# Application of Virtual Reality for Learning the Material Properties of Shape Memory Alloys
## 4 Teaching Experiment
### Comparison of Learning Achievement  
After the teaching experiment, an analysis of covariance (ANCOVA) is conducted to compare the learning effectiveness between the two groups to see whether a significant difference exists due to different teaching methods. This study uses the software IBM SPSS Statistics (2018, IBM Corp., Armonk, NY, USA) to analyze the results of the achievement tests. The average scores of the pretest and the posttest for the control group are 55.22 and 60.29, respectively; the average scores of the pretest and the posttest for the experimental group are 54.90 and 67.69, respectively. As we show in Table 2, the experimental group made a progress of 12.79, which is higher than the progress made by the control group (5.07). Figure 18: Different shapes of SMA wire folded by the control group. The Levene's test is used in this study to compare if there is a significant difference in the pretest results of SMA knowledge between the two groups. The results, f = 1.93 and \(p\) = 0.17 \(>\) 0.05, show that no significant difference exists, so the SMA knowledge of the two groups before the teaching activities was approximately equivalent. This study performs a statistical analysis on the pretest and posttest results for both groups by using a paired sample t-test to find out if there is a significant progress made by the students using different learning tools. The results for the control group show that t = 2.98 and \(p\) = 0.004 \(<\) 0.01, revealing the real SMA experiment can enhance the learning achievement effectively. The results for the experiment group show that t = 6.55 and \(p\) < 0.001, revealing the virtual experiment can also enhance their learning achievement effectively (Table 3). When performing the ANCOVA, it is required to satisfy the homogeneity of variance as well as the homogeneity of within-group regression coefficients. * Homogeneity of variance  
The [PERSON]'s test is used in this study to confirm the homogeneity of variance between the control group and the experimental group. The Levene's test results show that the variance has not achieved the significant standard (f = 0.7 and \(p\) = 0.4 \(>\) 0.05) and therefore the assumption for the homogeneity of variance is satisfied. * Homogeneity of within-group regression coefficients  
For both groups, the homogeneity of within-group regression coefficients must be met before performing the ANCOVA. Similarly, the test results have not achieved the significant standard (f = 1.37 and \(p\) = 0.24 \(>\) 0.05). Consequently, the dependent variable, as well as the covariance, are not affected by the independent variable and thus the assumption is satisfied. An ANCOVA is used in the teaching experiment to compare the learning achievements between the experimental group and the control group. It is done by excluding the effect of dependent variable and covariance. The ANCOVA results show that the impact of the teaching method (independent variable) has affected the learning achievement (Table 4). A significant difference exists between the experimental group and the control group (\(p\) = 0.001). Since the learning achievement of the former is higher than that of the latter, it is inferred that learning achievements of students on the SMA knowledge can be improved more effectively by the virtual experiment than the real experiment. \begin{table}
\begin{tabular}{c c c c c c} \hline \hline  & **Achievement** & **Number of** & **Average** & **Standard** & **Standard** \\  & **Test** & **Students** & **Score** & **Error** & **Deviation** \\ \hline \multirow{2}{*}{Control group} & Pretest & 70 & 55.22 & 1.58 & 13.23 \\ \cline{2-6}  & Posttest & 70 & 60.29 & 1.54 & 12.85 \\ \hline \multirow{2}{*}{Experimental Group} & Pretest & 52 & 54.90 & 1.59 & 11.48 \\ \cline{2-6}  & Posttest & 52 & 67.69 & 2.10 & 15.13 \\ \hline \hline \end{tabular}
\end{table} 
Table 2: Descriptive statistics of achievement test.