# A Virtual Experiment for Learning the Principle of Daniell Cell Based on Augmented Reality
## 3 Empirical Research
### Analytical Results  
The statistical software SPSS was used to analyze the achievement test results. The descriptive statistics of the pre-test and post-test scores for the two groups are listed in Table 2.  
This study used the Mann-Whitney U test to check if a significant difference in the initial abilities existed between the two groups. The results in Table 3 show that \(p=0.42>0.05\), indicating no significant difference, and thus their background knowledge was about the same before the experiment. To investigate if the students could make significant progress after conducting the experiment, this study used the Mann-Whitney U test to analyze the pre-test and post-test scores of both groups (Table 4). For the experimental group, the asymptotic significance \(p<0.001\), showing the virtual experiment can effectively improve the learning achievement. For the control group, the asymptotic significance \(p=0.014\), indicating the real experiment can also improve the learning achievement. In this study, the analysis of covariance (ANCOVA) was used to analyze whether a significant difference exists in the learning effectiveness between the control group and the experimental group. Before performing the ANCOVA, the assumptions for the homogeneity of variance and within-group regression coefficients had to be satisfied. * Homogeneity of variance The Levene test was used to check if there is homogeneity of variance between the two groups. The analytical result shows \(p=0.57>0.05\), indicating the variance has not achieved the significant level, and thus the assumption for the homogeneity of variance is satisfied. * Homogeneity of within-group regression coefficients Before performing the ANCOVA, the homogeneity of within-group regression coefficients must be satisfied. The analytical result shows \(p=0.60>0.05\), also without achieving \begin{table}
\begin{tabular}{c c c c} \hline \hline \multirow{2}{*}{**Group**} & \multicolumn{2}{c}{**Mean Rank (Sum of Rank)**} & \multirow{2}{*}{**Asymptotic Significance (\(p\))**} \\ \cline{2-2} \cline{4-4}  & **Pre-Test** & & & **Significance (\(p\))** \\ \hline Experimental group (N = 26) & 6.00 (18.00) & 13.43 (282.00) & 0.000 *** \\ \hline Control group (N = 24) & 9.21 (64.50) & 13.85 (235.50) & 0.014 * \\ \hline \hline \end{tabular}
\end{table} 
Table 4: The Mann–Whitney U test results between pre-test and post-test. \begin{table}
\begin{tabular}{c c c c c c} \hline \hline
**Group** & **Test** & **Students** & **Average** & **Standard Deviation** & **Progress** \\ \hline Experimental group & Pre-test & 26 & 43.54 & 20.87 & 15.69 \\  & Post-test & 26 & 59.23 & 23.54 & 15.69 \\ Control group & Pre-test & 24 & 38.17 & 19.31 & \\  & Post-test & 24 & 52.67 & 28.05 & 14.50 \\ \hline \hline \end{tabular}
\end{table} 
Table 2: Descriptive statistics of the pre-test and post-test scores. \begin{table}
\begin{tabular}{c c c c} \hline \hline \multicolumn{2}{c}{**Mean Rank (Sum of Rank)**} & \multirow{2}{*}{**Mann-Whitney U**} & \multirow{2}{*}{**Asymptotic Significance (\(p\))**} \\ \cline{2-2} \cline{4-4}
**Experimental Group** & & & **Control Group** \\
**(N = 26)** & & **(N = 24)** & & **Significance (\(p\))** \\ \hline
27.10 (704.50) & 23.77 (570.50) & 270.50 & 0.42 \\ \hline \hline \end{tabular}
\end{table} 
Table 3: The Mann–Whitney U test results between the two groups. the significant level. Therefore, the covariance (pre-test score) and dependent variable (post-test score) were not influenced by the independent variable (experimental operation) and thus the ANCOVA could be performed. * ANCOVA results  
After excluding the effects of the covariance on the dependent variable, the impact of independent variable on the learning effectiveness was calculated as \(p\) = 0.70 \(>\) 0.05 (Table 5), showing no significant difference between the two groups. As a result, both the virtual experiment and the real experiment can improve students' learning achievement effectively.