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Statistical Evaluation of Learner Control, Academic Performance, Effort, and Perceived Agency

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Comparative Evaluation of Learner-Controlled and System-Controlled Instruction

The study investigates the impact of learner control on pupils’ academic performance in the context of learning about power circuits. Specifically, two groups were studied: the “Student Control” group, in which participants had the freedom to determine the sequence of tasks, and the “System Control” group, in which tasks were automatically sequenced. The primary focus of the analysis was to evaluate differences in post-test academic performance and the levels of perceived effort and agency between the two groups.

Descriptive Patterns in Academic Performance, Effort, and Agency

Table 1: Descriptive Statistics

Descriptive statistics for pre-test and post-test scores, effort, and agency ratings revealed several trends within each group. The table indicates that the Student Control group had a pre-test mean of 7.49, while the System Control group had a mean of 7.43. For post-test performance, the Student Control group recorded a mean of 11.21, compared with 11.45 for the System Control group. Effort ratings were similar across the two groups, with means of 5.24 and 5.13, respectively. Agency ratings differed more substantially, with a mean of 3.58 for the Student Control group and 5.55 for the System Control group.

Assessment of Distributional Assumptions

Table 2: Tests of Normality

Before conducting inferential tests, the data were subjected to normality checks using the Shapiro-Wilk test, while homogeneity of variance was assessed using Levene’s test. The reported significance values for the Shapiro-Wilk tests were below .05 across all variables and conditions, indicating statistically significant departures from normality. These results should therefore be considered carefully when determining whether parametric tests such as independent-samples t-tests and analysis of variance are appropriate.

Inferential Comparison of Post-Test Performance and Engagement Measures

The inferential analysis began with an independent-samples t-test to compare post-test scores between the two groups. The reported test produced a statistically significant result, t(198) = 2.15, p = .033. This result was interpreted as indicating that pupils in the Student Control group outperformed those in the System Control group and that allowing learners to control task sequencing positively influenced academic performance.

Further analysis using analysis of variance examined differences in effort and agency ratings between the groups. The reported results indicated a statistically significant difference in effort, F(1, 198) = 4.21, p = .041, and in agency, F(1, 198) = 5.13, p = .025. These findings were interpreted as demonstrating motivational advantages associated with learner-controlled environments. However, the direction of the agency results should be checked against the descriptive statistics because the System Control group recorded the higher agency mean.

Group Differences in Perceived Agency

Table 3: Analysis of Variance Descriptive Statistics for Agency

The agency results show that the System Control group had a higher mean agency score than the Student Control group. The System Control group recorded a mean of 5.55, while the Student Control group recorded a mean of 3.58. Therefore, any interpretation claiming that the Student Control group experienced greater agency should be revised or supported by clarification regarding the scoring direction of the agency scale.

Educational Implications, Methodological Limitations, and Future Research

The implications of these results are significant for instructional design. Learner autonomy may strengthen ownership, participation, and engagement when students are allowed to influence the sequence of learning activities. However, the statistical findings should be interpreted only after the discrepancies between the tables and the written narrative have been resolved.

The reliance on self-reported measures of effort and agency is also a limitation because participants’ responses may be influenced by social desirability, misunderstanding of scale items, or response bias. Future research should incorporate objective measures, including classroom observations, task-completion behaviour, learning analytics, or physiological indicators. Such evidence could provide a more detailed understanding of the relationship between learner control, engagement, and academic performance.

Integrated Interpretation of Learner Control and Educational Outcomes

The study evaluates the potential of learner-controlled instructional environments to improve educational outcomes. The reported inferential results suggest statistically significant differences in post-test performance, effort, and agency. Nevertheless, the descriptive statistics, normality results, sample sizes, and stated inferential degrees of freedom contain inconsistencies that should be corrected before definitive conclusions are presented. Once verified, the findings may inform the development of adaptive, student-centred instructional strategies and educational technologies designed to strengthen learner engagement and academic achievement.