DIM-Pack provides tools for conducting statistical dimensionality analyses on assessments consisting of dichotomously scored tasks. To understand these tools and what they do, one first needs to understand, of course, what is meant by “dimensions”. The dimensions of an assessment instrument can be thought of as the attributes that are intended to be measured on the test takers. For example, in an educational measurement setting, we may want to measure a student's level of achievement in mathematics, reading, science, and writing – a case of four dimensions. Any one of those four dimensions may be further hypothesized to be decomposable into lower dimensional skills. In general, it is not usually clear how many dimensions are on a test.
With this understanding of what we mean by dimensions, we can proceed to talk in more detail about dimensionality analysis. The purpose of a dimensionality analysis is generally two-fold:
- Determine if there is more than one statistically detectable dimension (the presence of one dimension is termed “unidimensionality”) and
- If there are multiple detectable dimensions (“multidimensionality”), describe the nature of the multiple dimensions.