Perception Chap. 1

Why will a probability plot of sensation magnitude evoked by internal noise alone appear in the form of a normal distribution?

Because a major source of noise is the baseline firing of nerve cells that produces spontaneous activity in sensory pathways.

Function

A mathematical descriptor of how one variable is related to another and generally expressed as a formula. If S represents perceived intensity of sensation and I represents stimulus intensity, then a linear function would have the form S = k x I where k represents the slope of the function.

Signal Detection Theory

A theory based on statistical concepts that takes into account detection and discrimination sensitivity as well as non-sensory factors that may affect the decision-making process.

Signal

An event, action or object that serves as a stimulus for detection or discrimination. The terms signal and stimulus are often used interchangeably.

Two-alternative forced choice 2 AFC

An experimental procedure where 2 presentations are made with only one of them containing the stimulus. The subject's task is to identify the presentation with the stimulus. Criterion effects are minimized in this procedure because the subject is told that only one of the two is right.

Linear Function

For any given increase in physical intensity, there is a certain increment in the perceived intensity. The proportion between the two remains constant across the whole range. In other words, the slope remains constant.

Ekman's Law

Detectable changes in sensation (just noticeable differences) rather than being constant at all levels were related to sensation in a linear manner. The relationship between changes in sensation that are just detectable at a particular sensation level or magnitude is exactly analogous to Weber's law.

Hearing

Detection threshold is so small that it represents movement of the eardrum by only 10^-10 cm. This is smaller than the diameter of a hydrogen molecule.

Power law exponents

For some sensory dimensions, the exponent is less than 1.0. For others, it is greater.

Fechner's Law

Fechner knew that to uncover the relation between sensory magnitude and stimulus intensity, it was necessary to know the way in which the function changed at progressively greater supra-threshold values. He considered Weber's law, which states that higher levels of supra-threshold intensity require a correspondingly greater change in intensity (delta I) to produce a change in sensation (delta S) that is just distinguishable (JND). Fechner knew nothing about the actual magnitude of delta S needed to produce a JND or whether the value changed at different levels of sensation. Taking Fechner's assumption into account, Fechner's law asserts that at low intensity levels, the magnitude of our sensations can change quite rapidly with small changes in stimulus intensity, whereas we become much less sensitive with higher intensities.

Fechner vs. Ekman

Fechner: The JND remains constant along the sensory continuum. Ekman: The JND does not remain constant along the sensory continuum.

Cross-Modal Matching

Subjects were asked to compare stimuli from one sensory modality to another. What makes this procedure unusual is that comparisons are required not within a single sensory dimension, where the task is easier, but rather two entirely different sensory experiences, where the task is to make a judgment of equal sensory magnitude. It turns out that we are also quite good at these kinds of comparisons.

Vision

The eye can be exposed to as little as 54-148 photons to produce a detectable sensation of light. If losses in transmission through the eye are considered, it turns out that this represents the absorption of a single photon in about 5 to 14 detector cells of the retina.

Sensory Transducer Theory

The notion that transformation or transduction of physical energy in the stimulus into biological/neural signals is the basis of the power law. According to this theory, the power law exponent depends on the sensory mechanisms that are involved in this process.

Exponential Function

The perceived sensation intensity changes very slowly at low values of physical intensity. After a certain point, the function takes off such that small changes in stimulus intensity produce a dramatic increase in perception. The slope itself progressively increases with physical intensity.

What happens if the subject employs a liberal criterion? DELETE

The point would be located toward the up

What is the value of the power or exponent?

There was no one general exponent value that served all of the senses. Different sensory experiences are related to stimulus intensity by a particular exponent. The actual exponent value depends on the particular aspect of that sensory dimension.

What happens if d' = 0.5?

There will be a greater similarity in hit and false alarm rates because of the closeness of the 2 distributions.

Stevens suggested that the power law reflects the operation of sensory systems at their lowest levels. What does he mean by this?

They operate at the interface where the physical stimulus becomes converted into a biological signal. Accordingly, the neural output of sensory systems must follow a power law relation with the incoming stimulus. The exponent is determined by the nature of the transformation at this site.

What are the 2 extreme cases of power law exponents?

brightness for extended targets (0.33) electric shock (3.5)

Correct Rejection

When no stimulus is present in a trial and the subject answers NO.

False Alarm

When no stimulus is present in a trial and the subject answers YES.

Miss

When the stimulus is present in a trial (signal + noise) and the subject answers NO.

Hit

When the stimulus is present in a trial (signal + noise) and the subject answers YES.

Discrimination scaling of non-sensory parameters produce...

logarithmic functions

ratio scaling procedures yield

power functions

What is the vale of k in Ekman's law?

0.03

Approach 1 to obtain the relation between physical events and perceptual experience.

1. Ask human subjects to rate the perceived intensity of a certain stimulus at various physical intensities. 2. Plot the 2 sets of values and determine which of the general functions best describes the transformation of a physical input into a perceptual event.

How do you determine the value of K, or Weber's Fraction?

1. Determine the difference threshold at a number of different intensities. 2. Difference thresholds are plotted at Y-axis against difference values of intensity on X-axis to reveal a straight line. 3. The slope of this linear function is the Weber fraction If slope is 0.08, then an 8% increase or decrease in light intensity is enough to produce a JND and allow us to detect that change in perceived brightness.

What are the advantages to understanding the mathematical relation between the physical and the perceptual world?

1. It provides an estimate of the perceptual quality of a stimulus in numerical terms and allows comparisons with other stimuli. 2. They allow comparisons among individuals and species.

Approach 2 to obtain the relation between physical events and perceptual experience.

1. It requires a measure of the smallest change in stimulus input that causes a just discriminable change in sensation. 2. To understand how this can reveal anything important, we have to examine the ideas first proposed by 19th century experimental psychologists, who understood that a mathematical relation between physical and perceptual qualities could be established by obtaining two basic characteristics or descriptors of a function.

Fechner's Assumption

1. It's impossible to measure sensations. 2. Fechner knew nothing about delta S needed to produce a JND. 3. He didn't know if the value changed at different levels of sensation. 4. He proposed that the same value of delta S was needed at all sensory magnitudes because a JND is a standard unit of change that represents a psychological constant. 5. The higher intensity levels require a greater change in the physical stimulus (delta I) to produce identical changes in sensation (delta S). 6. A JND is presumed to occur through identical changes in sensation (Fechner's assumption) that are brought about by progressively greater changes in stimulus intensity (Fechner's law).

Prothetic

1. Sensory experiences where subjects can make a judgment of how much. 2. Sensations that rely on an additive process. 3. Changing some aspect of the stimulus alters the magnitude of sensory perception. 4. The additive produces an increase or decrease in the activity of sensory neurones.

The "signal plus noise" distribution is a reflection of which 2 parameters?

1. Signal intensity 2. Detection Sensitivity

What are the two factors we have considered so far? p. 23

1. Stimulus expectancy 2. Motivation

What are the two variables of perception?

1. The physical stimulus 2. The resulting perceptual impression

To establish the relation between physical and perceptual experience, experimental psychologists understood that a math relation between physical and perceptual qualities could be established by obtaining 2 basic characteristics or descriptors of that function. What were they?

1. The starting point 2. The slope

By convention, most psycho-physicists use which response level as the measure of noticeable decrement in stimulus? Decrement Threshold

25% brighter. The target light intensity needs to be lowered to c. a - c = difference threshold.

What does doubling loudness (0.67 exponent value) require?

3 times increase in sound intensity

What arbitrary response level have psycho-physicists used to obtain absolute threshold?

50% response level. The physical intensity that produces this response is taken to be the absolute threshold.

Weber's Law

60 lit candles + 1 = detectable JND 120 lit candles + 1 = non-detectable JND Difference Threshold = Delta I Proportion of Stimulus Intensity = K Stimulus Intensity = I Delta I = K x I The difference threshold is NOT a constant value but some proportion of the stimulus intensity. Higher levels of supra-threshold intensity (I) require a correspondingly greater change in intensity (Delta I) to produce a change in sensation (Delta S) that is just distinguishable (JND)

By convention, most psycho-physicists use which response level as the measure of noticeable increment in stimulus? Increment Threshold

75% brighter. When the target light intensity is raised to b, we achieve this result. b - a = difference threshold.

What does doubling brightness (0.33 exponent value) require?

8 times increase in light intensity.

Ideal Detector

A detector, animal or machine, that can always detect a signal when its intensity is above a certain defined level (threshold) and always fails to detect it when it is below that level.

Radiometer

A devise that can determine the intensity of light reflected by an object. It will specify the intensity in a set of units for which it has been calibrated.

Touch

A dimpling of the skin by as little as 10^-5 cm is sufficient to be detected.

Scaling

A general psychophysical procedure to estimate the amount of magnitude of something related to perception or some other aspect of psychology.

The ROC Curve

A graphical plot of hits vs. false alarms that shows how these values change with respect to each other at all possible criterion levels.

Experiment 2 - Stimulus 70%

A more liberal criterion will be adopted, reflecting the higher probability of stimulus appearance. The criterion will now move to the left of the one shown in Figure 1.10. Much lower sensory magnitudes will now be sufficient to elicit a YES response because the subject will expect more trials to contain a stimulus. Depending on an inherent expectation of stimulus appearance, the subject will be either more or perhaps less inclined to give a positive answer on each trial., even though none of the other parameters in the experiment have changed. When the subject is notified that stimulus appearance probability will be set at 70%, the accompanying leftward liberal criterion shift results in higher rates of false alarms and hits - 0.64 and 0.91, respectively.

Method of Adjustment

A psychophysical method in which the subject directly adjusts stimulus intensity to produce a detectable sensation. The initial intensity would be set either above or below threshold, and the subject would change the value until the stimulus is just perceptible or when the sensation just disappears.

Magnitude Estimation

A psychophysical scaling procedure developed by SS Stevens in which human subjects are required to make numerical estimates of the sensory magnitudes that are evoked by stimuli of different physical intensities.

Step Function

A response function that makes an abrupt transition from one level to another.

Social Psychophysics

A set of scaling methods to establish measures of subjective magnitude in the areas of esthetic preference or social/political opinion.

criterion (ß)

A set-point or cut-off point that is internally established by the subject. On those trials where the sensory magnitude exceeds ß, the subject will indicate that a detectable sensory event has occurred and will respond YES (decision could be a hit or false alarm) If the sensory magnitude fails to reach ß, then the subject will respond NO. (decision could be correct rejection or miss).

Equal Sensation Functions

Across 10 different experiments, subjects were asked to adjust sound level until it matched the perceived intensity of a stimulus from another sensory domain. These functions show different results depending on the power function for the sensory parameter that was being compared. The actual slope of these functions turned out to be very close to the predicted slope based on the power law exponents for loudness and the particular sensory parameter to which it was being matched. Electric shock shows a steep relationship for cross-modal matching with loudness, implying that small changes in electric current require large changes in sound setting for a judgment of equality. The opposite is true for cross-modal matches with brightness, which has a small exponent value.

Multidimensional Scaling

After the method of trials, when enough data has been collected with a sufficient number of colours, you can represent the information by way of a similarity map where those colours perceived to be similar occupy nearby positions and those dissimilar are farther apart. Psychological similarity is now represented by physical distance in a spatial map. This allows an investigator to peer into the underlying attributes or qualities of the stimulus that produce similar or dissimilar perceptual experiences. Multi-dimensional scaling is now well-established as the tool of choice for pairwise evaluations of entities in many fields.

Ogive

An S-shaped response function that is typically seen in psychophysical experiments where detection or discrimination performance is measured.

Where does the conservative criterion go on the Receiver Operating Characteristic Curve?

At the lower end of the receiver operating characteristic curve.

Where does the liberal criterion go on the Receiver Operating Characteristic Curve?

At the upper end of the receiver operating characteristic curve.

Noise

Background activity that is unrelated to the stimulus and which can interfere with its detection.

Intra-modal Matching

Comparing different aspects of a stimulus within a particular sensory domain or modality. E.g. different wavelengths of light on brightness perception different tone frequencies on loudness perception taste sensations generated by sweet vs. sour substances

Cross-modal comparison

Comparison among the different sensory modalities.

Ekman's law equation

Delta S = k x S

JND vs. Difference Threshold

Difference Threshold = The minimum change in physical intensity required for a noticeable change in sensation. They are always determined at supra-threshold levels. JND = A change in sensation that is sufficient to allow a mental event to be just detected. The JND, which is a psychological parameter and cannot be experimentally determined, is the subjective counterpart of the difference threshold, a physical parameter that can be experimentally derived.

JND vs. Difference Threshold (Delta I)

Difference Threshold: A change in sensation that is sufficient to allow that mental event to be just detected. JND: psychological parameter that CANNOT be experimentally determined. It is also the subjective counterpart of the difference threshold, which is a physical parameter that can be experimentally derived.

Ratio Scaling

Direct estimations of sensory magnitudes produced by stimuli of different intensities. The technique is based on the theory that sensory magnitudes fall on a ratio scale and can be directly measured by the perceiver.

Gustav Fechner

He believed that: 1. there existed a general relationship between physical and perceptual qualities 2. it was similar for all types of sensations. 3. it could be obtained by knowing the stimulus energy at which the output can just be detected or discriminated (absolute and difference thresholds).

Ernst Weber

He was interested in determining the gradations of sensory experience at supra-threshold levels. His question: How much a stimulus needed to change to produce a detectable change in sensation. Difference in physical intensity that was required to accomplish this became known as the difference threshold. Weber worked mainly with discrimination of object weights, carrying out a series of careful experiments on the smallest detectable change for a series of different starting weights.

What happens if Weber's law and Ekman's law are applied? Why?

If Weber's law and Ekman's law are applied, then the mathematical outcome becomes Stevens' power law.

Liberal Threshold vs. Conservative Threshold

If the subject is told in advance that each hit is 50 cents and each false alarm is 10 penalty, then there will be a greater tendency for YES votes. If the condition for false alarms is greater than that for hits, the subject will tend to be very cautious and take fewer risks.

60% YES Value

It is possible to use as the definition of threshold sensation. In this case, the stimulus intensity that produces this would be taken as the absolute threshold of detection. In reality, there is no all-or-none condition for stimulus detection.

Multiple Discrimination Threshold Experiments

It shows the psychometric functions we would obtain if we conducted the experiment three times by setting the reference light at progressively higher intensities each time. The psychometric functions are displaced to the right and become flatter. For each, we can determine the difference threshold. Let's analyze increment threshold: 1. We determine the target light intensities that are perceptually equivalent in brightness to the reference light for all three cases (a1, a2, a3). 2. We find the intensities producing 75% brighter responses (b1, b2, b3). The increment threshold for the first psychometric function (b1 - a1) will be less than that of the second function (b2 - a2) which is less than that of the third (b3 - a3). The greater the intensity level at which we have to make a JND judgment, the greater the difference threshold needed to attain a JND.

Brightness curve

It shows what is described as a negatively accelerating function. It grows rapidly with increasing light intensity, though further increments will gradually reduce the rate at which perceived brightness increases.

First Payoff Condition - Liberal

It will place the criterion value more toward the left side of the noise/signal + noise distributions and will produce hit and false alarm rates that will plot toward the upper end of the ROC curve.

Second Payoff Condition - Conservative

It will produce a criterion more toward the right side of the noise/signal + noise distributions and will yield a point on the lower end of the ROC curve. If we employed other payoff conditions, then the reward/penalty ratio would produce appropriate points elsewhere on the ROC curve. We find that motivational states induced by different payoff conditions produce criterion shifts that are similar to those we saw on the previous page for stimulus expectancies.

What happens to K at extreme situations of high or low intensities?

K can change dramatically, such that generalities of Weber's law no longer apply.

Which function relating intensity and sensation can account for Fechner's law?

Logarithmic Function

Is an outsider capable of measuring our own perceptions?

No.

Stimulus

Object or event in the physical world that may be perceived through stimulation of one of the sensory systems.

What is Supra-threshold? How is it determined?

Physical intensity values that are above absolute threshold and generally detectable. To determine this, we have to determine how the slope changes as a function of physical intensity. The slope would have to be determined for several supra-threshold points to see how it is changing.

Subthreshold

Physical intensity values that are below absolute threshold and not detectable.

Weber's Fraction

Proportion K

Which processes generally obey the power law, prothetic or metaethic?

Prothetic

Is there a universal Weber fraction that applies to all sensory systems?

There is no universal Weber fraction that applies to all sensory systems but considerable variation such that certain sensory processes are very sensitive to change, whereas others are not.

Fechner's Law formula

S = k x log (I)

Power Law

S = sensation K = scaling constant that takes into account units used to represent stimulus intensity I = physical intensity b = exponent or power value

Meta-ethic

Sensations that rely on a SUBSTITUTIVE process such that changing some aspect of the stimulus alters the quality of the sensory impression. E.g. In colour, there are no quantitative differences between the hues of red and green. They show a change in quality associated with the substitution of one kind of neural excitation by another.

Method of Limits - Ascending and Descending Series

Stimulus intensity is systematically increased or decreased by the experimenter until the subject gives a change in response. This technique provides more reliable estimates. If ascending series is used for subject, intensity of stimulus is initially set at a sub-threshold value and increased by a fixed amount in successive trials until the subject reports that it is perceived. If descending series, supra-threshold intensity value is gradually reduced until the percept disappears.

Method of Constant Stimuli

Stimulus intensity values are randomly chosen from a preset range. Neither the experimenter nor the subject know the value of the next stimulus to be presented. The subject merely replies if a sensation occurred or not. The subject responses over many trials are stored and later used to generate a response frequency for each intensity level. In these experiments, the stimulus intensity will be randomly chosen by the computer from a predefined set of values. The lowest intensity value must be one that is never detected. The highest value should always be detected. The threshold intensity would be located somewhere within this range.

Method of Trials

Subjects are presented with 3 colours at a time and asked to judge which pair is the most similar.

d'

The difference between the means of the noise and signal + noise distributions. According to SDT, d' can increase either by increasing the strength of the signal or by increasing the sensitivity of the detector.

Discrimination or Confusion Scaling

The application of difference threshold measurements to estimate sensory magnitude functions. The theoretical foundation for this approach is based on the notion that JNDs represent a constant unit of sensory change, regardless of the actual operating level.

Response Bias

The influence of factors unrelated to the sensory stimulus in the decision-making process that leads to judgments about that stimulus.

Deriving the stimulus-sensation relationship

The intensity values from the difference threshold experiment are shown on the x-axis. The progressively greater change in difference threshold that was revealed in the Weber experiment can now be related to Fechner's assumption of triangle S being constant on all levels for a JND.

What happens if d' = 3.0?

The large separation of noise and signal + noise distributions will ensure that the hit rate far exceeds the false alarm rate for moderate to liberal criterion levels.

What happens if d' = 0?

The limit is reached when the two distributions overlap each other and produce a straight line. Either there is no signal or the subject is incapable of detecting the stimulus.

Difference Threshold/Discrimination Threshold

The minimum change in physical intensity required for a noticeable change in sensation. Difference thresholds are always determined at supra-threshold levels and can be used to estimate how the slope changes in them. Once we know this, we can determine which function best describes the transformation of physical stimuli in the real world into psychological events that we experience as perception.

Absolute Threshold

The minimum physical intensity required for a stimulus to be detected.

Psychometric Function

The relationship between performance on a psychophysical task (proportion of times a stimulus is detected) and some features of the stimulus (intensity).

Power law relationship for values greater than 1.0

The sensation of electric shock rises slowly at first but then takes off dramatically with further increases in electric current.

Logarithmic Function

The slope is very large at the beginning such that perceived intensities can change dramatically with small changes in stimulus intensity. This effect diminishes and the function tails off at higher stimulus intensities. It displays a decreasing slope over its entire range. A sensory system would no longer be additionally responsive to further increments in stimulus intensity beyond a certain point.

Staircase procedure

The stimulus level can be varied in relation to the subject's responses. Stimulus intensity may be continually increased as long as the subject is making incorrect responses. Stimulus intensity can be decreased when only correct responses are given. This alternation in stimulus intensity is continued until a specified number of response reversals takes place. The signal intensity at this point can be used as a measure of sensitivity.

Psychophysics

The study of quantitative relationships between physical events and psychological experiences.

A difference threshold experiment on the visual system

The subject has to examine 2 stimuli: 1. A reference light with constant intensity 2. A target light with intensity lower or higher to reference light. The subject must compare the two and say if the target light is brighter or dimmer. A computer randomly chooses the intensity level of the target light from a range and displays that stimulus along with a fixed reference stimulus. The subject hits one of two buttons to register the response. This sequence is repeated until 50 trials have been accumulated for each intensity point. We then judge the proportion or % of trials in which the subject judged the target to be lighter (or dimmer, doesn't matter). Possibility 1: All truly dimmer intensities were judged correctly as were all truly brighter intensities. In this case, the subject behaved like an ideal detector because he never failed in distinguishing true differences in stimulus intensities. Real Life: We do not behave as ideal detectors. Data displays an ogive rather than a step function. Certain intensities generate mixed responses. The intensity that produced 50% brighter responses can be taken as the point of perceptual equivalence. At this intensity, our subject could not decide whether the target light was brighter or dimmer. It was perceptually equivalent to reference light.

Absolute Threshold Experiment

The subject is asked to detect a weak stimulus against a random background activity. Since the stimulus must be detected by the same noisy nervous system, a probability plot of sensation magnitude evoked by the stimulus will also show a normal distribution because the signal must be added to the noise distribution. Because of this additivity, the combined signal + noise distribution must always lie to the right of the noise distribution alone.

Stevens Experimental Design

The subject is presented with a standard stimulus, known as the modulus, and told it represents a certain value like 10. The numerical estimate represents the subject's judgment of the sensation triggered by that particular stimulus. Variation 1: Subjects are not presented with a modulus to constrain their judgments. Rather, they are free to develop their own modulus and assign numbers in proportion to the sensation magnitude that they experience. Outcome: Subjects were consistent in their rating. There were similarities in the trends observed among different individuals. Actual numbers obtained = different across subjects because they were free to choose their own scale. When numbers were equated by taking into account subject variability, there was considerable agreement among different people with regard to their sensory ratings for any given type of stimulus.

Experiment 1 - Stimulus 30%

The subject will not expect a stimulus on the majority of trials and will likely adopt a conservative criterion. The criterion value will shift to the right, implying that the subject will only choose to respond YES when the evoked sensory magnitude is quite large. A stimulus appearance probability of 30% and the accompanying rightward conservative criterion shift, results in rates of 0.09 and 0.36 for false alarms and hits, respectively.

Study - Sellin and Wolfgang

There is a general consensus across society on the perceived seriousness of a variety of criminal offences. Using magnitude estimation procedures, they showed the theft of progressively greater sums of money was accompanied by growth in the judged seriousness. The power function for judged seriousness grew with the amount stolen by an exponent value of 0.17. 60 times as much money needs to be stolen in order to be perceived as being twice as serious by most people. Sellin and Wolfgang also found that the judged seriousness of a crime is related to jail time prescribed by the Pennsylvania Penal Code by a power function with an exponent value of 0.7.

Power law relationship for values equal to 1.0

There is an exact perceptual relationship with intensity such that our mental impression changes exactly in step with changes in the stimulus.

Just Noticeable Difference

To determine the difference threshold, we need the extra bit of physical intensity that is added or subtracted from the target light intensity at this perceptual equivalence point for there to be a JND. This amount will depend on exactly what level of noticeable difference we want as our criterion

What are the two purposes of an STD experiment?

To obtain values for both d' and ß.

Smell

Under optimal conditions, the absorption of only 40 molecules by detectors in the nose is sufficient to produce a detectable smell.

Are we capable of measuring our own perceptions?

Yes.

The more sensitive a person is to this particular stimulus, the greater the sensation evoked by that stimulus. Since the signal + noise distribution is a probability plot of sensory magnitudes...

a highly sensitive individual will have a distribution shifted farther to the right and away from the noise distribution. The same stimulus will generate greater sensory magnitudes in a more sensitive person and produce a more rightward shifted signal + noise distribution.