Although other fields suffer their own complications when it comes to measuring the world (e.g. How does one measure the size of the Earth? Or how much of the amyloid protein in a solution has clumped to form a deposit?), psychologists have the particular problem of wanting to measure things that many people believe are unmeasurable. You cannot directly take a ruler to somebody's thoughts, so a more subtle solution is required.
Psychophysics is a set of theoretical tools which make sensations measurable. The internal states of the subject are modelled by a set of variables and processes, based on assumptions about how perceptual decisions are made. Experiments can be designed to probe these internal mechanisms by relating them to the behaviours they would predict under a carefully chosen set of conditions. The models typically involve some sort of variability (e.g. noisy neuronal responses) so rather than predicting a specific response to a stimulus they instead make a probabilistic prediction of how often each of a set of responses should be expected.
The basic measurements which psychophysicists make are therefore the probabilities with which subjects respond in a particular way to a stimulus under some experimental paradigm. A simple example would be showing a subject a faint (low contrast) striped pattern and asking them whether they see it or not. The observer will make both "yes" and "no" responses on different trials (even with an identical stimulus). The probability with which the observer says "yes" can then be used to infer the magnitude of some internal response variable. The way in which that can be done will be the subject of future blog post.