# Visuo-Haptic Simulations to Understand the Dependence of Electric Forces on Distance
## 4 Data Analysis and Results
### Learning Gains  
A study of the students' learning gains after working with the visuo-haptic scenarios was performed. Average students' learning gains were calculated, using Equation (4), as the difference between the post-test and the pre-test average grades of each section and also for the entire student sample. \[<G>\ =\ <Post>\ -\ <Pre> \tag{4}\]  
Relative learning gains were then also calculated using Equation (5) [30]. \[<G_{rel}>\ =\ \frac{<Post>\ -\ <Pre>}{100-<Pre>} \tag{5}\]  
This relation represents the fraction of the absolute learning gain relative to the maximum learning gain that can be attained. The results are presented in Table 5.  
As it can be seen from Table 5, all EM sections obtained considerable absolute and relative learning gains. In Figure 8, a graphical comparison between the average pre-test and average post-test grades for the five sections indicated in Table 2 was made, considering the 5 questions mentioned above. In general, the average post-test is about 10 points higher tha \begin{table}
\begin{tabular}{l l} \hline \hline
**ID** & **Question** \\ \hline \multirow{3}{*}{\(QP1\)} & I consider that the simulator (a,b,c) helped me to better understand the way in which \\  & electrical forces behave between a point charge and \((a)\) another point-charge, \((b)\) an infinite \\  & charged line and \((c)\) an infinite charged plane. \\ \hline \(QP2\) & I consider that the manipulation of the simulator (a,b,c) was simple and intuitive. \\ \hline \(QP3\) & I consider that the visualization of the simulator (a,b,c) is appropriate and attractive. \\ \hline \(QP4\) & I consider that overall, the visuo-haptic simulations helped me to better understand electric \\  & forces between charge systems. \\ \hline \(QP5\) & I recommend to use visuo-haptic simulators to learn \((a)\) other electricity and magnetism \\  & themes and \((b)\) other Physics courses. \\ \hline \hline \end{tabular}
\end{table} 
Table 4: Questions of the exit perception survey. \begin{table}
\begin{tabular}{c c c c c c c c} \hline \hline
**Section** & \(N\) & \multicolumn{3}{c}{**Pre**} & \multicolumn{3}{c}{**Post**} & \(<G>\) & \(<G_{rel}>\) \\  & & **Mean** & **Std. Dev** & **Mean** & **Std. Dev** & **\% G** & \% G** \\ \hline EM1 & 27 & 69.6 & 15.1 & 85.2 & 17.2 & 15.6 & 0.512 \\ EM2 & 21 & 77.1 & 20.3 & 88.6 & 18.0 & 11.4 & 0.500 \\ EM3 & 21 & 74.3 & 15.7 & 87.6 & 11.8 & 13.3 & 0.519 \\ EM4 & 18 & 72.2 & 15.6 & 82.2 & 15.2 & 10.0 & 0.360 \\ EF1 & 24 & 95.0 & 12.2 & 96.7 & 11.3 & 1.67 & 0.333 \\ Total sample & 111 & 78.0 & 18.2 & 88.3 & 14.6 & 10.5 & 0.472 \\ \hline \hline \end{tabular}
\end{table} 
Table 5: Absolute and relative learning gains. A study of learning gains per question was also carried out for the total student sample. Each question was graded as 1 if the choice was correct or 0 if it was incorrect. Then the average grade per question was calculated for both the pre-test and post-test, and relative gains per question were then calculated. The corresponding results are presented in Table 6. Therefore, the relative learning gain was now calculated using Equation (6). \[G_{rel}\ =\ \frac{Post-\ Pre}{1-Pre} \tag{6}\]  
where \(Pre\) and \(Post\) refer to the proportions of correct answers in each question. From Table 6, it can be seen that in questions \(Q1\) and \(Q2\) (attractive or repulsive nature of electric forces) the learning gains were zero. For questions \(Q4\) (line charge simulator) and \(Q5\) (plane charge simulator), the absolute and relative gains were very good, in particular for \(Q5\), where the relative learning gain is very close to 1. On the other hand, a slight negative learning gain is observed for question \(Q3\) regarding the distance dependence for point charges. Therefore, a relative learning _loss_ was recalculated for \(Q3\) with Equation (7). This represents the ratio between the average absolute learning loss and the maximum possible grade loss, the latter being the average pre-test value.