Abstract
The phi-gamma hypothesis is a special case of the general hypothesis of a cumulative symmetrical distribution. Assuming any cumulative symmetrical distribution, with stimuli equally spaced about the axis of symmetry, (a) the descending method of limits (DML) threshold distribution is asymmetrical and is a mirror image of the ascending method of limits (AML) threshold distribution; (b) the combined method of limits (CML) threshold distribution is symmetrical; (c)with the subscripts A, D, and C referring to AML, DML, and CML distributions: MA<MC<MD; σA=σD; σC>σA; (d) as step size increases: MA increases, Mjy decreases,M C remains constant, σA and op increase, oc first decreases and then increases; (e) the mean threshold of the method of constant stimuli (MCS) equals MC. For a particular assumption of a cumulative symmetrical distribution, statistical measures of the method of limits can be used to estimate MCS statistics. The analyses are supported by data from brightness discrimination experiments.
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Herrick, R.M. Psychophysical methodology: Deductions from the phi-gamma hypothesis and related hypotheses. Perception & Psychophysics 7, 73–78 (1970). https://doi.org/10.3758/BF03210136
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DOI: https://doi.org/10.3758/BF03210136