There are three principal alternative assumptions about the form of threshold data collected by presenting each of a number of light intensities repeatedly and determining the probability of discrimination for each. These assumptions are that the data will conform to (a) Poisson sums; (b) normal ogives; or (c) log normal ogives. Decision among these assumed curves is of interest for theoretical reasons, and also to permit selection of a procedure for the analysis of visual threshold data. The present study indicates the similarity among the assumed curves, and reports an analysis of the number of experimental data required to differentiate among them, which number is so large that it appears unlikely that published threshold data are adequate for this purpose. Experimental data are reported which are sufficiently numerous to permit a partial decision among the assumed curves. A total of 27 482 measurements was made by 4 subjects, under constant physical conditions. Data from three of the subjects can be fitted by normal ogives, but not by log normal ogives. Data for the fourth subject can be fitted by log normal ogives, but not by normal ogives. All the data can probably be fitted by one or another Poisson sum, provided there are no theoretical limits on their parameters. That the curves actually represent Poisson sums is regarded as unlikely, however, since a prediction concerning the magnitude of the thresholds is not verified. Our analyses suggest that threshold data can probably be adequately analyzed in terms of either normal or log normal ogives and that visual theories should depend upon other predictions than the form of the threshold data.
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