standard deviation of one in our analyses. We standardize skill scores to improve comparisons of scores across test periods. Standardization addresses potential variations in test difficulty, content, and overall student development across test periods, which raw scores alone may not fully account for. By standardizing the scores, we adjust for shifts in the distribution of scores within each test period. Consequently, we focus on the relative performance of students rather than on absolute performance. In the panel VAR analyses, standardization allows us to capture how these skills evolve in relation to each other while controlling for test period-specific variations. This ensures that the estimated relationships reflect genuine cross-skill dynamics rather than being confounded by shifts in the overall performance level across different time points. As the skill scores for reading, spelling, and math all have a mean of zero and a standard deviation of one, providing summary statistics may not be particularly insightful. However, visualizing the skill scores can help us to get a first idea of the relationships of these skills within our data. To this end, we present a heat plot in Figure 4.1, where the scores for reading, spelling, and math are displayed. In this figure, the x-axis represents the math scores of students in standard deviation (SD), while the y-axis shows the spelling scores of students. The black line in the figure illustrates the correlation between spelling and math skills. The combinations of these spelling and math scores are then plotted over the reading scores, which are visualized using a color scale ranging from blue to red. Blue indicates lower reading scores, while red represents higher reading scores. skills, so reading, spelling, and math skills. 85
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