as well as their contribution in predicting overall achievement. In the final step of each model, the statistical significance of the interactions between student gender and each of the predictor variables in predicting achievement was explored. Each interaction term was entered into the model individually and all the statistically significant interaction terms were entered into the final model. To facilitate interpretation of the statistically significant interaction terms, those were plotted using the predicted values based on the last step (step 7) of each model. Hence, the interaction plots in the next section present the predicted, rather than the raw, gender differences in each variable in terms of mathematics and science achievement, after accounting for a range of student- and class/school-level predictor variables.

**Table 1. Steps in building the hierarchical two-level linear regression models**

||**Step 1**|**Step 2**|**Step 3**|**Step 4**|**Step 5**|**Step 6**|**Step 7**|
|---|---|---|---|---|---|---|---|
|Student gender|✓|✓|✓|✓|✓|✓|✓|
|Demographics and home background||✓|✓|✓|✓|✓|✓|
|Student engagement and attitudes|||✓|✓|✓|✓|✓|
|School climate||||✓|✓|✓|✓|
|Teacher qualifications and practices|||||✓|✓|✓|
|School leadership and resources||||||✓|✓|
|Interaction terms|||||||✓|

_<mark>Note:</mark>_ <mark>✓ indicates variables included in each step.</mark> Equation 1 represents the null multilevel models (i.e., models with no predictor variables), which were applied to the TIMSS data, controlling for their clustering and allowing for the estimation of the proportions of the total variance in the outcome variable that is attributable within and between clusters (i.e., intraclass correlation ( _ICC_ ) coefficients). i 0 i (1) where i is the outcome variable (e.g., mathematics achievement) of student _i_ in class/school _j_ , 0 is the 0ii mean intercept, is the variation of class/school yy = ββ + uu _j_ from the mean intercept, and + ee i is the student-level residual error term. yy ββ 0ii uu ee Equation 2 represents the multilevel models, which were applied to the TIMSS data, including ν number of predictor variables while controlling for the clustering of the data. i 0 1i i (2) where i is the outcome variable (e.g., mathematics achievement) of student i in class/school j, yy = ββ + ββ1iixx + . . . + ββννiixxννi + uu0ii + ee 0 is the mean intercept, is the regression slope for the predictor variable 1 of student i in class/school j, is the regression slope for the predictor variable yy of student i in class/school j, is the variation of ββ 1ii ννii class/school j from the mean intercept, and ββ i is the student-level residual error term. xx ββ νν 0ii xx uu Reported statistics for each of the models include: proportions of variance ( ee _R_<sup>_2_</sup> ; expressed as a percentage of the total variance) in achievement explained at each level and step; intercepts with their _SEs_ ; unstandardized coefficients ( _Bs_ ) and standardized coefficients ( _βs_ ) each accompanied by their _SEs_ for each predictor variable; fit statistics (Loglikelihood _(H0)_ , Akaike Information Criterion _(AIC)_ , and Bayesian Information Criterion _(BIC)_ ) for each step, including the null model; and _ICC_ coefficients for the null model. _Bs_ are expressed in the original unit of each of the predictor variables, while _βs_ can be used to compare 9