theory and measurement

How does theory infect scientific observations? When are observations "theory-laden"?

One answer, obviously, is in terms of the interpretation of data, even in the subjective assessment of data.

A second answer, however, comes from the practice of measurement itself. Many quantities of scientific interest are difficult to measure directly. As a consequence, we must instead measure a proxy. The relationship between this proxy and the quantity of interest is purely theoretical. For example, Galileo's experiments rolling balls down inclined planes were an attempt to use height as a proxy for velocity in order to measure the effects of gravity (anachronous, but that's how we would put it today) near the surface of the earth. There was simply no direct way to make appropriately exact measurements of velocity.

A modern example: measurements of brain activity. When an fMRI scan is performed flow of blood to an area of the brain is a proxy for "activity" (as very loosely construed), which is itself a proxy for the real topic of interest, the modular role of different areas of the brain in complex mental calculations.