## 2 Materials and Methods
### Software Tool Effectiveness Assessment
#### 3.2.2 Analysis of Statistical Data on the Usability of the Developed Training Software  
Statistical data analysis of solved tasks is a fundamental method for evaluating the effectiveness of software training models. It allows the detection of weaknesses, gives evidence for the pedagogical objectives, and permits targeted model improvements. Besides, statistics prove the scientific reliability of the model and can serve as one more motivational tool for learners to let them see the progress achieved. This approach is essential for developing effective and adaptive learning solutions [36]. The interactive software model for learning Hamming codes using the general algorithm has been successfully implemented in the learning process since 2021. The total number of solved tasks with the model at the time of writing the article is 3097. Figure 18 provides general information on the solved tasks by year. This statistic shows a significant increase in the activity of solving tasks over the years, which may indicate that the software successfully engages users and supports their learning. Figure 19 illustrates the error rates of tasks completed with the Hamming model for the experimental group. The data show that a large proportion of the tasks were done correctly, with 63% of the encoding tasks (Figure 19a) and 59% of the decoding tasks (Figure 19b). Moreover, the proportion of the tasks having more than seven errors in either mode is rather small. The distribution shown suggests that the model is proficient in task handling, with a tendency to reduce the occurrence of errors. However, since this data set represents only the experimental group and does not include comparable data from a control group, no further conclusions can be made about the overall effectiveness of the model. The average times for solving tasks have an important statistical value in analyzing the effectiveness of the model because they provide information about the speed with which students learn and apply their knowledge. Figure 20 illustrates box-plot diagrams of the average times to complete tasks using the Hamming model through the general algorithm. To minimize the influence of random factors or outliers, averages were calculated based on three tasks for both the initial (first three tasks) and final (last three tasks) stages of the student's performance. The trend, as can be seen in Figure 20, shows a decreasing direction of average times for encoding and decoding tasks. In the computation of data presented in Figure 20, tasks of approximately the same complexity were taken into consideration. To this extent, complexity was a function of the number of check bits (\(k\)). The first three tasks and the last three tasks are comparable in complexity since all of them use the same number of check bits (\(k=4\)). This means that with time, students master the concepts better and solve the problems faster, and it can be concluded that there are gains from training with the model developed. Figure 18: Distribution of solved tasks with the Hamming code software model by the general algorithm. The analysis of statistical data shows that the interactive software model for studying Hamming codes using the general algorithm successfully supports learning. During the time interval of the study, 3097 tasks were solved, with an increasing trend in activity. The majority of tasks were solved without errors (63% in encoding and 59% in decoding), and the minimal number of serious errors confirms the effectiveness of the model. The average solving times decrease, which indicates that students master the concepts faster and more effectively. All this gives reason to claim that students gradually master the concepts better and solve the tasks faster, which confirms the positive effect of the software tool on the learning process. Figure 19: Statistics of solved tasks according to errors made when using the Hamming model by the general algorithm, respectively: **(a)** tasks in the encoding mode and **(b)** tasks in the decoding mode.