# 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  
At this point, it is checked whether there is a statistically significant difference in the average grade of the students from the control and experimental groups based on the average grade of the previous two semesters at the beginning of the experiment. The aim is to check whether the students were initially at approximately the same level before the influence of using the software models from the virtual laboratory. * Formulation of the hypotheses H\({}_{0}\) and H\({}_{1}\) The following two hypotheses for the average grades are formulated: \[ \begin{array}{ll}\circ&\text{Null hypothesis $H_{0}$--There is no statistically significant difference;}\\ \circ&\text{Alternative hypothesis $H_{1}$--There is a statistically significant difference.}\end{array} \]  
Figure 7: Structure of the experiment. * Determination of the risk of error \(\alpha\) The risk of error \(\alpha\) The risk of error or significance level (\(\alpha\)) is the probability of rejecting the null hypothesis when it is true. It is set by the researcher and is usually referred to as the significance level. In practice, the risk of error is most often chosen to be \(\alpha=0.05\) or \(\alpha=0.01\), which means that a risk of 5% or 1% is taken to reject the null hypothesis [28]. In this particular case, \(\alpha=0.05\) is chosen as the risk of error. * Null hypothesis \(H_{0}\)--the variable has a normal distribution;
- Alternative hypothesis \(H_{1}\)--the variable does not follow a normal distribution. (2) Testing for normal distribution of the parameter for both groups There are many criteria (tests) for normal distribution, e.g., _Lilliefors test_, _Kolmogorov-Smirnov test_, _Anderson-Darling test_, etc. The Kolmogorov-Smirnov test is a non-parametric statistical test that is based on comparing the empirical cumulative distribution function (CDF) of a sample with that of a reference theoretical distribution. It measures the maximum difference between the two CDFs and is used to assess the similarity between different data sets or to check that they belong to the same theoretical distribution without requiring assumptions about the parameters of the distribution [29]. The results of the Kolmogorov-Smirnov test for a normal distribution of the average grades of students from the control and experimental groups are shown in Tables 2 and 3, respectively. The most important result of the test is the so-called \"asymptotic statistical significance\", which in the SPSS environment is marked with _Asymp Sig_. The decision criterion is as follows: \begin{table}
\begin{tabular}{l c c c} \hline \multicolumn{4}{c}{**Average Grade from the Previous Two Semesters**} \\ \hline
**Group** & & **Statistic** & **Std. Error** \\ \hline Mean & & 4.5829 & 0.10109 \\ \cline{2-4}  & 95\% Confidence Interval for Mean & Lower Bound & 4.3805 & \\ \cline{2-4}  & \multirow{2}{*}{Upper Bound} & 4.7852 & \\ \cline{2-4}  & 5\% Trimmed Mean & 4.5778 & \\ \cline{2-4}  & Median & 4.5000 & \\ \cline{2-4}  & Variance & 0.603 & \\ \cline{2-4} Control & Std. Deviation & 0.77649 & \\ \cline{2-4}  & Minimum & 3.00 & \\ \cline{2-4}  & Maximum & 6.00 & \\ \cline{2-4}  & Range & 3.00 & \\ \cline{2-4}  & Interquartile Range & 1.34 & \\ \cline{2-4}  & Skewness & 0.209 & 0.311 \\ \cline{2-4}  & Kurtosis & \(-\)0.878 & 0.613 \\ \hline Mean & & 4.6810 & 0.08408 \\ \cline{2-4}  & 95\% Confidence Interval for Mean & Lower Bound & 4.5127 & \\ \cline{2-4}  & Interval for Mean & Upper Bound & 4.8493 & \\ \cline{2-4}  & 5\% Trimmed Mean & 4.6699 & \\ \cline{2-4}  & Median & 4.6700 & \\ \cline{2-4}  & Variance & 0.417 & \\ \cline{2-4} Experimental & Std. Deviation & 0.64586 & \\ \cline{2-4}  & Minimum & 3.20 & \\ \cline{2-4}  & Maximum & 6.00 & \\ \cline{2-4}  & Range & 2.80 & \\ \cline{2-4}  & Interquartile Range & 1.00 & \\ \cline{2-4}  & Skewness & 0.131 & 0.311 \\ \cline{2-4}  & Kurtosis & \(-\)0.554 & 0.613 \\ \hline \end{tabular}
\end{table} 
Table 1: Descriptive statistics of both groups at the initial state.