ABSTRACT
Alternative mathematical structures for Signal Detection Theory (or for short, SDT) as a form of statistical decision theory with parametrized distributions for noise have been extensively catalogued by Egan (1975) and generally presuppose (i) two stochastic processes, N and S+N on (ii) a decision axis x, (iii) responses which are either two-category or reducible to a two-category form by coalescing steps on a category scale, and (iv) two internal parameters d′ and ß. The parameter d′ is a standardised measure of the difference between the first moments of N and S+N ( so that µN ≠ µs+N and σN = σs+N = σ in x units are implicit in d′ ), and the second parameter ß is a measure of what is variously called bias or criterion for the observer to report that a signal is present in the decision situation created by the possibilities of N and S+N both being non-null on any trial.
