## 5 Experimental Results
This scale usually falls somewhere between 0 (completely arbitrary agreement between evaluators) and 1 (complete agreement between graders). If there are \(S\) possible ratings (1, 2,... _S_), and two evaluators have scored each article, then we can say that essay responses has \(S\) possible ratings. (e.g., human and computer). We can determine this measure by performing the following:  
\[kp=1-\frac{\sum_{i,j}W_{i,j}\ O_{i,j}}{\sum_{i,j}W_{i,j}\ e_{i,j}} \tag{23}\]  
where \(W\) represents weights, \(O\) represents the actual rating matrix, and \(e\) represents the expected rating matrix. The weights assigned by each evaluator are stored in a S- by- S matrix called \(W_{i,j}\), where \(i\) is the _i_-th weight and \(j\) is the _j_-th weight. \[W_{i,j}=\frac{(i-j)^{2}}{\left(S-1\right)^{2}} \tag{24}\]  
Matrix of evaluations that have been collected by constructing a S-by- S histogram (agreement) matrix \(O\) over the essay ratings, where \(O\),_ij_ represents the number of essays assigned a grade of \(i\) by grader A and a grade of \(j\) by grader B, and where _RE_ represents an S-by-S histogram of predicted grades:  
\[RE_{scj}=\frac{H_{Ai}\.H_{Bj}}{No} \tag{25}\]  
Number of essays graded by grader A with score _sc_ is denoted by \(H_{Ai}\), \(i\) = 1,..., \(S\), _No_ = total number of essays graded. The sum of _RE_ and \(O\) is equal after normalization with _No_. To validate the suggested model, a set of experiments was conducted to analyze the potential benefits of the spatial measures and their significance to predictive accuracy. Then, experiments continued to compare the predictive accuracy of the suggested model by comparing its results to those of other state-of-the-art systems. The last experiment was to check the error rate of the suggested detection system. All experiments were conducted after transforming the essay into a semantic space by moving a window over it by 10 words. To determine if the inclusion of semantic attributes improves model performance, experiment 1 (semantic attribute significance) compares the proposed model to two related statistical-based AES systems: AGE (Automated Grader for Essays with only linguistic and content attributes) and AGE+ (the AGE system with additional coherence attributes) [51; 70; 71]. The proposed system for assessing writing was more effective. Quadratic weighted kappa and exact agreement are displayed in Tables 4 and 5, respectively, for AEG, AGE+, and the suggested model. The results reveal that the model's accuracy significantly increases by approximately 6% to 7% over AGE and AGE+. In the exact agreement measure, the proposed model increases by 6% in the case of AGE and by 5% in the case of AGE+ for all datasets. The proposed model's superiority is predicated on the fact that the AGE system simply validates syntactic characteristics. Only syntax and coherence are validated by the AGE+ system. The suggested approach, however, takes into account all three characteristics (syntax, coherence, and consistency) simultaneously, leading to better results. Syntax means grammar and spelling mistakes, coherence means that ideas in a paragraph flow smoothly from one sentence to the next, and consistency means that the paragraphs of the essay are linked well and evolve around the main idea of the essay. In experiment two (a comparative study with commercial systems), the aim is to compare the suggested model to the state-of-the-art systems that were mentioned in [71]. Project Essay Grade (PEG) is one such system; it employs a database of training essays graded by humans to create a model that evaluates the quality of unscored essays using sophisticated statistical methods. E-Rater assigns grades to essays after identifying and extracting a collection of features that stand for key components of writing quality. Next, a statistical model is used to aggregate these features and assign weights to them based on a statistical procedure, ultimately yielding an estimated score.