“…Typically, in the measurements of PT, whether or not students received PT is used as a dummy variable (Zhang, 2013 ) for comparing the achievements of tutored and non-tutored students (e.g., Baker et al., 2001 ; Bray, 2014 ; Byun, 2014 ; Guill et al., 2019 ; He et al, 2021 ; Kuan, 2011 ; Ömeroğulları et al., 2020 ; Zhang, 2013 ; Zhang et al, 2021 ). More recent studies have explored the effect of this dummy variable on mathematical achievement in China, based on different kinds of databases (e.g., Fang et al, 2018 ; Guo et al, 2020 ; Sun et al, 2020 ; Zeng & Zhou, 2012 ; Zhang, 2011 , 2013 ; Zhang et al, 2021 ; Zhao & Xue, 2021 ; Zheng et al, 2020 ).…”