The assessment of computational thinking (CT) is crucial for improving pedagogical practice, identifying areas for improvement, and implementing efficient educational interventions. Despite growing interest in CT in primary education, existing assessments often focus on specific dimensions, providing a fragmented understanding. In this research, a CT system of assessments for primary education was assembled and applied in a cross-sectional survey study with 1306 students from the 6th grade in a region of Spain. A three-way ANOVA and correlation analyses explored the effects of programming experience, educational context, and gender on CT skills and self-efficacy. Results highlighted a significant effect of programming experience but no significant effects of context or gender, alongside low overall correlations between CT skills and self-efficacy. These findings highlight the need to avoid focusing CT assessments on a single variable and support the combined use of multiple assessment instruments to measure CT accurately and effectively.