# Readability Formulas for Elementary School Texts in Mexican Spanish
## 2 Related Work
### Traditional Readability Formulas  
The earliest formulas to automatically compute the difficulty of a text were devised for English. One of the first readability formulas (and possibly the most influential) is the Flesch Reading Ease scale [15], which gives a text a score between 0 (most difficult) and 100 (easiest). A score of 100 approximately corresponds to elementary school grade-level 4. The Flesch index, shown in Equation (1), is based on structural text features such as the average sentence length (\(ASL\)) and the average number of syllables per word (\(ASW\)). \[\text{Flesch}=206.835-(1.015\times ASL)-(84.6\times ASW). \tag{1}\]  
An adaptation of the basic Flesch formula for the Spanish language was proposed by [PERSON] in [16]. This adaptation primarily involves slight adjustments to the weight coefficients for 100-word samples. Equation (2) presents a modification of the Fernandez-Huerta formula that works for a passage containing any number of words by considering the total number of sentences (\(S\)) and words (\(W\)) (this modified version of the [PERSON] formula is proposed in [[https://linguistlist.org/issues/22/22-2332/](https://linguistlist.org/issues/22/22-2332/)]([https://linguistlist.org/issues/22/22-2332/](https://linguistlist.org/issues/22/22-2332/)), accessed on 20 May 2025). The Flesch and Fernandez-Huerta formulas are structured into seven levels ranging from 0 to 100, wherein a higher score indicates that the text is easier to read. \[\text{Fernandez-Huerta}=206.84-(60\times ASW)-(102\times S/W). \tag{2}\]  
Later, [PERSON] [17] proposed one of the first readability formulas devised originally for the Spanish language (without adaptations). The Gutierrez de Polini index, shown in Equation (3), combines structural text features such as the number of letters (\(L\)), number of words (\(W\)), and number of sentences (\(S\)) for samples of 100 words. Similarly to the Fernandez-Huerta formula, the lower the value computed for a text, the harder it is to read. However, the Gutierrez de Polini formula is intended only for sixth-grade school texts. \[\text{[PERSON]}=95.2-(9.7\times L)/W-(0.35\times W)/S. \tag{3}\]  
Another precursor in developing readability formulas for Spanish texts is the formula proposed by [PERSON] in [18], as depicted in Equation (4). He establishes a correlation between readability and the comprehensive nature of the content in terms of perspicuity--the ability to understand something clearly and without ambiguity. Thisformula evaluates texts based on the total number of syllables (\(Y\)), words (\(W\)), and sentences (\(S\)), with lower scores indicating more intricate texts and higher scores suggesting easier comprehension. The Szigriszt-Pazos scale categorizes texts as standard when they score between 51 and 65, with scores closer to 0 or 100 indicating increasing difficulty or ease of understanding, respectively. In [19], [PERSON] proposed the Inflesz scale, an alternative interpretation of the Szigriszt-Pazos formula. According to [PERSON], the interpretation of [PERSON] perspicuity formula needs adjustment as it may have been based on non-representative or haphazard selection of texts. The Inflesz scale completes the process opened by [PERSON], reviews his scale comparing it with [PERSON]'s original, and proposes a scale more adjusted to Spanish reading habits. \[\text{Szigriszt-Pazos}=206.835-(62.3\times Y)/W-W/S. \tag{4}\]  
Another readability index tailored for the Spanish language is the \(\mu\) formula, devised by [PERSON] in [20]. This formula employs the characters or letters within a text as its fundamental metric unit for computing statistics related to measures of central tendency and dispersion. According to this methodology, the lexical \"richness\" of a text correlates consistently with the dispersion around the average number of characters per word. Equation (5) illustrates the \(\mu\) formula, where \(\overline{x_{L}}\) represents the mean number of letters per word and \(\sigma_{t}^{2}\) denotes its variance.