The script relativity hypothesis proposes that the scripts we read and write affect our cognition. The current study tested this hypothesis by comparing Chinese and English cognitive-linguistic skills and three cognitive abilities, including verbal working memory capacity, nonverbal IQ, and arithmetic calculation, across groups of children with different Chinese and English word reading performances. Using the untimed word reading performances as the criterion, four groups of children were identified from a sample of 662 Hong Kong grade 1 Chinse children, including 49 children who were “good” at both Chinese and English word reading (the GB group), 30 children who were “poor” in Chinese word reading only (the PC group), 40 children who were “poor” in English word reading only (the PE group), and 65 children who were “poor” in both (the PB group). Significant group differences were found on almost all the cognitive-linguistic skills, including phonological awareness, morphological awareness, vocabulary knowledge, and rapid digit naming, and the three cognitive abilities, with the GB group performing the best and the PB group performing the most poorly, suggesting a general positive association between script and cognition. Pairwise comparisons showed that the PC group performed better than the PE group in the English cognitive-linguistic tasks and the PE group performed better than the PC group in the Chinese cognitive-linguistic tasks, as expected. More importantly, the PC group showed poorer arithmetic calculation performance when compared to the PE group, suggesting a stronger association between Chinese word reading and arithmetic calculation.