scholarly journals On the difficulty to think in ratios: a methodological bias in Stevens’ magnitude estimation procedure

2021 ◽  
Author(s):  
Alica Mertens ◽  
Ulf K. Mertens ◽  
Veronika Lerche
Keyword(s):  
Power Function ◽  
Magnitude Estimation ◽  
Psychophysical Function ◽  
Standard Condition ◽  
Estimation Procedure ◽  
Numerical Response ◽  
Power Functions ◽  
Brightness Perception ◽  
Response Dimension ◽  
Methodological Bias

AbstractIn the field of new psychophysics, the magnitude estimation procedure is one of the most frequently used methods. It requires participants to assess the intensity of a stimulus in relation to a reference. In three studies, we examined whether difficulties of thinking in ratios influence participants’ intensity perceptions. In Study 1, a standard magnitude estimation procedure was compared to an adapted procedure in which the numerical response dimension was reversed so that smaller (larger) numbers indicated brighter (darker) stimuli. In Study 2, participants first had to indicate whether a stimulus was brighter or darker compared to the reference, and only afterwards they estimated the magnitude of this difference, always using ratings above the reference to indicate their perception. In Study 3, we applied the same procedure as in Study 2 to a different physical dimension (red saturation). Results from Study 1 (N = 20) showed that participants in the reversal condition used more (less) extreme ratings for brighter (darker) stimuli compared to the standard condition. Data from the unidirectional method applied in Study 2 (N = 34) suggested a linear psychophysical function for brightness perception. Similar results were found for red saturation in Study 3 (N = 36) with a less curved power function describing the association between objective red saturation and perceived redness perception. We conclude that the typical power functions that emerge when using a standard magnitude estimation procedure might be biased due to difficulties experienced by participants to think in ratios.

Scaling Apparent Distance in a Large Open Field: Some New Data

1983 ◽  
Vol 56 (1) ◽  
pp. 135-138 ◽  
Author(s):  
José Aparecido Da Silva ◽  
Cleuza Beatriz Da Silva
Keyword(s):  
Standard Deviation ◽  
Open Field ◽  
Power Function ◽  
Magnitude Estimation ◽  
Apparent Distance ◽  
Physical Distance ◽  
Power Functions ◽  
The Mean

Judged distance in a large open field, scaled by the method of magnitude estimation, is related to physical distance by a power function with an exponent smaller than unity. The exponents obtained with two ranges of distance were not affected by the availability of a standard. The mean exponent for all 80 individual power functions was 0.86, with a standard deviation of 0.11.

Effects of Concentration and Temperature on Gustatory Persistence

1984 ◽  
Vol 58 (2) ◽  
pp. 647-650 ◽  
Author(s):  
Amalia Mirta Calviño
Keyword(s):  
Sodium Chloride ◽  
Citric Acid ◽  
Magnitude Estimation ◽  
Estimation Procedure ◽  
Power Functions ◽  
Relative Persistence

The effects of concentration and temperature on the perceived persistence of citric acid, sodium chloride, sucrose, and urea were determined. The results obtained by a modified magnitude-estimation procedure suggest that power functions of the form P = K · Cn related the perceived persistence ( P in seconds) to the concentration ( C in % W/V) at each temperature and for each taste compound. Furthermore, the relative persistence ( K) and the slope of the functions of persistence ( n) showed changes when the temperature of taste stimuli varied.

scholarly journals Commutative semigroups whose endomorphisms are power functions

2021 ◽  
Author(s):  
Ryszard Mazurek
Keyword(s):  
Positive Integer ◽  
Power Function ◽  
Cyclic Group ◽  
Commutative Semigroup ◽  
Commutative Monoid ◽  
Power Functions ◽  
Commutative Semigroups ◽  
Finite Cyclic Group

AbstractFor any commutative semigroup S and positive integer m the power function $$f: S \rightarrow S$$ f : S → S defined by $$f(x) = x^m$$ f ( x ) = x m is an endomorphism of S. We partly solve the Lesokhin–Oman problem of characterizing the commutative semigroups whose all endomorphisms are power functions. Namely, we prove that every endomorphism of a commutative monoid S is a power function if and only if S is a finite cyclic group, and that every endomorphism of a commutative ACCP-semigroup S with an idempotent is a power function if and only if S is a finite cyclic semigroup. Furthermore, we prove that every endomorphism of a nontrivial commutative atomic monoid S with 0, preserving 0 and 1, is a power function if and only if either S is a finite cyclic group with zero adjoined or S is a cyclic nilsemigroup with identity adjoined. We also prove that every endomorphism of a 2-generated commutative semigroup S without idempotents is a power function if and only if S is a subsemigroup of the infinite cyclic semigroup.

The Wind-Sand Flux Structure of Grassland on the Northern Foot of Yinshan Mountain

2014 ◽  
Vol 668-669 ◽  
pp. 1530-1537
Author(s):  
Hong Tao Jiang ◽  
Chun Rong Guo ◽  
Chun Xing Hai ◽  
Shan Shan Sun ◽  
Yun Hu Xie ◽  
...  
Keyword(s):  
Vertical Distribution ◽  
Power Function ◽  
Exponential Function ◽  
Vertical Direction ◽  
Power Functions ◽  
Height Range ◽  
Sand Flux ◽  
Soil Flux ◽  
The Vertical Distribution ◽  
Better Than

Sand samplers were layed out in the grassland located in the northern foot of Yinshan Mountain for collecting soil flux samples from 0 to 1.5m height above the surface from Mar., 1, 2008 to Feb., 29, 2009.Exponential and Power functions were both used for describing vertical distribution of sand flux in the grassland, the results indicated that determination coefficient of Power function varied from 0.898 to 0.992 while 0.432 to 0.661 for exponential function. Power function is better than exponential function in describing the vertical distribution of both annual and seasonal soil flux, summer excluded. Annual cumulative percentage of each height was determined indirectly according to the power function mentioned above, the result indicated that up to 2m height,15-25% of soil flux concentrated with in 10cm above the surface,25-35% of soil flux concentrated within 20cm above the surface,30-40% of soil flux concentrated within 30 cm above the surface, 43-54% of soil flux concentrated within 50 cm above the surface,85-90% of soil flux concentrated within 150 cm above the surface, respectively. No significant differences of soil flux structures in spring, autumn, winter and in the whole year were found. The research on wind erosion of grassland in the vertical direction more dispersed, in the height range of sediment accumulated percentage was lower than that of the previous research.

Scaling of Very, Very Short Visual Extents

1980 ◽  
Vol 51 (1) ◽  
pp. 279-282 ◽  
Author(s):  
S. C. Masin
Keyword(s):  
Magnitude Estimation ◽  
Linear Relation ◽  
Psychophysical Function ◽  
Past Experience ◽  
Perceptual Constancy ◽  
Production Methods ◽  
Straight Line

Using the magnitude estimation and production methods, the psychophysical function for very, very short visual extents was shown to be a straight line. The argument is made that the linearity of the psychophysical function is independent of past experience. Such a linear relation is plausibly due to the linearity of the transformation, through perceptual constancy, of the physical extents into apparent extents.

Magnitude Estimation of Absolute Distance Underwater

1972 ◽  
Vol 35 (3) ◽  
pp. 963-971 ◽  
Author(s):  
Steven H. Ferris
Keyword(s):  
Power Function ◽  
Magnitude Estimation ◽  
Distance Estimation ◽  
Optical Distortion ◽  
General Tendency ◽  
Absolute Distance ◽  
Water Turbidity ◽  
Power Function Exponent

Direct estimates of absolute distance were obtained in air and in water of varying turbidity. Distance in water was under- or overestimated, depending on the interaction of 3 factors: (1) a general tendency to underestimate; (2) optical distortion, which causes underestimation; and (3) water turbidity, which increases the magnitude of judgments, and whose effect increases with distance. Also, whereas the power-function exponent for distance estimation in air was slightly less than 1.0, exponents in water were greater than 1.0 and increased with increased turbidity.

scholarly journals Assessing power function relationships in magnitude estimation

1981 ◽  
Vol 29 (2) ◽  
pp. 178-180 ◽  
Author(s):  
Barsha J. Coleman ◽  
Richard G. Graf ◽  
Edward F. Alf
Keyword(s):  
Power Function ◽  
Magnitude Estimation

Aversion to Daytime Illumination in Patients with Congenital Achromatopsia

1987 ◽  
Vol 64 (3) ◽  
pp. 923-926
Author(s):  
Rockefeller S. L. Young ◽  
James Price ◽  
Joseph Harrison
Keyword(s):  
Magnitude Estimation ◽  
Estimation Procedure ◽  
Normal Subjects

The aversion to daytime illumination in patients with congenital achromatopsia is not well understood. In the present study, we used a magnitude estimation procedure to compare the perceived brightness for 5 congenital achromats and for seven normal subjects. Contrary to the patients' beliefs, results suggest patients' brightness estimates are similar to those of normal subjects.

scholarly journals Acoustic Correlates of Breathy Vocal Quality

1994 ◽  
Vol 37 (4) ◽  
pp. 769-778 ◽  
Author(s):  
James Hillenbrand ◽  
Ronald A. Cleveland ◽  
Robert L. Erickson
Keyword(s):  
Magnitude Estimation ◽  
Estimation Procedure ◽  
Harmonic Amplitude ◽  
Acoustic Measures ◽  
Acoustic Correlates ◽  
Two Measures ◽  
Vocal Quality ◽  
Normal Women ◽  
Normal Men ◽  
Spectral Tilt

The purpose of this study was to evaluate the effectiveness of several acoustic measures in predicting breathiness ratings. Recordings were made of eight normal men and seven normal women producing normally phonated, moderately breathy, and very breathy sustained vowels. Twenty listeners rated the degree of breathiness using a direct magnitude estimation procedure. Acoustic measures were made of: (a) signal periodicity, (b) first harmonic amplitude, and (c) spectral tilt. Periodicity measures provided the most accurate predictions of perceived breathiness, accounting for approximately 80% of the variance in breathiness ratings. The relative amplitude of the first harmonic correlated moderately with breathiness ratings, and two measures of spectral tilt correlated weakly with perceived breathiness.

Using Psychophysics to Design Speech Warnings

2000 ◽  
Vol 44 (22) ◽  
pp. 698-701
Author(s):  
E. Hellier ◽  
B. Weedon ◽  
J. Edworthy ◽  
K. Walters
Keyword(s):  
Power Function ◽  
Magnitude Estimation ◽  
Power Law ◽  
Warning Signal ◽  
Acoustic Parameter ◽  
Psychophysical Scaling ◽  
The Relationship ◽  
Power Function Exponent

An experiment is reported which applies psychophysical scaling techniques to the design of speech warnings. Participants used magnitude estimation to rate the perceived urgency of computer generated warning signal words (Deadly, Danger, Warning, Caution, Note) that varied systematically in speed. Stevens (1957) Power Law was used to model the relationship between changes in the acoustic parameter and changes in the perceived urgency of a particular signal word. The value for warning designers of the power function exponent, which quantifies and predicts the effect of acoustic changes on perceived urgency, is discussed.

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