Identifiability of a class of theories with states not directly observed over trials

The problem of identifying probabilities for sequences involving K underlying states is investigated for experiments in which there are K observed states, with the conditional distribution for these states specified for each underlying state. Conditions for finding unique estimates of the underlying probabilities are outlined for situations in which underlying transitions depend upon the last observed state as well as for situations in which no such dependency is assumed. No restrictions upon the nature of underlying transitions are assumed for a large number of trials. Applications to some known experimental situations are suggested.     

Forward, backward and combined masking: Implications for an auditory integration period

Auditory temporal psychometric functions were obtained for forward masking, backward masking, and for combined forward and backward masking for the case of an impulsive signal in white noise. Temporal psychometric functions show a large interaction between forward masking and backward masking when evaluated against an independence model of performance. The results are not consistent with the concept of a sharp rectangular temporal integrating period (“moment”) to account for the interaction.     

Depth of visual information processing

The depth of visual information processing is identified with the longest randomly-generated binary-encoded spatial pattern whose partial repetitions can be detected. In contrast with the auditory detection of sequentially-presented constraints, the depth of perceptible visual encoding of spatially-presented constraints is sharply limited. Depths of about 35 were achieved for one-dimensional constraints; depths of perhaps 3 or 4 were achieved for two-dimensional constraints imposed in only one direction and depths of perhaps 2 for two-dimensional constraints imposed in two directions. With one-dimensional constraints, it is shown that the inferred depth of processing is partially determined by the number of pattern representations and by the spatial distance between successive representation for visual displays of fixed size.     

Temporal anagrams: Word identification with successively presented letters in scrambled order

High-frequency seven-letter words were displayed letter by letter in scrambled temporal orders upon an oscilloscope. After each incorrect identification, the sequence was repeated. Highest word-identification scores were obtained with initial and terminal starting positions, with shortest and longest spacingbetween successive letters, and at the slowest and fastest rates of letter presentation. The relative contribution of each variable was maintained in combination with other variables. The conditional probability of a correct word identification, given that the word was not identified on a previous presentation, plunges sharply with successive presentations. This apparent nonindependence of performance over successive presentations is, however, shown to be an artifact of pooling the results of heterogeneous experimental variables.     

On the general form of Stevens’ law for loudness and softness

The loudness of a 1000-Hz tone at weak sound pressures and its softness at intense ones were scaled by the method of magnitude estimation. Estimates of loudness plotted as a function of sound pressure on double logarithmic coordinates showed the well-documented steepening near threshold. A similar steepening occurred in the softness function at high intensities. Stevens’ law, which is linear on these coordinates, could be recovered either by translating the pressure scale to a new origin, or by translating the response scale. Translations of the response scale were preferred because they produced functions in which loudness and softness were reciprocally related, whereas transformations of the stimulus made the softness function almost three times as steep as the loudness function.     

Averaging processes in ratings and choices based on numerical information

Ss were presented sets of numbers said to represent sample price information from grocery stores. Ss rated the relative desirability of shopping at each of a series of stores and were also asked to make paired-comparison preference choices. In Experiment I, some sets contained favorable information, some contained unfavorable information, and some contained neutral information added to the favorable or unfavorable information. The addition of neutral information led to a decrease in the polarity of responses. This is consistent with an averaging, but not an adding, formulation of how the information is integrated. In Experiment II, sets of favorable or unfavorable information varied in size and a set-size effect was obtained. The greater the amount of favorable or unfavorable information, the more extreme the response. This was accounted for by assuming that an initial neutral expectancy is averaged with the information presented.