A third source of validity evidence is evidence based on internal structure. There are ways of looking at tests and data to determine what is going on underneath the surface of observed responses. One of the common applications of evidence based on test structure is to support sub-score reporting. This is very typical in mathematics.
The National Council of Teachers of Mathematics suggests that math tests report sub-scores in strands, (e.g., numbers and operations, algebra, geometry, measurement) to determine how a student is performing in a particular skill area. This requires that items in the numbers and operations strand measure something distinct from the items in the algebra strand. An analysis can determine whether a collection of items supports inferences about a student’s distinct knowledge or skill. This analysis is called an assessment of dimensionality, as it attempts to discern how many constructs are being measured. Typical statistical methods used to evaluate the dimensionality and homogeneity of a set of items are factor analysis and coefficient alpha. If the items seem to form a homogeneous subset, then that would support reporting scores based on distinct strands.