# Design and Research of a Virtual Laboratory for Coding Theory
## 3 Results
### Analysis of the Results of the Student Success Rate
#### 3.2.2 Statistical Testing of Hypotheses About the Final State of the Two Groups  
The purpose of this investigation is to determine the impact of the virtual laboratory on student achievement. In the analysis of the results for the final state, an average evaluation of control works of the following three types of tasks will be used:  
* Hamming code by general method;
* Hamming code by matrix method;
* Cyclic code by polynomial method. * Formulation of the hypotheses H\({}_{0}\) and H\({}_{1}\) \(\circ\) Null hypothesis \(H_{0}\)--There is no statistically significant difference; \(\circ\) Alternative hypothesis \(H_{1}\)--There is a statistically significant difference. * _Determination of the risk of error \(\alpha\)_ = 0.05 is chosen for the risk of error. * Checking for normal distribution by hypothesis testing (1)  
Formulation of the hypotheses for a normal distribution:  
* Null hypothesis \(H_{0}\)--the variable has a normal distribution;
* Alternative hypothesis \(H_{1}\)--the variable does not follow a normal distribution. * Testing for normal distribution of the parameter for both groups. The _Kolmogorov-Smirnov test_ is again used to check for normal distribution. The results of the Kolmogorov-Smirnov test for the control and experimental groups are shown in Tables 6 and 7, respectively. \begin{table}
\begin{tabular}{l c c c} \hline \hline \multicolumn{4}{c}{**Average Test Scores**} \\ \hline
**Group** & & **Statistic** & **Std. Error** \\ \hline Mean & & 5.1371 & 0.09150 \\ \cline{2-4}
95\% Confidence Interval for Mean & Lower Bound & 4.9540 & \\ \cline{2-4}
5\% Trimmed Mean & Upper Bound & 5.3203 & \\ \cline{2-4}
5\% Trimmed Mean & & 5.1865 & \\ \cline{2-4}
5\% Median & & 5.2500 & \\ \cline{2-4}
5\% Variance & & 0.494 & \\ \cline{2-4}
5\% Std. Deviation & & 0.70284 & \\ \cline{2-4}
5\% Minimum & & 3.00 & \\ \cline{2-4}
5\% Maximum & & 6.00 & \\ \cline{2-4}
5\% Range & & 3.00 & \\ \cline{2-4}
5\% Trimmed Mean & & 1.00 & \\ \cline{2-4}
5\% Trimmed Mean & & \(-0.899\) & 0.311 \\ \cline{2-4}
5\% Variance & & 0.509 & 0.613 \\ \cline{2-4}
5\% Confidence Interval for Mean & Lower Bound & 5.5443 & \\ \cline{2-4}
5\% Trimmed Mean & Upper Bound & 5.7357 & \\ \cline{2-4}
5\% Trimmed Mean & & 5.6710 & \\ \cline{2-4}
5\% Variance & & 0.135 & \\ \cline{2-4}
5\% Trimmed Mean & & 0.36713 & \\ \cline{2-4}
5\% Variance & & 4.67 & \\ \cline{2-4}
5\% Confidence Interval for Mean & & 6.00 & \\ \cline{2-4}
5\% Trimmed Mean & & 1.33 & \\ \cline{2-4}
5\% Variance & & 0.67 & \\ \cline{2-4}
5\% Variance & & \(-0.962\) & 0.311 \\ \cline{2-4}
5\% Variance & & 0.229 & 0.613 \\ \hline \hline \end{tabular}
\end{table} 
Table 5: Descriptive statistics of both groups at the final state. According to the results of Tables 6 and 7, for the distribution of data of the control and experimental group in the final state, the hypothesis \(\mathbf{H_{1}}\) is accepted, i.e., the data do not follow a normal distribution because for the control group, \(\alpha=0.05>\alpha_{s}=0.012\), and for the experimental group, \(\alpha=0.05>\alpha_{s}=0.000\). After it has been determined that both samples do not follow a normal distribution, a **non-parametric test for two independent samples** should be performed. * If \(\alpha\leq\alpha_{s}\), the hypothesis \(\mathbf{H_{0}}\) is accepted (there is no statistically significant difference \(\overline{X_{c}}=\overline{X_{c}}\));
- If \(\alpha>\alpha_{s}\), the hypothesis \(\mathbf{H_{1}}\) is accepted (there is a statistically significant difference \(\overline{X_{c}}\
eq\overline{X_{c}}\)). This check is performed on a non-parametric basis using the _Mann-Whitney test_. The Mann-Whitney test is based on the ranks of the data. Ranks are assigned to the data, starting with the smallest and proceeding to the largest [18]. The test results are given in Tables 8 and 9.