Sunday, November 25, 2012

Psychophysics in Operation Research


On behalf of my workshop at Kathmandu, I am writing few chapters here. I am grateful to Professor Sunity Shreshtha Hadda for her interest in my lecture. 


Chapter 1: Introduction to Psychophysics
The Key issue in Operation research is  optimization of resources to bring maximum benefit and minimize the cost. This is done by changing physical attributes of the product. Knowledge about psychophysics helps the operation research scientist to select which attribute of the product will be changed so that the change is perceptible, reliable and satisfying to the customers. Therefore psychophysics bridges the gap between  product engineers and marketing managers.

Change perception

Each  product has multidimensional physical attributes like weight, height, width, depth, color, duration etc. The attributes are sensed by different sensory organs like visual (eye), auditory, (ear),  olfactory (nose), gustatory (tongue) and cutaneous (skin) sensory organs.  Besides the above five, kinesthetic sensation (muscular sensation) also helps to sense change in product attribute like weight. Each sensory organ has different threshold of perception and in different units.  Wavelength of color and decibel of sound are the common units of threshold for perceiving change in visual and auditory organs.
Figure 1.1 Change perception

Threshold

Threshold is the limit wherein 50% of total trials one can sense the change in product attribute. 

                Figure 1.1 shows that when stimulus intensity is 25 units, there is 50% probability  to perceive the change in intensity level. Below 25 units, change in stimulus intensity cannot be perceived and after 25, change is perceptible.  Here 25 unit is threshold.  
In the above example, we have seen two scales – physical and psychological. Stimulus intensity is measured by physical scale (X-axis) and probability of perception is assessed by psychological scale (y-axis). Psychophysics is the study of science that  investigates quantitative relationship between  changes in physical events or attributes and changes in corresponding psychological events. It helps us in determining thresholds of perception. Study of threshold is used  in designing torch light, bulb, car horns, product weight, supersonic planes etc. There are three thresholds or limens – absolute, differential and terminal.

Absolute threshold :           

It is the lower limit of stimulus intensity, below which presence of stimulus can not be experienced. For example, one can not see light when it is far away as intensity of light is very low. Similarly,  tone can not be perceived when sound  intensity is below the decibel of absolute threshold.  

Terminal threshold

It is the upper limit of stimulus intensity,  above which presence of stimulus can not be experienced. For example, sound of supersonic  plane can not be sensed when it moves over the head. Terminal threshold is just opposite of absolute threshold. Absolute is the lower limit and terminal is the upper limit of stimulus intensity. The event occurs after differential threshold. Below the terminal threshold, presence of stimulus can be experienced.

Figure 1.2 Location of Absolute and Terminal thresholds
Figure 1.2 shows two scales in both lower and upper extremes. R scale is psychological and S scale is stimulus scales. In R-scale, ‘- - - - ‘ indicates no experience in stimulus. At the lower extreme, where in ‘- - - - -‘ ends, absolute threshold lies. Similarly at the upper level, wherein ‘- - - - -‘ starts terminal threshold lies. In the S-scale, there is no ‘- - - - -‘ indicating continuous presence of stimulus. ‘>’ indicates gradual increase in stimulus intensity.
Differential threshold
It is the limit of stimulus intensity, below which change in stimulus intensity can not be experienced. Like absolute it is not the lower limit of stimulus intensity. It is found after the absolute threshold.  With  gradual change in stimulus intensity after absolute threshold,  one event comes wherein change in stimulus intensity can not be perceived 50% of total trials. This limit is called differential threshold. It is the limit of just noticeable difference (jnd).
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Figure 1.3  The three thresholds.  S indicates stimulus and R indicates response continua
In Figure 1.3, the distance between S20 and R20 is symmetrical. This indicates subject experiences change in stimulus intensity at same level. But the distance between S40 and S44 is relatively higher than the same between R40 and R44. The limit wherein subject can just discriminate change in stimulus level is differential threshold.


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Chapter 2: Research Design
Research design of psychophysics can be understood with following formula:
R = f ( O, S, T)
Formula suggests subject’s response to the change in stimulus attribute is the function bof interaction among three things –  Organism (O), stimulus value (S) and trials (T).
Response: It varies with stimulus modalities, the psychophysical methods followed. Classical psychophysics follows categorical response scale. For example, ‘I can not see’ or ‘I can see’ or ‘I do not find difference’. Responses are symbolized for recording.
RESPONSES
SYMBOLS
I can not see/ I can not feel/ I can not hear
-
I can see / I can feel/ I can hear
+
I do not find difference
=
Uncertainty
?

Organism :  It may be any animal. But here organism is person to whom the stimulus will be administered for judgment. Administration and judgment depend on physical , psychological and demography characteristics of subject. Physical characteristics are acquity of sensory organs,  brain maturity, and neural functions. Psychological characteristics are ability to discriminate and to integrate sensory experiences, perceptual organization, learning, memorizing, reasoning for comparative judgments,  motivation , interest, temperament and personality patterns. Demographic characteristics are educational level, socio-economic status.
Stimulus value:   It is the unit of stimulus or product attribute. For kinesthetic, it is the weight, for visual, it is wavelength of color, for hearing, it is the decibel and for the skin, it is temperature. Product attribute varies with stimulus characteristics and sensory modalities.  Height, width, length, color are the characteristics for visual experiencing the product.  Tone, pitch, loudness are for auditory experiences. Heat, cold, rough, smoothness are the characteristics when one experiences product with skin or cutaneous sensory organs. One experiences food characteristics through tasting some characteristics as sweet, sour, bitter, salted. Another type of product  characteristics are durability,  reliability, usability and aesthetic. But these are not very important in research on classical psychophysics.

Trials: Trials are of ascending and descending in nature. Usually, administration of stimulus follows descending order. For descending, stimulus value starts from the upper side of base line level and for ascending stimulus value starts from lower side of the base level.
      Classical psychophysics is done within laboratory so that independent variable can be administered systematically by controlling all the intervening variables. When O is asked to judge the weight discrimination, he or she will not be allowed to look at the weight and it will be done in the noise proof room so that no sound can divert his attention. One checklist will be administered before starting the experiment to know the current status of O. Instruction should be standardized and be understood by the O.
    Aim of psychophysics is determination of thresholds. It can be done with three methods as method of minimal changes, method of frequency and method of average error.  In method of minimal changes stimulus are presented systematically with minimum changes in stimulus value. Systematic means first trial is descending and the next trial is ascending in order. But in frequency method, stimulus values are random. For average error, O is administered the stimulus in both non and random variation. The three methods are discussed in the next chapter.