Teaching to the test alters what you can interpret from test scores because it involves teaching specific content. Therefore, it also weakens the direct inference that can be reasonably drawn about students' knowledge. Rarely would you want to limit your inference about knowledge to the specific questions asked in a specific format. Generally, you want to make inferences about a broader domain of skills. Further complicating matters, many people wish to use test scores to draw indirect inferences about why students score the way they do.
Indirect inferences can lead to weaker and possibly incorrect interpretations about school programs.
Indirect inferences cannot possibly be accurate unless the direct inference of student achievement is made to the correct domain. Rarely does one wish to limit the inference about knowledge to the specific questions in a test or even the specific objectives tested. For example, if parents want to infer how well their children will do in another school next year, they need to make inferences about the broader domain and not about the specific objectives that are tested on a particular standardized test. For that inference to be accurate, the instruction must not be limited to the narrow set of objectives of a given test. Thus, for the most typical inferences, the line demarking legitimate and illegitimate teaching of the test must be drawn between Points 3 and 4.