Background and context: Despite the growing importance of computer science (CS) education, high-quality CS curricula for students in kindergarten to lower elementary grades are lacking. It is also unclear how students from underrepresented groups such as female students, students from low socioeconomic status, and students with disability respond to CS curriculum at this age range. Objective: This study is aimed to examine the effectiveness of a novel CS curriculum (Coding as Another Language -- ScratchJr) on the development of programming and computational thinking skills for students in kindergarten to second grade classrooms. Method: We conducted a randomized controlled trial with 1057 students and used multilevel regression analysis to examine the impact of the CAL curriculum on students' coding and computational thinking skills, as well as moderation analysis to investigate how students' demographic characteristics including gender, socioeconomic status, English learners and disability interacted with the intervention effectiveness. Findings: The CAL curriculum was effective in improving students' programming skills, but no significant differences were detected for students' computational thinking skills. Students with limited English proficiency and students from low socioeconomic backgrounds achieved similar gain in coding skills but students with disabilities and female students did not demonstrate the same improvements as their peers. Implications: These findings shed light on the educational efficacy of CAL as a promising CS curriculum for young children and underscore the importance of understanding how underrepresented minority students respond to the curriculum in order to better guide the development and design of the CS programs.