  We have developed the Physics Inventory of Quantitative Literacy (PIQL) as a
tool to measure students' quantitative literacy in the context of introductory
physics topics. We present the results from various quantitative analyses used
to establish the validity of both the individual items and the PIQL as a whole.
We show how examining the results from classical test theory analyses, factor
analysis, and item response curves informed decisions regarding the inclusion,
removal, or modification of items. We also discuss how the choice to include
multiple-choice/multiple-response items has informed both our choices for
analyses and the interpretations of their results. We are confident that the
most recent version of the PIQL is a valid and reliable instrument for
measuring students' physics quantitative literacy in calculus-based
introductory physics courses at our primary research site. More data are needed
to establish its validity for use at other institutions and in other courses.
