AUTOMATIC SHORT ANSWER GRADING AND FEEDBACK USING TEXT MINING METHODS
Table 3. Estimation of parameters and the MSE for MM, i=1,2,3,4, for the corresponding questions (see Appendix A); MSE is the mean square deviation of predicted marks from the average of two markers’ grades.
['Model', '[ITALIC] β0', '[ITALIC] β1', '[ITALIC] β2', 'MSE (MM)', 'MSE (TM)']
The value of β0 represents the overall position of the curve on the y-axis; that is, the maximum mark which can be predicted by the model MM (when the distance is 0). We found a maximum mark of 4.91. The negative sign of β1 tells us that scores decrease with distance. The value of β2 indicates how quickly the score decreases with distance from the the base line β0. To compare the accuracy of our model with human marking, we calculate the deviation of teacher grades from the average mark of two teachers. We see that the the teacher marks diverge from their average more than does the mathematical model for this question. This is unsurprising as it suggests the average is more predictable than the individual scores.