On Characterization of Norm-Referenced Achievement Grading Schemes toward Explainability and Selectability

Table 13

Grading scheme selection guideline.

Method	Characteristic	Suitability
K-means	It prioritizes intracluster similarity, that is, score similarity within each learner group.	(i) This method is suitable when the same grade is always supposed to be held by learners with closely similar abilities.
		(ii) As indicated in Figure 7, K-means is also suitable for heavily skewed distribution like SD+ and SD− data sets.
PAM	PAM that produced the most A and the least F by average implies that the group GPA of learners tends to be high when grading with PAM.	PAM is also suitable for heavily skewed distribution like SD+ and SD− data sets as indicated in Figure 7.
Our algorithm	(i) In contrast with K-means, our algorithm prioritizes intercluster dissimilarity, that is, gaps between scores at the borders of different groups.	(i) This method is of a good choice when different grades are supposed to distinguish learning ability divides.
	(ii) Our algorithm is friendly to not only the heavily skewed distribution (i.e., SD+ and SD−) but also normal (i.e., ND) and slightly-to-moderately skewed distributions (i.e., RD−, RD+, and WD).	(ii) Our algorithm is generally appropriate for all kinds of data distributions. The reason is that our algorithm’s strategy is the determination of score gaps, which draw the clear-cut boundaries of clusters.
z score	(i) z score method disregards the notion of cluster (dis) similarity by engaging the even ranges of the best and the worst scores within each learner group.	(i) This method should be used when all grades are supposed to encompass an equal score range. Let us consider Table 10. Grade C produced by our algorithm ranges from 42 to 63.5 points which is relatively wider than the score ranges of the other grades. This situation is avoided in z score’s results. In other words, z score tries to equalize score ranges across all grades.
	(ii) z score method is not good at dealing with norm-referenced grading in general mainly because its operation is blind to inherent raw-score gaps.	(ii) Unlike the other methods, z score method is recommended for grading a score set that holds some wide divide (i.e., WD) because z score method allows skippable grades.