The remarkable thing in the above informal definition is that Popham knows bloody well that the kind of testing and especially of test questions, will determine what it is that the students will prepare for. Therefore, the purpose of testing would be to make sure that students learn the right kind of thing. Calling that 'inference making' does not seem to be one hundred percent truthful.
Popham is keeping all options open here. The restriction is to in-school testing.
A most important point, and Popham is so right to mention it in the forceful way he does. He does however not try to explain that it is inherent in the character of assessment - sampling right-wrong items from the student's imperfect mastery - that there are relatively large swings possible in the test result for the individual student. This radically and fundamentally differs from the prototypical kind of measurement in the physical world: that of length and weight.
W. James Popham (2005). America's 'failing' schools. How parents and teachers can cope with No Child Left Behind. Routledge. isbn 0415451283, 157 pp. paperback, near mint, €
This really is a miserable definition; Mislevy can do much bettr than this. It is miserable because it does not exclude anything; anything goes here. Nevertheless, it has appeared in print, and as such it reveals a kind of over-simplifying that tends to be typical of a lot of psychometric work. It seems the thinking goes into the models themselves, not in the situations they are supposedly representing.
The educational decisions, by the way, are strictly reserved to instutional representatives. Mislevy does not see students as making their own decisions, whether on the basis of test results, or any other information. This, in my opinion, is unprofessional neglect that has somehow come to be regarded as professional - notwithstanding that one chapter in Cronbach and Gleser, 1957, emphasizing the individual decision maker.
Robert J. Mislevy (1993). A framework for studying differences between multiple-choice and free-response test items. In Randy Elliot Bennett and William C. Ward Construction versus choice in cognitive measurement (p. 75-106). Erlbaum.