It is widely assumed, based on Chocholle's (1940) research, that stimuli that appear equal in loudness will generate the same reaction times. In Experiment 1, we first obtained equal-loudness functions for five stimulus frequencies at four different intensity levels. It was found that equal loudness produced equal RT a~80 phons and 60 phons, but not at 40 phons and 20 phons. It is likely that Chocholle obtained equivalence between loudness and RT at all intensity levels because of relay-click transients in his RT signals. One main conclusion drawn from Experiment 1 is that signal detection (in reaction time) and stimulus discrimination (in loudness estimation) require different perceptual processes. In the second phase of this investigation, the RT-intensity functions from six different experiments were used to generate scales of auditory intensity. Our analyses indicate that when the nonsensory or "residual" component is removed from auditory RT measures, the remaining sensory-detection component is inversely related to sound pressure according to a power function whose exponent is about -.3. The absolute value of this exponent is the same as the .3 exponent for loudness when interval-scaling procedures are used, and is one-half the size of the .6 exponent which is commonly assumed for loudness scaling.The historic traditions that underlie the present research are formidable. Psychophysicists have consistently found a direct relation between auditory stimulus intensity and loudness. Specifically, Stevens and his colleagues have established that perceived loudness grows as a power function of stimulus intensity (Marks, 1974(Marks, , 1979. Equally impressive is the evidence in support of an inverse relation between stimulus intensity and simple auditory reaction time (RT). Classic experiments by Cattell (1886), Chocholle (1940), Pieron (1920), and Wundt (1874) have convincingly shown that RT decreases monotonically with corresponding increases in auditory stimulus intensity.Based on the fact that stimulus frequency, along with stimulus intensity, are the primary determinants of both loudness and RT, the present paper comprises two major sections in which these two stimulus attributes are evaluated. First, we evaluated the relation between equal loudness (across frequencies) and RT, using Chocholle's (1940) attempted to synthesize the data from several RT experiments in order to construct a uniform scale of sensory intensity that is based on RT measures. PHASE 1: EQUAL LOUDNESS AND REACTION TIMEIt is remarkable how many investigators have cited Chocholle's research, conducted over 40 years ago at the Sorbonne Laboratory, as the definitive study of the relation between auditory RT and signal intensity and frequency. His experiments were extensive but simple in design. Three experienced subjects generated RT-intensity functions over a wide range of intensity levels for frequencies of 20, 50, 250, 500, 1,000, 2,000, 4,000, 6,000, and 10,000 Hz. From these initial results, he drew "equal-RT" contours; that is, stimul...

Equal-loudness contours were first obtained for five stimulus frequencies at four stimulus intensities. These 20 stimuli were then presented as reaction-time signals in a Donders C paradigm. The Z.transform method of convolution, as applied in linear systems identification, was used to deconvolve an empirically generated response (or "residual") distribution (T'R) from each of the 20 reaction-time (RT) distributions obtained at different intensities and frequencies. The resulting sensory-detection (tel) models formed exponential densities at strong intensities (60 and 80 phons), but their shapes were either gamma or normal at relatively weak intensities (20 and 40 phons). Our analyses support the idea that the simple reactiontime process (RT) is a convolution (or sum) of two component stages: stimulus detection (tell, followed by response evocation (tr). Based on the shapes of td, a neural-impulse theory is offered to account for the detection of simple auditory RT signals.In two previous papers (Kohfeld, Santee, & Wallace, 1981;Santee& Kohfeld, 1977), we reported that equally loud stimuli across five frequencies produced equal reaction times at 80-and 6O-phon intensities, but at the 40 and 20-phon levels the latencies were longer at 1,000 Hz than at the higher and lower stimulus frequencies. In order to provide a rigorous evaluation of these results, our present intent is to analyze the observed RT distributions generated from 100-, 500-, 1,000-,5,000-, and lO,OOO-Hz signals at intensities of 20, 40, 60, and 80 phons. Any dissimilarities among the shapes of these RT distributions, especially at the 20-and 4O-phon levels, should provide some insights as to whether the components of the RT process are different across stimulus frequencies when equivalently weak signals are employed.One basic premise in this paper is that signal detection and response initiation are the two component stages in the simple reaction time (RT) process. This notion is not new, as Green and Luce (1971), Hohle (1965), and McGill (1963 the RT process which begin with the assumption that observed RT distributions represent a convolution of the densities of two component random variables, one of which reflects the detection, or decision process (ld), and the other having to do with the response or "residual" latency (t r ) . The forms of these component densities have been open to controversy; for example, McGill (1963) assumed that td is normally distributed and t r is exponentially distributed, whereas Hohle (1965) argued for the exact opposite interpretation. More recently, Green and Luce (1971) attempted to find the shape of t r by constructing td theoretically (based on a Poisson pulse model of sensory detection), and then deconvolving ld from the empirical RT distribution. Although somewhat successful, Green and Luce were unable to identify a completely realistic model of t r , thus leading them to conclude that their initial model of ld would require further revision.In view of the difficulties encountered by Green and Luce in t...

When the shape parameter, a, is integral, generating gamma random variables with a digital computer is straightforward. There is no simple method for generating gamma random variates with non-integral shape parameters. A common procedure is to approximately generate such random variables by use of the so-called probability switch method. Another procedure, which is exact, is due to Jiihnk. This paper presents a rejection method for exactly generating gamma random variables when a is greater than 1. The efficiency of the rejection method is shown to be better than the efficiency of JiJhnk's method. The paper concludes that when a is non-integral the following mix cf procedures yields the best combination of accuracy and efficiency:(1) when a is less than 1, use Jiihnk's method; (2) when 1 is less than a and a is less than 5, use the rejection method; (3) when a is greater than 5, use the probability switch method.

No abstract

A maximum entropy approach leads to a truncated normal distribution for the activity time in PERT analysis. Three different methods of fit are discussed, and a comparison with the standard assumption of a Beta distribution is made. The results suggest new ways of performing the PERT analysis.