psychophysical assessment of visual function as an o.d. you will measure (assess) vision. how well...

Psychophysical Assessment

of Visual Function

As an O.D. you will measure (assess) vision.

How well does the person see?

Results depend on how you make the measurement

You: Any problems with your vision?

Pt: Don’t seem to see so well, Doc.

What do you do (how do you learn how well the patient sees)?

You measure the patient’s vision.

This course is about the science that stands behind why you measure vision certain ways in the clinic.

Which chart to use? How many letters per line? How far apart are the

letters and lines? How much smaller are the

letters on the next line? Which letters to use? How far down the chart

must the patient try to read?

How score the result?

There are many different eye charts

The acuity you get will differ depending these factors

It is a matter of judgment that determines how the visual system is tested and what constitutes normal variation in sensory processes.

The clinician must understand the scientific basis on which these judgments are made and how they can be made in the future as new tests of visual function are developed. That’s what this course is about

and why it is clinically relevant

Dr. Tom Norton

606 Worrell Building

934-6742

[email protected]

Graduate Student Teaching Assistant:

Jason Wilson

mailto:[email protected]

Class – Mon- 9-10:50

Tues, 9-10:50

Wed, 11:00–11:50

Lab on 4 Thursdays

Check the schedule for your day and time

(Schedule will be distributed tomorrow)

This week: Group C 1-3; gp A 3-5

Exams #1 Wed. Jan. 19 (100 pts) Ch 1-3

#2 Tues. Feb. 8 (100 pts) Ch 4-5

Final during Final Exam Period (130 pts)

(110 pts new, 20 pts cumulative)

Labs (4 x 10 pts)

Possible pop quizzes (up to 30 pts total)

Total possible points, 370 (up to 400)

Letter grade determined @ end of course

LabsAttend at the assigned day and time

(unless you make other arrangements with Dr. Norton in advance)

Lab Reports due at Monday class after your lab

Accurately recording and graphing your data is an important part of your lab grade

Student-submitted exam questions

A way to control your own future!

Procedure:

Due several days before exam (email or Word files preferred)

Norton reviews, corrects, photocopies

Distributed to class (can use as a study guide)

Some of the questions will be used on the exam

Three main purposes of course

1) Learn how vision is measured (scientific basis)

2) Basic facts about monocular visual function

What is normal?

3) Neural basis of visual function

Why does the visual system respond as it does?

Textbook

The Psychophysical Measurement of Visual Function

Norton*, Corliss, Bailey

Richmond Products, Inc

(*TTN’s author royalties [$2420.41 so far] donated to the UABSO)

We will cover 9 Chapters

1) Principles of Psychophysical Measurement

2) Absolute Threshold of Vision

3) Intensity Discrimination

4) Adaptation to Light and Dark

5) Spatial Acuity

6) Spatial Vision

7) Temporal Factors in Vision

Skip Chapter 8 (color)

8) Postnatal Human Vision Development

9) The Aging Visual System

Overview

At the beginning of each chapter.

Contains a summary of the content of the chapter.

Declarative section headings summarize the section they precede

“In the Method of Constant Stimuli the examiner randomly presents a set of stimuli with fixed, predetermined values”

“Correct for guessing by incorporating catch trials”

Study Guide

Questions at the end of each chapter intended to help you clarify your knowledge – (not as useful as I had hoped)

Lecture overlaps with the book a lot

… but questions also come from the book on topics I don’t cover in class!

Glossary – intended to help you know what terms mean for exam

Definitions given in the text – definite full credit if you know them verbatim

Equations – must tell what the variables mean

Equations – must tell what the variables mean

“What is the Stevens Power Function?”

where (psi) is the sensory magnitude, (kappa) is an arbitrary constant determining the scale unit, (phi) is the stimulus magnitude, and (alpha) is an exponent that is characteristic of the stimulus used.

Graphs – The hardest part of this class

(because they tend to all look alike)

… but important because they show the relationship between stimuli and responses

Graphs – how to dissect and learn them

What is on the X-axis? (& approx. scale)

Physical Stimulus on X-axis (Independent Variable)

Usual arrangement:



What is on the Y-axis? (& approx. scale)

Response on Y-axis

What you are measuring(Dependent Variable)

Usual arrangement:

Physical Stimulus on X-axis (Independent Variable)



What is on the Y-axis? (& approx. scale)

How plot a data point?

Physical Stimulus on X-axis

(Independent Variable)

Usual arrangement:

Response on Y-axis


Graphs

What is different in each graph in a “family” of curves?

Flash Duration (s)

0.001 0.01 0.1 1 10 100

4

5

6

7

8

9

Log Threshold Luminance(quanta/s/deg2)

Stimulus area = 0.011 deg2

Log Background Intensity

7.83 5.94 4.96 3.65 No Background

Lots of details to learn.

Philosophy: better to have learned and forgotten than to not have learned in the first place.

example

“Joke break”

Break the monotony

… but remember that the course has a serious purpose, and the exams can be difficult.

Student Response System

Test to see if it works Will use for feedback Will not look at who responds

Set to room code (23)

Chapter 1

Principles of Psychophysical Measurement

Objectives:

Psychophysical Methods

Threshold

Constant Stimuli

Limits

Adjustment

Signal detection theory

Sensory Magnitude

Definition:

Psychophysics is the study

of the relationship

between physical stimuli

and perceptual responses

We study visual psychophysics, but there also is auditory psychophysics, somatosensory psychophysics, etc.

Why are there so many graphs in this course?

Because graphs show relationships

Physical Stimulus on X-axis

(Independent Variable)

Usual arrangement:

Response on Y-axis


Two basic types

of psychophysical measures

1) Threshold measures (Do you see it”)

2) Sensory Magnitude measures

(“What does it look like”)

Threshold measure:

Psychophysics is the study of the relationship

between physical stimuli and perceptual responses

Do you see the light?

Physical stimulus – light intensity

Perceptual response – Seeing the light

How far down an eye chart can you read?

Physical stimulus – Letter size

Perceptual response – Identifying letters

Threshold measure:



letter size is the stimulus identifying letters is

response

We use psychophysical tools to find the threshold – the letter size you can see 50% of the time

Sensory Magnitude:



Which is better, 1 or 2?

Physical stimulus – Lens power

Perceptual response – Clarity of the image

Why study psychophysics?Psychophysical measurements are

fundamental in clinical practice

Need to know the scientific basis for measuring vision

The results you get depend on the way you measure vision

New clinical tools will be developed after you graduate – you need the knowledge base to understand how they work and evaluate whether they are useful in your practice.

Psychophysics questions have been plentiful on the boards

Psychophysical measurements

are used for descriptive and for analytical purposes

and to follow the course of treatment

Visual thresholds are the most common psychophysical measurement

Definition

Threshold is defined as the minimum value of a

stimulus required to elicit a perceptual response or an

altered perceptual response.

Two types of threshold measurement:

absolute threshold (in vision) is the minimum value of

a stimulus required to detect the presence of light

under ideal conditions. (Ch. 2)

A difference (or increment) threshold is defined as

the minimum change in stimulus value that must be

added or subtracted to a stimulus to elicit an altered

perceptual response. (Ch. 3)

The task required of a patient or subject during threshold

measurements varies in complexity

detection task – (in vision) does the subject or patient see

something?

discrimination task – (in vision) distinguishing between two

stimuli with regard to some stimulus characteristic when each

stimulus is visible by itself.

recognition task. – providing a name or category of a test object

that is visible.

The distinctions among these various types of tasks are not sharp,

but are hierarchical.

Important Stimulus Dimensions

intensity

wavelength

size

exposure duration

frequency

shape

relative locations of elements of the stimulus

cognitive meaning

In addition,(NOT stimulus Dimensions!)

location on the subject’s retina

light adaptation of the subject’s visual system

Key in measuring thresholds: Try to keep all dimensions unchanged except the one being measured

Stimulus Configurations

Spot on an adapting field (increment thresholds)

Bipartite field

Bipartite field with an adapting field

Spatially separated stimuli (difference thresholds)

LLTLLT

L T = L + L L T = L - L

L

LT=L+L

LT=L-L

+L

-L

0

A B

Luminance

There are many possible values of L,

But only 1 value (theoretically) for

threshold L

(demo)

Definition




LLTLLT

L T = L + L L T = L - L

L

LT=L+L

LT=L-L

+L

-L

0

A B

Luminance

Definition




But threshold can vary over time (somewhat)

Psychophysically measured threshold values vary

because of

fluctuations in the stimulus (Ch. 2)

fluctuations in neural activity

fluctuations in alertness or attention

psychological bias

Fluctuations in neural activity

For us to see, neural signals must leave the retina and travel to central brain structures.

In the early retinal cells (photoreceptors, bipolars, horizontal cells, most amacrines), there are only “graded potentials” (hyperpolarization and depolarization of the cell)

In order to send signals out of the retina, “action potentials” (“spikes”) must be generated and travel down the ganglion cell’s axon to the next location (lateral geniculate nucleus, then to visual cortex)

Graded potentials

The signal changes from graded potentials (voltage changes) into a “digital signal” in which the number of action potentials per second (firing rate) carries the visual signal.

We can “eavesdrop” on the neurons in the visual pathway with a microelectrode, nestled up against a neuron or its axon and record the responses (number of spikes per second) in response to visual stimuli.

B: Action potentials recorded from a single LGN neuron. The same stimulus (a spot of light positioned in the “receptive field” was presented many 20 times. A: a “histogram” of the cell’s responses

0 . 0 0 . 5 1 . 0 1 . 5 2 . 0 2 . 5 3 . 0O n O f fT i m e ( s )

R e s p o n s e s o f a n e u r o n i n t h e l a t e r a l g e n i c u l a t e n u c l e u s o f a n a n e s t h e t i z e d c a t t o t h r e e s e p a r a t e p r e s e n t a t i o n s o f a n e a r - t h r e s h o l d v i s u a l s t i m u l u s . E a c h s m a l l v e r t i c a l l i n e r e p r e s e n t s a n a c t i o n p o t e n t i a l p r o d u c e d b y t h e n e u r o n . E a c h r o w s h o w s t h e r e s p o n s e s o f t h e n e u r o n i n a 3 s p e r i o d . F r o m 0 u n t i l 2 . 5 s a b a c k g r o u n d l u m i n a n c e w a s p r e s e n t . T h e s t i m u l u s ( a l i g h t ) w a s t u r n e d o n a t 2 . 5 s a n d t u r n e d o f f a t 3 . 0 s , s o t h e s t i m u l u s w a s o n f o r o n l y 0 . 5 s . ( U n p u b l i s h e d d a t a f r o m D . W . G o d w i n a n d T . T . N o r t o n , . )

Action potentials recorded from a single LGN neuron

Neural fluctuations: the neuron sometimes responds more, sometimes less, to the same stimulus.

Also, the neuron has variable background (“maintained”) activity that makes it hard for the neuron to detect when the stimulus is present.

Psychophysically measured threshold values vary

because of

fluctuations in the stimulus

fluctuations in neural activity

fluctuations in alertness or attention

psychological bias

This leads us to consider threshold as a probability that a stimulus is detected and to find the stimulus value that is detected 50% of the time (or some other criterion value)

Threshold Determination Methods

Method of Constant Stimuli

Method of Limits

-Staircase

-Tracking

Method of Adjustment

In the Method of Constant Stimuli the examiner

randomly presents a set of stimuli with fixed,

predetermined values

Test Field Intensity, LT (arbitrary units)

0 1 2 3 4 5 6 7 8 9 10

Percent "YES" responses

0

25

50

75

100

Background Field IntensityL = 0 units

Figure 1-4. Idealized psychometric function for a threshold detection task using the Method of Constant Stimuli. The threshold stimulus value is obtained by drawing a horizontal line from the 50% value on the response axis to the psychometric function and then dropping a vertical line from the function to the test field intensity axis.

In Class Demo

Rule: Plot straight lines between data points

“Silliest Plotting Error”

Plot data points from left to right

“Most Interesting Curves”


0 1 2 3 4 5 6 7 8 9 10


0

25

50

75

100



Whole Class 2010

0.00.10.20.30.40.50.60.70.80.91.0

0 2 4 6 8 10

Stimulus Value

Fre

qu

ency

of

"Yes

" R

esp

on

se

Front Rows (1-3)

0.00.10.20.30.40.50.60.70.80.91.0

0 1 2 3 4 5 6 7 8 9 10

Stimulus Value

Fre

qu

en

cy

of

"Ye

s"

Re

sp

on

se

Back Rows (4-6)

0.00.10.20.30.40.50.60.70.80.91.0

0 1 2 3 4 5 6 7 8 9 10

Stimulus Value

Fra

ctio

n o

f "Y

es"

Res

po

nse

s

One point (added to the exam #1 grade) to the first

person to correctly tell me:

Why might the threshold be lower for the front half of

the room?

Hint: think about a stimulus parameter that might

change from the front to the back of the room.

The Importance of Using Straight Lines to Connect Data Points

1) The data points are the only evidence we have of threshold

2) We assume a linear progression from one data point to the next

3) Can use linear interpolation to determine the threshold accurately

The Importance of Using Straight Lines to Connect Data Points

A dramatic example: If you measure vision incorrectly, you get an incorrect answer about how well a person sees.

Another way to mis-estimate threshold

We are looking for the 50% point, not the closest data point, so we use linear interpolation

We want to measure threshold as accurately as possible. Why be satisfied with “6” when 5.8 is more accurate?

The Method of Constant Stimuli is the most precise

method for determining threshold (the “Gold

Standard”).

But, this method is cumbersome and time-consuming

so it is rarely, if ever, used in clinical practice.



Method of Limits

-Staircase

-Tracking


What is another name for the psychometric function?

1. Threshold line

2. Frequency-of-seeing curve

3. Method of Constant Stimuli

4. Power function

In the Method of Limits the examiner sequentially

presents a set of stimuli with fixed values

Trial Number (Stimulus Presentation Direction)Stimulus Value 1

(Ascending)2

(Descending)3

(Ascending)4

(Descending)5

(Ascending)1 N N N2 N N N N3 Y N N Y4 N Y Y N Y5 N Y Y N6 Y Y Y7 Y Y N8 Y Y9 Y10 Y Average

Transition 5.5 3.5 3.5 5.5 2.5 4.1

Table 1- 1. Example of subject’s responses over five trials using themethod of limits.

In Class Demo

The Method of Limits is more efficient than the

Method of Constant Stimuli because fewer trials are

presented.

Two potential problems:

anticipation

perseveration

Staircase procedure.

Developed during WWII to test bomb detonators


Stimulus Value

Trial Number

1 2 3 4 5 6 7 8 9 10

11

12

13

14

15

16 17

1 2 N 3 N N N

4 N Y N N

5 Y Y N Y

6 N Y 7 Y 8 Y 9 Y

Table 1- 2. Example of a subject’s responses over 17 trials using the staircase variation on the Method of Limits.

T r a c k i n g p r o c e d u r e

"Beep-Beep"

"Beep-Beep"

"Beep"

1

2

3

4

5

6

7

8

Contr

ast

0

See grating, pressing button

Grating not visible, release button

High-contrast Sample of grating

Time

(Developed by Nobel Prize-winning auditory physiologist, Georg von Bekésy)



Method of Limits

-Staircase

-Tracking


In the Method of Adjustment

the subject controls the stimulus values

LLTLLT

L T = L + L L T = L - L

L

LT=L+L

LT=L-L

+L

-L

0

A B

Luminance

In Class Demo

LT<L Intensity Difference, LT-L (arbitrary units) LT>L

-3 -2 -1 0 1 2 3

Probability of seeing LT

as equal to L +0.68 SDMean-0.68 SD

The distribution of values of LT that a subject decides are equal to Lforms a normal distribution if enough trials are used. The mean ofthe distribution will be very close to L. The threshold is taken as thevalue of LT that, when added to or subtracted from L gives an LT

that is detectable on 50% of the trials. This occurs 0.68 standarddeviations above and below the mean.

Frequency with which LT is seen as equal to L

The Method of Adjustment is most easily used when

the stimulus can be changed in a continuous manner,

rather than in steps.

Subjects generally enjoy the Method of Adjustment

because they actively participate.

Boredom and inattention are less of a problem with the

Method of Adjustment than with the other methods.

Potential problem with the Method of Adjustment

subjects may use the position of the dial as a cue to

where threshold "ought" to be.

This strategy can by foiled by using a dial that has no

numbers and has a variable amount of slip.

Controlling response bias and guessing

Correct for guessing by incorporating “catch” trials

Establish the guessing rate by forcing the subject to

make choices (“forced choice” technique)


0 1 2 3 4 5 6 7 8 9 10

Percent "YES"Responses

0

25

50

75

100Uncorrected for guessingCorrected for Guessing


What do you do if the psychometric function doesn’t drop down

to 0% “Yes” responses for low stimulus values?

Assume subject/patient has a bias to guess “Yes.”

Correct for guessing by incorporating “catch” trials

where the stimulus is not presented at all. This gives the

guessing rate.


0 1 2 3 4 5 6 7 8 9 10


0

25

50

75



Correct for guessing by incorporating “catch” trials. In this

case no stimulus at all was presented for a value of “0”, so

this was a “catch trial.”

The catch trial gives the guessing rate. Then subtract the guessing rate from the data to get the “True percent of ‘Yes’ responses”

T h e c o r r e c t i o n f a c t o r i s :

100Rate Guessing1

Rate GuessingResponses YES ofFraction ObservedResponses YES ofPercent True X


0 1 2 3 4 5 6 7 8 9 10


0

25

50

75



Do not memorize the formula! It isn’t used much. Instead, people use the “forced choice” procedureDo not memorize the formula! It isn’t used much. Instead, people use the “forced choice” procedure

Establish the guessing rate by forcing the subject

to make choices

The Forced Choice procedure

In Class Demo

Two-alternative forced choiceTwo-alternative forced choice

The correction factor is still:

100Rate Guessing1

Rate GuessingResponses YES ofFraction ObservedResponses YES ofPercent True X

But if there are two alternatives (two-alternative forced-choice) you know the guessing rate is 0.5


0 1 2 3 4 5 6 7 8 9 10


0

25

50

75

100



Results from yesterday’s Method of Constant Stimuli Threshold Measurement

Whole Class, 2009

0.000.100.200.300.400.500.600.700.800.901.00

0 1 2 3 4 5 6 7 8 9 10

Stimulus Value

Fra

ctio

n o

f "Y

es"

Res

po

nse

s

Front Rows

0.000.100.200.300.400.500.600.700.800.901.00

0 1 2 3 4 5 6 7 8 9 10

Stimulus Value

Fra

ctio

n o

f "Y

es"

Res

po

nse

s

Back Rows

0.00

0.10

0.20

0.30

0.40

0.50

0.60

0.70

0.80

0.90

1.00

0 1 2 3 4 5 6 7 8 9 10

Stimulus Value

Fra

ctio

n o

f "Y

es"

Res

po

nse

s


0 1 2 3 4 5 6 7 8 9 10


0

25

50

75



Results from yesterday’s Two-alternative Forced Choice Measurement

Intensity Discrimination Lab tomorrow

Groups C (1 – 3) and A (3 – 5)– List posted on bulletin board

Planning to have the lab unless UAB cancels classes due to snow

Snow amount is predicted to be small

2009

Two-alternative Forced-choice in-class Demo2010

-10.0

0.0

10.0

20.0

30.0

40.0

50.0

60.0

70.0

80.0

90.0

100.0

1 2 3 4

Stimulus

Per

cen

t C

orr

ect

Res

po

nse

s

Obtained percent correct

True percent correct

5 4 3 2


-10.0

0.0

10.0

20.0

30.0

40.0

50.0

60.0

70.0

80.0

90.0

100.0

1 2 3 4

Stimulus

Per

cen

t C

orr

ect

Res

po

nse

s



5 4 3 2


-10.0

0.0

10.0

20.0

30.0

40.0

50.0

60.0

70.0

80.0

90.0

100.0

1 2 3 4

Stimulus

Per

cen

t C

orr

ect

Res

po

nse

s



5 4 3 2

Either way gives the same threshold, but it is easier to use a 75% threshold and not bother to correct

http://www.opt.uab.edu/nortonpsychophysics/

Chapter 1


Objectives:


Threshold

Constant Stimuli

Limits

Adjustment


Sensory Magnitude

Using Signal Detection Theory

1) to Understand Threshold Variability and

2) to Control Subject Bias

Using Signal Detection Theory

1) to Understand Threshold Variability and

2) to Control Subject Bias

Big point!!

Lesser point

At threshold, neurons must “decide” whether a

stimulus is present against a background of

“noise”

Stimuli that are near threshold always are difficult to see! Did I see that, or didn’t I?

The brain (comprised of neurons) must “decide” if a stimulus was present against a background of neural “noise”.

Your brain causes perception. Cells in the brain do not respond to light. They respond because they are activated by a chain of cells that start with photoreceptors, which do “see” light.

We can “eavesdrop” on the neurons in the visual pathway with a microelectrode, nestled up against a neuron or its axon and record the responses (number of spikes per second) in response to visual stimuli.

B: Action potentials recorded from a single LGN neuron. The same stimulus (a spot of light positioned in the “receptive field” was presented many 20 times. A: a “histogram” of the cell’s responses

The visual system has to decide if a stimulus is present “on the fly” – as events happen

In studying how the visual system responds, we have the luxury of studying neural responses over many repeated trials

Use this information to understand why thresholds can be affected by “bias”

0 . 0 0 . 5 1 . 0 1 . 5 2 . 0 2 . 5 3 . 0O n O f fT i m e ( s )

R e s p o n s e s o f a n e u r o n i n t h e l a t e r a l g e n i c u l a t e n u c l e u s o f a na n e s t h e t i z e d c a t t o t h r e e p r e s e n t a t i o n s o f a n e a r - t h r e s h o l d v i s u a ls t i m u l u s . E a c h s m a l l v e r t i c a l l i n e r e p r e s e n t s a n a c t i o n p o t e n t i a lp r o d u c e d b y t h e n e u r o n . E a c h r o w s h o w s t h e r e s p o n s e s o f t h en e u r o n i n a 3 s p e r i o d . F r o m 0 u n t i l 2 . 5 s a b a c k g r o u n d l u m i n a n c ew a s p r e s e n t . T h e s t i m u l u s ( a l i g h t ) w a s t u r n e d o n a t 2 . 5 s a n d t u r n e do ff a t 3 . 0 s , s o t h e s t i m u l u s w a s o n f o r o n l y 0 . 5 s . ( U n p u b l i s h e d d a t af r o m D . W . G o d w i n a n d T . T . N o r t o n , . )

NoiseNoise

Signal + Noise

Signal + Noise

0 . 0 0 . 5 1 . 0 1 . 5 2 . 0 2 . 5 3 . 0O n O f fT i m e ( s )


Below is a “peristimulus” histogram made from the responses to 30 stimulus repetitions like the three lines shown above.

We want to compare responses during

“noise” and “signal + Noise”

0 . 0 0 . 5 1 . 0 1 . 5 2 . 0 2 . 5 3 . 0O n O f fT i m e ( s )


We are interested in how many action potentials are generated, over many stimulus presentations, during a 50 msec period when there is no stimulus (maintained discharge) and a 50 msec period when the stimulus is present.

Why 50 msec? Arbitrary, but it is about the amount of time the CNS seems to use.

0.0 0.5 1.0 1.5 2.0 2.5 3.0On OffTime (s)

2

83

0 3

2 15

Making a frequency distribution of neural responses during “noise” and “signal + noise”

50 ms “bins”

Number of action potentials in each bin

“noise” Stimulus + noise

During “noise”, 0 spikes occur 1 time, 3 spikes occur 1 time, 2 occur 1 time

During “signal + noise”, 3 spikes occur 1 time, 8 spikes occur 1 time, 15 occur 1 time

Do this across 30 stimulus presentations to get a distribution of the frequency with which a certain number of spikes occurs

Frequency ofOccurence

0

1

2

3

4

5

6

7

Mean of Noise

Number of Action Potentials in 50 msec Period

0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15

0

1

2

3

4

5

6

7

Mean of Noise + Signal

Overlap: PossibleConfusion

Maintained Discharge (Noise)Distribution

Maintained Discharge (Noise) +Response to Flash (Signal)

Distribution

A

B

There is no single “optimal” criterion number of action

potentials that the nervous system (such as a cell in

the visual cortex) should use to decide whether to

respond as though a stimulus was present, or to

respond as though a stimulus was not present.

How can the brain “decide” if a near-threshold stimulus is present?

If a strong stimulus is presented, it produces many more action potentials during the “signal + noise” than are produced during the “noise”. But when a stimulus is near threshold, there is overlap between the number of spikes produced during “noise” and “signal + noise”

One can try various criteria –

Changing the criterion (the threshold one adopts) affects the pattern of hits, misses, false alarms and correct rejections

“The saga of the snake in the grass”

This changing threshold is partly responsible for fluctuations in threshold.

Imagine the situation faced by a mouse, needing to forage for food, but worrying that a snake might be hanging around and eat the mouse when the mouse goes out to eat

Imagine the situation faced by a mouse, needing to forage for food, but worrying that a snake might be hanging around and eat the mouse when the mouse goes out to eat


0

1

2

3

4

5

6

7

Mean of Noise


0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15

0

1

2

3

4

5

6

7





Distribution

A

B

Set criterion low, to always detect the snake

If 6 or more action potentials, decide “snake!!”


0

1

2

3

4

5

6

7

Mean of Noise


0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15

0

1

2

3

4

5

6

7





Distribution

A

B

Set criterion low, to always detect the snake

If 6 or more action potentials, decide “snake!!”

Problem: will also “see” snake some times when it is just the noise of the visual system

Out of the four possible outcomes there are two ways

to be correct:

by deciding the stimulus is there when it is present (a

Hit)

and by deciding that it is not there when it is absent (a

Correct Rejection).

There are also two ways to be wrong:

by deciding the stimulus is present when it is absent (a

False Alarm)

and by deciding it is not present when it is (a Miss).


0

1

2

3

4

5

6

7

Mean of Noise


0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15

0

1

2

3

4

5

6

7





Distribution

A

B

Many false alarmsMany false alarms

If set a low criterion (threshold), hit rate is perfect, but

A. Criterion for “seeing” = 6 action potentials

Response Stimulus Present Stimulus Absent

“I see it” Hits (H) n = 30

False Alarms (FA) n = 11

“I don’t see it.” Misses (M) n = 0

Correct Rejections (CR) n = 19

Hit Rate = H/(H+M) = 30/(30+0) = 1.00

False Alarm Rate = FA/(FA+CR) = 11/(11+19) = 0.37

Miss Rate = M/(H+M) = 0/(30+0) = 0

Correct Rejection Rate = CR/(FA+CR) = 19/(11+19) = 0.63

B. Criterion for “seeing” = 9 action potentials






Hit Rate = H/(H+M) = 19/(19+11) = 0.63


Miss Rate = M/(H+M) = 11/(19+11) = 0.37


10


0

1

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3

4

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6

7

Mean of Noise


0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15

0

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6

7





Distribution

A

B


0

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Mean of Noise


0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15

0

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7





Distribution

A

B

So, try changing the criterion – mouse gets hungrier, willing to “take a chance”

If set a high criterion (threshold) have no false alarms but also fewer hits (more misses)

A. Criterion for “seeing” = 6 action potentials






Hit Rate = H/(H+M) = 30/(30+0) = 1.00


Miss Rate = M/(H+M) = 0/(30+0) = 0


B. Criterion for “seeing” = 9 action potentials






Hit Rate = H/(H+M) = 19/(19+11) = 0.63


Miss Rate = M/(H+M) = 11/(19+11) = 0.37


10


0

1

2

3

4

5

6

7

Mean of Noise


0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15

0

1

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7





Distribution

A

B

Can calculate hit rate and false alarm rate for ANY criterion

Receiver Operating Characteristic (ROC) curve for the responses shown in the previous figure. If the threshold isset at 15 action potentials, there are 0 Hits and 0 False Alarms. If it is set at 14, there will be a few Hits, but 0 FalseAlarms. As the threshold is decreased further, the P(Hit) increases but the P(False Alarm) remains at 0 until thethreshold reaches 9, at which point False Alarms begin to increase. As the threshold is further lowered, throughthe overlap region in the previous figure, the probability of both Hits and False Alarms increase. For thresholdsbelow 6, there is no further increase in hit rate, but the false alarm rate climbs toward 1.0.

False Alarm Rate

0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.0

Hit Rate

0.0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1.0

14

13

12

11

10

9

87 6 5 4 321

15

Receiver Operating Characteristic (ROC) curve


0

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Mean of Noise


0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15

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Distribution

A

B

Signal Detection Theory also applies to human

perceptual responses

Distribution of hypothetical “perceptual response” in a human subject over many trialswhen the stimulus was absent (top) and when the stimulus was present (bottom). Thecriterion value (vertical line) indicates the criterion a subject would adopt if Hits, Misses,False Alarms and Correct Rejections had the rewards and costs listed in another figure.

Magnitude of Sensation (arbitrary units)

-3 -2 -1 0 1 2 3

Frequency

0.0

0.0

Criterion Value

d'

False Alarms

Hits

Correct Rejections

Misses

Stimulus Absent

Stimulus Present

False Alarm Rate

0.0 0.2 0.4 0.6 0.8 1.0

Hit Rate

0.0

0.2

0.4

0.6

0.8

1.0 Receiver Operating Characteristic(ROC) Curve

The distributions on the previous slide would produce this

d’ (“d prime”) is a measure of the separation of two normal distributions.

d’ = the difference between the means of the “noise” and “signal plus noise” distributions divided by the common standard deviation of the two distributions.

d’ quantifies the detectability of the signal (small d’ = signal is hard to detect)

Srimulus AbsentStimulus Present

d'=1.5d'=1.0d'=0.5

A

B

C

ROC Curve

Can Use Signal Detection Theory to control bias

when measuring threshold (This is the “minor

point”)

Big point: Where a neuron, or an entire creature (human or animal) sets its criterion depends on circumstances (fear vs. hunger which causes a change in “bias”). This contributes to threshold variability.

To control a subject’s criterion, the examiner

provides the subject, in advance, with:

the payoff amounts

and

information on the frequency of stimulus presentation

Use the “Payoff Game”

Skip the text on pages 24, 26, 27 and top of 28

“Signal detection theory can be used to control bias when measuring threshold”

Skip the text on pages 24, 26, 27 and top of 28

“Signal detection theory can be used to control bias when measuring threshold”

The concepts of Signal Detection Theory form the

basis of rational clinical decision making

Screening for refractive error:

Hits: Correct detection of refractive error

Correct rejection: pass the screening because child is emmetropic

False alarm (false positive): incorrectly refer for full exam based on screening (cost, concern, inconvenience)

Misses (false negative): fail to detect refractive error

Minimize false positives even though some refractive error is missed

The concepts of Signal Detection Theory form the

basis of rational clinical decision making

Detecting ocular melanoma:

Hits: Correct detection of melanoma (refer for possible surgery)

Correct rejection: pass because no melanoma

False positive – incorrectly refer based on screening (alarm, cost, inconvenience)

Misses (false negatives): fail to detect melanoma (possible death)

Minimize false negatives even though some false positives occur

You will hear in clinic about the “sensitivity” and “specificity” of diagnostic techniques.

Sensitivity is the hit rate

Specificity is the absence of false alarms

So plot (1 – specificity) on an ROC curve

Want a diagnostic tool that has high sensitivity and high specificity

“Do you see it?”

As was said the first day of class

Visual thresholds are the most common psychophysical measurement

The other major type of

psychophysical measurement:

Measuring the magnitude of sensations

“What does it look like?”

Perceptual responses (sensations) have

magnitude but no obvious scale or units

Increased light intensity is “brighter” but how much brighter?

Increased spot size is “larger”, but how much larger?

To measure sensory magnitude above threshold,

use scales that do not rely on any particular units

of measurement

1) Ratio Production - the subject is presented with a

reference stimulus and is asked to adjust the intensity

of a test stimulus so that it appears to be some fraction

or multiple of the reference stimulus.

2) Ratio Estimation - the examiner sets the physical

intensities of a reference and test stimulus and asks

the subject to estimate the ratio of the test to the

reference stimulus.

3) Magnitude Estimation (two variants)

a) an observer is presented with a reference stimulus

and told that it has a certain value (10, 100 etc.) A

series of test stimuli are then presented and the

observer assigns a number to these stimuli to

indicate their perceived magnitude relative to the

reference stimulus

b) (don’t bother with this)

4) Magnitude Production – a subject is presented

with a reference stimulus and is asked to adjust a

test stimulus so that is appears to be some fraction

or multiple of the reference stimulus.

Stevens' Pow er Law relates sensory m agnitude to the m agnitude of the stim ulus:

where (psi) is the sensory m agnitude, (kappa) is an arbitrary constant determ ining

the scale unit, (phi) is the stim ulus m agnitude, and (alpha) is an exponent that

is characteristic of the stim ulus used.

Sensory magnitude is proportional to the stimulus magnitude raised to some power

Stimulus Value (arbitrary units)

0 20 40 60 80 100

Sensory Magnitude(arbitrary units)

0

20

40

60

80

100

Length Brightness Shock

10 20 40 60 80 100

10

100

1000A B

When plotted on a log-log scale.

log log log

Value of Some Vision-related Exponents in the Stevens’ Power Law Equation

Sensation Exponent Stimulus Condition

Brightness 0.33 5 target in the dark

Brightness 0.50 Point source Brightness 0.50 Brief flash Visual Area 0.70 Projected square Brightness 1.00 Point source

briefly flashed Visual Length 1.00 Projected line

Clinicians rely on sensory magnitudes

to make judgments about pathologies

Measuring the magnitude of sensations

“What does it look like?”

Chapter 1


Objectives:


Threshold

Constant Stimuli

Limits

Adjustment


Sensory Magnitude

psychophysical assessment of visual function as an o.d. you will measure (assess) vision. how well...

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