@ Copyright 2003, Jeff Miller.
This program and its documentation may be duplicated and used without charge for any educational or noncommercial purposes. For commercial use, please contact the author.
PMetric estimates the parameters of a probability distribution from a data function relating the proportion of a certain (binary) response to a physical quantity. This type of data analysis---often called ``probit'' analysis---is used in several subject areas, including bioassay (analysis of dose/response curves) and psychophysics (analysis of psychometric functions). In brief, the program reads a file containing the observed data (e.g., quantal dose/response curve), and it computes either maximum-likelihood or minimum-chi-square estimates of the parameters (mean, median, standard deviation, etc) of the underlying probability distribution. It also computes the bootstrap standard error of each of each estimate.
PMetGen generates random data of the sort analyzed by PMetric, for use in power analysis and in computer simulation studies evaluating statistical procedures.
In bioassay, for example, a researcher might want to determine the relationship between the dosage of a certain herbicide and the probability that a certain weed exposed to that dose will die. In a typical study, each of k different dosages, C_1 ... C_k, is given to N_i different weeds. The number of weeds to actually die at dosage i, G_i, is counted to estimate the effectiveness of that dosage. Such data are typically analyzed with a statistical model assuming that any given weed has a minimum lethal dosage and that the weed dies if and only if it is given a dosage greater than or equal to its minimum lethal dose. Thus, an observed G_i/N_i value is an estimate of the population proportion of weeds for which the lethal dose is less than or equal to C_i.
The analogous problem arises in psychophysical research examining psychometric functions. In this case, the C_i values might be intensities of a given auditory tone. The tone is played to an observer N_i times at each intensity value, and each time the observer indicates whether or not he heard it. The statistical model assumes that the observer has a minimum detectable intensity value (fluctuating across time), and that the observer reports hearing the tone on each presentation if and only if it is more intense than the minimum intensity value at that moment. Thus, an observed G_i/N_i value is an estimate of the probability that the instantaneous minimum detectable intensity value is less than or equal to C_i.
In standard probit analysis, the underlying probability distribution is assumed to be normal (i.e., Gaussian). PMetric allows this assumption but does not require it. Instead, the user may do the comparable analysis assuming a variety of alternative underlying distributional shapes (e.g., gamma, uniform), and the user may obtain nonparametric estimates using the Spearman-Kaerber method. Based on extensive simulation studies, in fact, we would recommend that the Spearman-Kaerber method be used under a wide variety of circumstances (Miller & Ulrich, 2001; Ulrich & Miller, 2004).