# Design and Research of a Virtual Laboratory for Coding Theory
## 3 Results
### Analysis of the Results of the Student Success Rate
#### 3.2.1 Statistical Hypothesis Checking of the Initial State of the Two Groups
Figure 8: Histogram of both groups at the initial state: (**a**) for the control group; (**b**) for the experimental group. If \(\alpha=0.05\geq\alpha_{s}\) (\(Asymp\)\(Sig.\)), the distribution is not normal; \begin{table}
\begin{tabular}{l l r} \hline \hline \multicolumn{2}{c}{**One-Sample Kolmogorov–Smirnov Test 1 **} \\ \hline \hline \multicolumn{2}{c}{**Average Grade from the**} \\ \multicolumn{2}{c}{**Previous Two Semesters**} \\ \hline N & \multicolumn{2}{c}{59} \\ \hline Normal Parameters 2 **} \\ \hline \hline \multicolumn{2}{c}{**Average Grade from the**} \\ \multicolumn{2}{c}{**Previous Two Semesters**} \\ \hline N & \multicolumn{2}{c}{59} \\ \hline Normal Parameters 3 **} \\ \hline \hline \multicolumn{2}{c}{**Average Grade from the**} \\ \multicolumn{2}{c}{**Previous Two Semesters**} \\ \hline N & \multicolumn{2}{c}{4.6810} \\ \hline \hline \multicolumn{2}{c}{**Std. Deviation**} & \multicolumn{2}{c}{0.64586} \\ \hline \hline \multicolumn{2}{c}{**Absolute**} & \multicolumn{2}{c}{0.096} \\ \hline \multicolumn{2}{c}{**Positive**} & \multicolumn{2}{c}{0.094} \\ \hline \multicolumn{2}{c}{**Negative**} & \multicolumn{2}{c}{\(-0.096\)} \\ \hline \hline \multicolumn{2}{c}{**Test Statistic**} & \multicolumn{2}{c}{0.096} \\ \hline \hline \end{tabular}
\end{table} 
Table 2: Results of the Kolmogorov–Smirnov test for the distribution of mean scores (average grades) for the control group at baseline (at the initial state). \begin{table}
\begin{tabular}{l l r} \hline \hline \multicolumn{2}{c}{**One-Sample Kolmogorov–Smirnov Test 1 **} \\ \hline \hline \multicolumn{2}{c}{**Average Grade from the**} \\ \multicolumn{2}{c}{**Previous Two Semesters**} \\ \hline N & \multicolumn{2}{c}{59} \\ \hline N & \multicolumn{2}{c}{59} \\ \hline \hline \multicolumn{2}{c}{**Std. Deviation**} & \multicolumn{2}{c}{0.77649} \\ \hline \hline \multicolumn{2}{c}{**Absolute**} & \multicolumn{2}{c}{0.102} \\ \hline \multicolumn{2}{c}{**Positive**} & \multicolumn{2}{c}{0.102} \\ \hline \multicolumn{2}{c}{**Negative**} & \multicolumn{2}{c}{\(-0.072\)} \\ \hline \hline \multicolumn{2}{c}{**Test Statistic**} & \multicolumn{2}{c}{0.102} \\ \hline \hline \multicolumn{2}{c}{**Asymp. Sig. (2-tailed)**} & \multicolumn{2}{c}{0.200 **} \\ \hline \hline \end{tabular}
\end{table} 
Table 3: Results of the Kolmogorov–Smirnov test for the distribution of mean scores (average grades) for the experimental group at baseline (at the initial state). Figure 9: Box-plot diagram of both groups at the initial state. If \(\alpha=0.05<\alpha_{s}\) (\(Asymp\)\(Sig.\)), the distribution is normal. From the results thus obtained, it can be seen that for both groups the value of asymptotic statistical significance is \(\alpha_{s}=0.200\). Since \(\alpha=0.05<\alpha_{s}=0.200\), the hypothesis \(\mathbf{H}_{0}\) should be accepted, i.e., the average grade of the control and experimental group students followed a normal distribution. After it has been established that there is a normal distribution of the studied data, a parametric test for two independent samples should be conducted. _Parametric test for two independent samples_  
The empirical level of significance \(\mathbf{\alpha_{s}}\) in SPSS is denoted by Sig., and the _preset_ risk of error by \(\mathbf{\alpha}\) (the most often used value is 0.05). A hypothesis test is performed about the difference between the means of the two independent samples. This check is undertaken by the Student's parametric test (\(t\)-test). The conditions for using Student's \(t\)-test for independent samples are as follows [30]:  
- Application in null hypothesis testing;  
- The comparison parameter (average grade) is quantitative;  
- The comparison parameter has a normal distribution;  
- The two samples must be independent. The current situation meets all these conditions.