## 5 Exploiting Web Resources to Estimate Readability
### Frequency Classes and Readability  
Given the observations in the last section, the question arises, whether it is possible to automatically estimate the readability of a given text based on its frequency classes. In the previous section we observed the expected frequency class \(E(c(t))\) to correspond with an intuitive ranking of the readability of text categories. While above we looked at entire collections of texts from the same categories, we now change our focus to individual documents and see if we can observe a similar pattern.  
To gain some first insights we chose four different texts. Table 7 shows the readability of these texts according to SMOG and Gunning fog. Additionally the table shows the expected frequency class. It can be seen, that on this document level the three metrics do not agree. The values do not imply the same ranking of the documents.  
In a second, more extensive experiment we computed FRE and the expected frequency class \(E(c(t))\) for 60 documents of different readability. The readability of these documents ranged from an FRE index of 28.073 for the most difficult to a value of 88.499 for the easiest document. The value of \(E(c(t))\), instead, was in the ranged between 8.904 and 14.745. The values of FRE and \(E(c(t))\) showed a slight, but no significant Pearson correlation of 0.47. Thus, we can say that while the expected frequency class can give indications about the readability of a document, as an exclusive feature it is not sufficient to provide a precise analysis for a given text.  
This is quite surprising, given that the expected frequency class provided a good insight into the readability of an entire collection of documents belonging to the same category. One possible explanation for this unexpected behaviour on individual documents is data sparsity. A single document might not contain enough different words to extract a sound model of the term distribution over frequency classes. Hence, it might be necessary to apply smoothing methods to the observed distribution in order to get more reliable results. Another approach that can be pursued in parallel is to improve the results by using more information about the frequency class distribution itself for the prediction of the readability. Such additional information could come in the form of estimating the variance or directly using the actual discrete distribution. Beyond feature engineering, it might additionally be necessary to adjust a non-linear function to derive the level of readability from the multi-dimensional input data obtained from the frequency class distribution. However, while we laid the foundation for this analysis, the concrete steps to be taken are left for future work.  
\begin{table}
\begin{tabular}{l c c c} \hline \hline
**Document** & **SMOG** & **Gunning fog** & \(\mathbf{E(c(t))}\) \\ \hline [PERSON]: Famouse Five—Five Are Together Again & \(4.01\) & \(6.34\) & \(12.86\) \\ [PERSON]: Romeo and Juliet & \(4.05\) & \(7.04\) & \(13.65\) \\ Bible: Genesis 1–50 & \(4.08\) & \(7.39\) & \(13.29\) \\ [PERSON]: The Hound of the Baskervilles & \(4.27\) & \(8.62\) & \(12.95\) \\ \hline \hline \end{tabular}
\end{table}
Table 7: SMOG, Gunning fog and expected frequency class for selected documents.