 : "normal" bihavior vs "safe" bihavior
+I will keep the exact same parameters from the witness experiment, to see if my bihavior have an impact on my results.
+- Width : 5,10,15 px
+- Distance : 50,100,150,200 px
+- Number of trials : 6
+
+Here are the results (blue dots : with safe bihavior ; red dots : witness test, with "normal" bihavior) :
+
+![Test 5](https://gitlab.ensimag.fr/floresmo/Mosig-SMPE-2021/-/blob/master/Exercices/Fitt's%20Law/result_test_5.png)
+
+The graph confirms my hypothesis : 
+- globally I take more time to perform the same task 
+- when the task is easy, I don't take that much time 
+- when the task gets harder, I take a lot more time 
+
+## Conclusions 
+
+Here I sum up all the conclusion I can get from my experiments :
+- Globally, the Fitt's Law varies on a lot of parameters :
+    - the "initial" parameters, such as distance (see Test 3)
+    - it can also vary on more "human" parameters, such as the bihavior of the tester (see Test 5)
+    - Moreover, it can vary on the device we use to perform the task (see Test 4)
+