Magnitude estimation of apparent sums and differences

Os first scaled two continua by magnitude estimation: apparent area of circles and loudness of 1,000-Hz tones. They then gave magnitude estimations of apparent sums and apparent differences for IS pairs of stimuli on each of the two continua. The scales for sums and differences were in some cases nearly linearly related to the power function obtained when the same as scaled the underlying continuum. However, systematic departure from linearity was the usual result. The power law exponents obtained were generally smaller than those usually reported for the two sensory continua.     

Magnitude estimation of short electrocutaneous pulses

Summary A comparison was made of electrocutaneous magnitude estimation data across two experiments with contextual differences not involving stimulus parameters, such as number and range of stimuli and relative position of the standard in the stimulus range. The data were fitted by 2-parameter linear, log-linear and power functions. When the data are fitted by either linear or log-linear equations, both intercept and slope parameters are significantly affected by the different contextual factors. When the data are fitted by a power function, however, only the intercept is altered; the slope remains invariant despite contextual changes introduced in the second experiment.Although the empirically derived psychophysical power law has been applied to magnitude estimation data for all other sensory modalities, its application to electrocutaneous stimuli has been less successful.     

Magnitude production and magnitude estimation of taste intensity

Magnitude productions of sodium chloride (salty), quinine hydrochloride (bitter), and sucrose (sweet) yielded steeper psychophysical functions than those obtained with magnitude estimation. Hydrochloric acid (sour) produced the opposite effect. The results are discussed with respect to previous findings in taste intensity scaling and to general psychophysical considerations.     

Magnitude estimation of warmth: intra- and intersubject variability

Fifty-two subjects, both male and female, 18 to 62 years old, were asked to hold a metal bar maintained at different temperatures (33 degrees to 42 degrees C), and to estimate the magnitude of the resulting thermal sensation. On the average, the estimates were linearly related to the stimulus temperature, although most individual subjects either under- or overestimated middle-range values. Intersubject variability, which was twice as large as intrasubject variability, could not be accounted for by gender, age, or body-temperature differences.     

Magnitude estimation scaling judgments of speech intelligibility and speech acceptability.

20 female students in speech-language pathology provided magnitude estimation scaling responses for the speech intelligibility and acceptability of audio-taped speech samples varying systematically the number of consonant sounds produced correctly. Analysis indicated no significant over-all differences between listeners' judgments of intelligibility and acceptability; however, listeners tended to judge samples with fewer than 50% of the consonants correct as more acceptable than intelligible, and they judged samples with more than 50% consonants correct as less acceptable than intelligible.     

Magnitude estimation of conceptual data dimensions for use in sonification

Sonifications must match listener expectancies about representing data with sound. Three experiments showed the utility of magnitude estimation for this. In Experiment 1, 67 undergraduates judged the sizes of visual stimuli and the temperature, pressure, velocity, size, or dollars they represented. Similarly, in Experiment 2, 132 listeners judged the pitch or tempo of sounds and the data they represented. In both experiments, polarity and scaling preference depended on the conceptual data dimension. In Experiment 3, 60 listeners matched auditory graphs to data created with the results of Experiment 2, providing initial validation of scaling slopes. Magnitude estimation is proposed as a design tool in the development of data sonifications, with the level of polarity preference agreement predicting mapping effectiveness.     

The apparent length of a line as a function of its inclination

In the first of two experiments reported here, subjects adjusted the length of a variable line until it appeared to be as long as a standard line. There were two sizes of standard line, 3 and 6 inches, and each was shown vertically for some trials and horizontally for others. The variable line was presented in each of the 10° positions from 0° (horizontal), through 90° (vertical), to 170°. The principal results of the first experiment are:

(1) Vertical lines look longer than horizontal lines of the same length, but lines tilted 20°-30° to the left of vertical look longer than lines in any other orientation. The results are asymmetrical, because lines tilted to the right of vertical do not look as long as those tilted to the left of vertical.

(2) The variability of the settings increases as the angle increases between the standard and variable lines.

(3) When they are expressed in percentage terms, the data obtained with the 3-and 6-inch standards are virtually identical, i.e. the data for the 3-inch standard can be made to match those for the 6-inch standard simply by doubling the former.

(4) There are enormous differences among subjects in the patterns of settings made at the various angles. A few subjects apparently experienced no illusory effects since they adjusted the variable line to about the same physical length irrespective of its orientation. Other subjects showed exaggerated overestimations of the variable line for vertical and near-vertical positions.

In the first experiment, the variable line was always to the left of the standard, and it was natural to assume that this position effect had somehow produced the asymmetry noted in paragraph 1 above. This hypothesis was tested in the second experiment which alternatively showed the variable line above, below, to the right of, and to the left of the standard line. The results of this experiment generally confirm the data of the first experiment in showing that lines tilted 20°-30° to the left of vertical look longer than lines tilted to any other position. In addition, the second experiment shows that this asymmetry in the results is not a function of the relative positions of the variable and standard lines. In general, however, overestimations of length are smaller when the two lines are one above the other, greater when the two lines are side by side.     

Magnitude estimation of manually assessed elastic stiffness: stability of the exponent

Magnitude estimations were obtained for manual assessments of pure elastic stiffness stimuli (metal springs). 20 subjects of varied experience in manual assessment of spinal stiffness volunteered to participate. The mean exponent of the power function relating perceived magnitude of elastic stiffness to measured physical magnitude was 1.65. Exponents varied across the 20 individuals but were stable across testing sessions held at least 2 weeks apart, and the size of the exponent was not related to prior experience.     

Magnitude estimation and magnitude production: stimulus frequency effects on magnitudes of lingual vibrotactile sensation

The methods of magnitude estimation and magnitude production were employed to investigate the effects of stimulus frequency on supra-threshold lingual-vibrotactile sensation-magnitude functions. The method of magnitude estimation was used to obtain numerical judgments of sensation magnitudes for nine stimulus intensities presented to the anterior dorsum of the tongue. The vibrotactile stimulus frequencies employed for 10 subjects (M age = 21.1 yr.) were 100, 250, and 400 Hz. The numerical responses obtained during the magnitude-estimation task were in turn used as stimuli to obtain magnitude-production values for the same three vibrotactile stimulus frequencies. The results appeared to present two suggestions. First, the effects of stimulus frequency on lingual vibrotactile-sensation magnitudes may be dependent on the psychophysical method used in any particular experiment. Second, lingual-vibrotactile magnitude-estimation scales may demonstrate asymptotic growth functions above about 25 dB sensation level. The limitation in the growth of sensation magnitude occurred for all three vibrotactile stimulus frequencies employed.     

Beyond the average: walking infants take steps longer than their leg length

Traditionally, infant walking is characterized by small steps, attributed to limited balance control and strength. However, analyses of individual steps revealed that infants occasionally take large steps exceeding their leg length. These large steps provide evidence of advanced balance control and strength.     

The estimation of ultrametric and path length trees from rectangular proximity data

A least-squares algorithm for fitting ultrametric and path length or additive trees to two-way, two-mode proximity data is presented. The algorithm utilizes a penalty function to enforce the ultrametric inequality generalized for asymmetric, and generally rectangular (rather than square) proximity matrices in estimating an ultrametric tree. This stage is used in an alternating least-squares fashion with closed-form formulas for estimating path length constants for deriving path length trees. The algorithm is evaluated via two Monte Carlo studies. Examples of fitting ultrametric and path length trees are presented.G. De Soete is Aspirant of the Belgian Nationaal Fonds voor Wetenschappelijk Onderzoek at the University of Ghent, Belgium. W. S. DeSarbo and J. D. Carroll are Members of Technical Staff at AT&T Bell Laboratories, Murray Hill, N.J. G. W. Furnas is Member of Technical Staff at Bell Communications Research, Murray Hill, N.J.