# Readability Formulas for Elementary School Texts in Mexican Spanish
## 4 Experimental Study
### Experimental Results  
Figure 3 presents the familywise error rates obtained through [PERSON]'s HSD test, assessing the degree of separability among Mexican elementary grade levels for various readability formulas. In this context, \(p\)-values close to 0 indicate statistically significant differences between grade levels, while values near 1 suggest no meaningful distinction in textual difficulty between those levels. The findings reveal that most formulas struggle to clearly differentiate between texts from grades 4 to 6 and, to a lesser extent, between grades 1 and 3. However, some formulas do succeed in identifying distinctions within the lower grade levels (grades 1-4). This pattern of separability--forming two main blocks (grades 1-3 and 4-6)--is especially evident for the Linear-MX formula (g). It exhibits highly significant \(p\)-values (close to 0) across reading scores of text between grades 1 and 4 and grades 5 and 6. The GP-MX formula (h) also shows good separation, particularly between grades 1 and 2 and the higher grades. However, there are some non-significant \(p\)-values among mid-level grades (grades 3-5), suggesting a moderate overlap in readability scores for these levels. The SOL index (f) offers reasonably good performance as well, correctly distinguishing between many grade levels, although it tends to show higher \(p\)-values (weaker separability) between grades 4 and 6. Traditional Spanish formulas such as Gutierrez de Polini (b), Szigriszt-Pazos (c), \(\mu\) (d), and Crawford (e) exhibit moderate performance. They are generally capable of distinguishing early grade levels (especially grades 1 vs. 4 or 5), but their sensitivity declines sharply in upper grades, with \(p\)-values often exceeding 0.3, indicating little statistical distinction. Interestingly, among the foreign-language formulas, the Gulpease index (j) (Italian) performs surprisingly well, surpassing even some Spanish-specific formulas like \(\mu\) and Crawford. It provides good separation, especially in early grades, and remains relatively consistent through middle grades. In contrast, the Flesch (i) and Osman (k) formulas underperform in this context. While they show strong separation in the earliest grades (grades 1-2 vs. higher grades), their ability to distinguish between middle and upper elementary grades is notably weaker, confirming the challenges of applying non-Spanish formulas to Spanish texts without adaptation. Finally, the Fernandez-Huerta index (a), despite being designed for Spanish, exhibits the poorest performance. It shows almost no statistically significant differences between any grade levels, with most \(p\)-values near 1.0, suggesting it is largely insensitive to progressive changes in text complexity across the elementary grades. This weakness may stem from its simplistic formula and outdated assumptions about language structure. Figure 4 shows the distribution of readability scores generated by each readability index. Notably, the fourth grade often breaks the expected trend of progressively decreasing readability levels (or increasing, in the case of the Crawford and SOL formulas). In the case of the Gutierrez de Polini formula, the absence of a clear trend is justifiable, as this formula was specifically designed to assess sixth-grade educational texts, and thus may not generalize well across other grade levels. The Linear-MX and GP-MX formulas exhibit the clearest downward trends, aligning well with the expected progression in text complexity across elementary grades. Linear-MX, in particular, shows a consistent decline in median scores from grades 1 to 6 with limited overlap, indicating a regular grade-level sensitivity. By contrast, traditional formulas such as Fernandez-Huerta and Szigriszt-Pazos show flatter distributions, with limited variation across grades. This suggests these formulas may lack sufficient resolution to distinguish between the incremental increases in difficulty typical of elementary school materials.