## 2 Materials and Methods
### Software Tool Effectiveness Assessment
#### 3.2.1 Pedagogical Experiment for Student Success
* ANCOVA analysis  
ANCOVA (analysis of covariance) is a statistical method that assesses the influence of independent variables on a dependent variable, while at the same time reducing the influence of external variables (covariates) that may have an impact on the dependent variable, thereby isolating the effect of the main independent variable [34]. In the present case, it is suitable for studying the influence of the software tool on the success of students (grades from control works using Hamming codes--the general method), considering their previous academic success (average grade of the previous two semesters). This allows for the correction of differences in initial levels of knowledge, providing a more accurate assessment of the effectiveness of the tool compared to the traditional method. The definition of the ANCOVA variables for the current situation is as follows:  
* Dependent variable: Assessment (grade) from the control work. * Independent variable: Group, i.e., learning method (traditional method vs. interactive software). * Covariates:
* Average grade from the previous two semesters. * Period (2019-2020 vs. 2021-2022). \begin{table}
\begin{tabular}{l c c c c} \hline \hline \multicolumn{2}{c}{**Decsitives**} \\ \multicolumn{2}{c}{**Hamming Code GA Average Test Scores**} \\ \hline \multicolumn{2}{c}{**Group**} & \multicolumn{2}{c}{**Control**} & \multicolumn{2}{c}{**Experimental**} \\ \hline \multicolumn{2}{c}{**Statistic**} & \multicolumn{1}{c}{**Std. Error**} & \multicolumn{1}{c}{**Statistic**} & \multicolumn{1}{c}{**Std. Error**} \\ \hline Mean & & 5.1271 & 0.11297 & 5.6398 & 0.06818 \\ \hline
95\% Confidence Interval for Mean & Lower Bound & 4.9010 & 5.5033 & \\ \hline Upper Bound & 5.3533 & & 5.7763 & \\ \hline
5\% Trimmed Mean & 5.1879 & & 5.6926 & \\ \hline Median & 5.0000 & & 6.0000 & \\ \hline Variance & 0.753 & & 0.274 & \\ \hline Std. Deviation & 0.86773 & & 0.52373 & \\ \hline Minimum & 3.00 & & 4.00 & \\ \hline Maximum & 6.00 & & 6.00 & \\ \hline Range & 3.00 & & 2.00 & \\ \hline Interquartile Range & 1.50 & & 0.50 & \\ \hline Skewness & \(-\)0.735 & 0.311 & \(-\)1.274 & 0.311 \\ \hline Kurtosis & \(-\)0.332 & 0.613 & 0.661 & 0.613 \\ \hline \hline \end{tabular}
\end{table} 
Table 6: Results of the descriptive statistics from the control works using the Hamming codes—the general algorithm (final state). \begin{table}
\begin{tabular}{l c c c c} \hline \multicolumn{2}{c}{**Descriptives**} \\ \multicolumn{2}{c}{**Average Grade from the Previous Two Semesters**} \\ \hline \multicolumn{2}{c}{**Group**} & \multicolumn{2}{c}{**Control**} & \multicolumn{2}{c}{**Experimental**} \\ \hline \multicolumn{2}{c}{**Statistic**} & \multicolumn{1}{c}{**Std. Error**} & \multicolumn{1}{c}{**Statistic**} & \multicolumn{1}{c}{**Std. Error**} \\ \hline Mean & & 4.5829 & 0.10109 & 4.6810 & 0.08408 \\ \hline
95\% Confidence Interval for Mean & Lower Bound & 4.3805 & & 4.5127 & \\ \hline Upper Bound & 4.7852 & & 4.8493 & \\ \hline
5\% Trimmed Mean & 4.5778 & & 4.6699 & \\ \hline Median & 4.5000 & & 4.6700 & \\ \hline Variance & 0.603 & & 0.417 & \\ \hline Std. Deviation & 0.77649 & & 0.64586 & \\ \hline Minimum & 3.00 & & 3.20 & \\ \hline Maximum & 6.00 & & 6.00 & \\ \hline Range & 3.00 & & 2.00 & \\ \hline Interquartile Range & 1.50 & & 0.50 & \\ \hline Skewness & \(-\)0.735 & 0.311 & \(-\)1.274 & 0.311 \\ \hline Kurtosis & \(-\)0.332 & 0.613 & 0.661 & 0.613 \\ \hline \hline \end{tabular}
\end{table} 
Table 5: Descriptive statistics results for the previous two semesters (initial academic level). One of the important conditions for using ANCOVA is that there is equality of variances of the dependent variable [34]. The results of the test for equality of variances are given in Table 7 using the [PERSON]'s test. In the [PERSON]'s test, the hypotheses are formulated as follows: \(H_{0}\) (null hypothesis)--the variances of the two groups are homogeneous; \(H_{1}\) (alternative hypothesis)--there is a violation of the homogeneity of variances in the groups. From Table 7, the \(p\)-value (in SPSS it is denoted by Sig.)