Dataset for Number Line Estimation Patterns and their Relationship with Mathematical Performance

The sample included in this dataset represents children who participated in a cross-sectional study, a smaller cohort of which was followed up as part of a longitudinal study reported elsewhere (Bull et al., 2021). In the original study, 347 children were recruited.
As data was found to be likely missing completely at random (χ2 = 29.445, df = 24, p = .204, Little, 1998), listwise deletion was used, and 23 observations were deleted from the original dataset.
This dataset includes three hundred and twenty-four participants that composed the final sample of this study (162 boys, Mage = 6.2 years, SDage = 0.3 years). Children in this sample were in their second year of kindergarten (i.e., the year before starting primary school) in Singapore.
The dataset includes children's sociodemographic information (i.e., age and sex) and performance on different mathematical skills. Children were assessed on a computer-based 0-100 number line task and on the Mathematical Reasoning and Numerical Operations subtests from the Wechsler Individual Achievement Test II (WIAT II). The initial variables recorded on the dataset were children's estimates on each of the target numbers included on the 0-100 number line task, and their accuracy for both subtests of the WIAT II. Several more variables were created based on these original ones.
The variables included in the dataset are:
Age = Child’s age (in months)
Sex = Boy/Girl (parent reported; boy=1, girl=2)
Maths_reason = Mathematical reasoning (Math Reasoning subtest from the Wechsler Individual Achievement Test II)
Num_Ops = Numerical Operations (Numerical Operations subtest from the Weschler Individual Achievement Test II)
Mathematical_achievement = Mathematical achievement (Composite score created by adding the raw scores from the Numerical Operations and Mathematical Reasoning subtests from the Weschler Individual Achievement Test II)
P3 to P96 = Placement of the estimate on the 0-100 number line for each respective target number (i.e., P3 corresponds to the placement of the estimate provided when the target number was 3)
NLE100PAE = 0-100 number line (Percent absolute error)
NP100_Corr = Correlation of individual estimates to target numbers (Spearman’s correlation; p > .05= 0, p < .05 = 1)
NP100LinAICc = AICc value obtained for the linear model (9999 = model cannot be fitted)
NP100LogAICc = AICc value obtained for the logarithmic model (9999 = model cannot be fitted)
NP100PowerAICc = AICc value obtained for the unbounded power model (9999 = model cannot be fitted)
NP1001cycleAICc = AICc value obtained for the one-cycle power model (9999 = model cannot be fitted)
NP1002cycleAICc = AICc value obtained for the two-cycle power model (9999 = model cannot be fitted)
Best_fit_NP100_repshift = Best fitting model based on the representational shift account (0 = model cannot be fitted, 1 = linear, 2 = logarithmic)
AICc_bestmodel_repshift = AICc value of the best fitting model based on the representational shift account 
AICc_diff_repshift = AICc difference (ΔAICc) between both models (i.e, linear and logarithmic) based on the representational shift account
AICc_diff_cat_repshift = categorical value created based on AICc_diff_repshift (0 = model cannot be fitted, 1= best fitting model does not have strong support (ΔAIcc < 2), 2 = best fitting model has strong support (ΔAIcc > 2))
Best_fit_NP100_propjudg = Best fitting model based on the proportional judgment account (0 = model cannot be fitted, 3 = unbounded power model, 4 = one-cycle power model, 5 = two-cycle power model)
AICc_bestmodel_propjudg = AICc value of the best fitting model based on the proportional judgment account 
AICc_diff_propjudg_unb = AICc difference (ΔAIcc) between the best fitting model based on the proportional judgment account and the unbounded power model
AICc_diff_propjudg_1cyc = AICc difference (ΔAIcc) between the best fitting model based on the proportional judgment account and the one-cycle power model
AICc_diff_propjudg_2cyc = AICc difference (ΔAIcc) between the best fitting model based on the proportional judgment account and the two-cycle power model
AICc_diff_cat_propjudg = categorical value created based on AICc differences between the best fitting model and the following one based on the proportional judgment account (0 = model cannot be fitted, 1= best fitting model does not have strong support (ΔAIcc < 2), 2 = best fitting model has strong support (ΔAIcc > 2))
Best_fit_NP100_between = Best fitting model when comparing all models to each other (0= model cannot be fitted, 1 = linear, 2 = logarithmic, 3 = unbounded power model, 4 = one-cycle power model, 5 = two-cycle power model)
AICc_bestmodel_between = AICc value of the best fitting model from comparing all models to each other 
AICc_diff_linear_NP100 =AICc difference (ΔAIcc) between the best fitting model based on comparing all models to each other and the linear model
AICc_diff_log_NP100 =AICc difference (ΔAIcc) between the best fitting model based on comparing all model to each other and the logarithmic model
AICc_diff_power_NP100 =AICc difference (ΔAIcc) between the best fitting model based on comparing all models to each other and the unbounded power model
AICc_diff_1cycle_NP100 =AICc difference (ΔAIcc) between the best fitting model based on comparing all models to each other and the one-cycle power model
AICc_diff_2cycle_NP100 =AICc difference (ΔAIcc) between the best fitting model based on comparing all models to each other and the two-cycle power model
AICc_diff_cat_between = categorical value created based on AICc differences between the best fitting model and the following one based on the comparison of all models to each other (0 = model cannot be fitted, 1= best fitting model does not have strong support (ΔAIcc < 2), 2 = best fitting model has strong support (ΔAIcc > 2))

本数据集收录的样本来自参与一项横断面研究的儿童，其中的子队列被纳入一项纵向研究进行追踪，相关成果已在其他文献中发表（Bull等人，2021）。初始研究共招募了347名儿童。
经检验，数据极有可能为完全随机缺失（χ²=29.445，df=24，p=0.204；Little，1998），故采用列删法处理缺失值，从原始数据集中剔除了23条观测记录。
本数据集最终纳入324名受试者，为本研究的有效样本（其中男性162名，平均年龄M_age=6.2岁，年龄标准差SD_age=0.3岁）。该样本中的儿童均为新加坡幼儿园中班学生，即小学入学前一年的幼儿。
本数据集包含儿童的社会人口学信息（即年龄与性别）以及多项数学能力表现数据。受试者接受了基于计算机的0-100数字线任务测评，以及韦克斯勒个人成就测验第二版（Wechsler Individual Achievement Test II, WIAT II）中的数学推理和数字运算分测验。数据集初始记录的变量包括：儿童在0-100数字线任务中对各目标数字的估计值，以及在WIAT II两个分测验中的作答准确率。研究人员基于这些原始变量衍生出了多个衍生变量。
数据集包含的变量如下：
1. Age：儿童年龄（单位：月）
2. Sex：性别（男/女，家长报告；男=1，女=2）
3. Maths_reason：数学推理得分（韦克斯勒个人成就测验第二版数学推理分测验）
4. Num_Ops：数字运算得分（韦克斯勒个人成就测验第二版数字运算分测验）
5. Mathematical_achievement：数学成就综合得分（将韦克斯勒个人成就测验第二版数字运算与数学推理分测验的原始得分相加得到）
6. P3 to P96：各目标数字对应的0-100数字线任务估计值位置（例如P3对应目标数字为3时的估计值位置）
7. NLE100PAE：0-100数字线任务绝对误差百分比
8. NP100_Corr：个体估计值与目标数字的相关性（斯皮尔曼相关；p>0.05记为0，p<0.05记为1）
9. NP100LinAICc：线性模型的修正赤池信息准则（AICc）值（9999表示模型无法拟合）
10. NP100LogAICc：对数模型的修正赤池信息准则（AICc）值（9999表示模型无法拟合）
11. NP100PowerAICc：无界幂函数模型的修正赤池信息准则（AICc）值（9999表示模型无法拟合）
12. NP1001cycleAICc：单周期幂函数模型的修正赤池信息准则（AICc）值（9999表示模型无法拟合）
13. NP1002cycleAICc：双周期幂函数模型的修正赤池信息准则（AICc）值（9999表示模型无法拟合）
14. Best_fit_NP100_repshift：基于表征转换理论的最优拟合模型（0表示模型无法拟合，1为线性模型，2为对数模型）
15. AICc_bestmodel_repshift：基于表征转换理论的最优拟合模型的修正赤池信息准则（AICc）值
16. AICc_diff_repshift：基于表征转换理论的线性与对数模型间的修正赤池信息准则差值（ΔAICc）
17. AICc_diff_cat_repshift：基于AICc_diff_repshift生成的分类变量（0表示模型无法拟合，1为最优拟合模型无强支持证据（ΔAICc<2），2为最优拟合模型有强支持证据（ΔAICc>2））
18. Best_fit_NP100_propjudg：基于比例判断理论的最优拟合模型（0表示模型无法拟合，3为无界幂函数模型，4为单周期幂函数模型，5为双周期幂函数模型）
19. AICc_bestmodel_propjudg：基于比例判断理论的最优拟合模型的修正赤池信息准则（AICc）值
20. AICc_diff_propjudg_unb：基于比例判断理论的最优拟合模型与无界幂函数模型间的修正赤池信息准则差值（ΔAICc）
21. AICc_diff_propjudg_1cyc：基于比例判断理论的最优拟合模型与单周期幂函数模型间的修正赤池信息准则差值（ΔAICc）
22. AICc_diff_propjudg_2cyc：基于比例判断理论的最优拟合模型与双周期幂函数模型间的修正赤池信息准则差值（ΔAICc）
23. AICc_diff_cat_propjudg：基于比例判断理论下最优拟合模型与次优模型间的AICc差值生成的分类变量（0表示模型无法拟合，1为最优拟合模型无强支持证据（ΔAICc<2），2为最优拟合模型有强支持证据（ΔAICc>2））
24. Best_fit_NP100_between：全模型两两比较后的最优拟合模型（0表示模型无法拟合，1为线性模型，2为对数模型，3为无界幂函数模型，4为单周期幂函数模型，5为双周期幂函数模型）
25. AICc_bestmodel_between：全模型两两比较后得到的最优拟合模型的修正赤池信息准则（AICc）值
26. AICc_diff_linear_NP100：全模型两两比较得到的最优拟合模型与线性模型间的修正赤池信息准则差值（ΔAICc）
27. AICc_diff_log_NP100：全模型两两比较得到的最优拟合模型与对数模型间的修正赤池信息准则差值（ΔAICc）
28. AICc_diff_power_NP100：全模型两两比较得到的最优拟合模型与无界幂函数模型间的修正赤池信息准则差值（ΔAICc）
29. AICc_diff_1cycle_NP100：全模型两两比较得到的最优拟合模型与单周期幂函数模型间的修正赤池信息准则差值（ΔAICc）
30. AICc_diff_2cycle_NP100：全模型两两比较得到的最优拟合模型与双周期幂函数模型间的修正赤池信息准则差值（ΔAICc）
31. AICc_diff_cat_between：基于全模型两两比较下最优拟合模型与次优模型间的AICc差值生成的分类变量（0表示模型无法拟合，1为最优拟合模型无强支持证据（ΔAICc<2），2为最优拟合模型有强支持证据（ΔAICc>2））