quantifying sensitivity

Quantifying Sensitivity


• Response bias

• Two measures of discrimination

– Accuracy: how often is the judge correct?

– Sensitivity: how well does the judge distinguish the categories?

• Quantifying sensitivity

– Hits MissesFalse Alarms Correct Rejections

– Compare p(H) against p(FA)


• Is one of these more impressive?

– p(H) = 0.75, p(FA) = 0.25

– p(H) = 0.99, p(FA) = 0.49

• A measure that amplifies small percentage differences at extremes

z-scores

Normal Distribution

Mean (µ)

Dispersionaround mean

Standard DeviationA measure of dispersionaround the mean.

√( )∑(x - µ)2

n

The Empirical Rule

1 s.d. from mean: 68% of data


3 s.d. from mean: 99.7% of data


• A z-score is a reexpression of a data point in units of standard deviations.

(Sometimes also known as standard score)

• In z-score data, µ = 0, = 1

• Sensitivity score

d’ = z(H) - z(FA)

See Excel worksheet

sensitivity.xls

Quantifying Differences

(Näätänen et al. 1997)

(Aoshima et al. 2004)

(Maye et al. 2002)

Normal Distribution

Mean (µ)

Dispersionaround mean

Standard DeviationA measure of dispersionaround the mean.

√( )∑(x - µ)2

n

The Empirical Rule



3 s.d. from mean: 99.7% of data

Normal Distribution

Mean (µ)65.5 inches

Standard deviation = 2.5 inches

Heights of AmericanFemales, aged 18-24

• If we observe 1 individual, how likely is it that his score is at least 2 s.d. from the mean?

• Put differently, if we observe somebody whose score is 2 s.d. or more from the population mean, how likely is it that the person is drawn from that population?

• If we observe 2 people, how likely is it that they both fall 2 s.d. or more from the mean?

• …and if we observe 10 people, how likely is it that their mean score is 2 s.d. from the group mean?

• If we do find such a group, they’re probably from a different population

• Standard Error

is the Standard Deviation of sample means.

€

n

• If we observe a group whose mean differs from the population mean by 2 s.e., how likely is it that this group was drawn from the same population?

Development of Speech Perception in Infancy

Voice Onset Time (VOT)

60 msec

Perceiving VOT

‘Categorical Perception’

Discrimination

Same/Different0ms 60ms



A More Systematic Test

0ms

20ms

40ms

20ms

40ms

60ms

D T

D

T T

D

Within-Category Discrimination is Hard

Abstraction

• Representations – Sound encodings - clearly non-symbolic, but otherwise unclear

– Phonetic categories

– Memorized symbols: /k/ /æ/ /t/

• Behaviors– Successful discrimination

– Unsuccessful discrimination

– ‘Step-like’ identification functions

– Grouping different sounds

Three Classics

Development of Speech Perception

• Unusually well described in past 30 years

• Learning theories exist, and can be tested…

• Jakobson’s suggestion: children add feature contrasts to their phonological inventory during development

Roman Jakobson, 1896-1982Kindersprache, Aphasie und allgemeine Lautgesetze,

1941

Developmental Differentiation

0 months 6 months 12 months 18 months

UniversalPhonetics

Native Lg.Phonetics

Native Lg.Phonology

#1 - Infant Categorical Perception

Eimas, Siqueland, Jusczyk & Vigorito, 1971

Discrimination




A More Systematic Test

0ms

20ms

40ms

20ms

40ms

60ms

D T

D

T T

D

Within-Category Discrimination is Hard

high amplitude suckingnon-nutritive sucking

English VOT Perception

To Test 2-month olds

High Amplitude Sucking

Eimas et al. 1971

General Infant Abilities

• Infants’ show Categorical Perception of speech sounds - at 2 months and earlier

• Discriminate a wide range of speech contrasts (voicing, place, manner, etc.)

• Discriminate Non-Native speech contrastse.g., Japanese babies discriminate r-le.g., Canadian babies discriminate d-D[these findings based mostly on looking/headturn studies w/ 6 month olds]

Universal Listeners

• Infants may be able to discriminate all speech contrasts from the languages of the world!

How can they do this?

• Innate speech-processing capacity?

• General properties of auditory system?

What About Non-Humans?

• Chinchillas show categorical perception of voicing contrasts!

PK Kuhl & JD Miller, Science, 190, 69-72 (1975)

Joan Sinnott, U. of S. Alabama

More recent findings…

1. Auditory perceptual abilities in macaque monkeys and humans differ in various ways

2. Discrimination sensitivity for b-p continua is more fine-grained in (adult) humans (Sinnott & Adams, JASA, 1987)

3. Sensitivity to cues to r-l distinctions is different, although trading relations are observed in humans and macaques alike (Sinnott & Brown, JASA, 1997)

4. Some differences in vowel sensitivity…

Suitability of Animal Models

#2 - Becoming a Native Listener

Werker & Tees, 1984

When does Change Occur?

• About 10 months

Janet Werker

U. of British ColumbiaConditioned Headturn Procedure

When does Change Occur?

• Hindi and Salishcontrasts testedon English kids

Janet Werker

U. of British ColumbiaConditioned Headturn Procedure

What do Werker’s results show?

• Is this the beginning of efficient memory representations (phonological categories)?

• Are the infants learning words?

• Or something else?

Korean has [l] & [r]

[rupi] “ruby”[kiri] “road”[saram] “person”[irumi] “name”[ratio] “radio”[mul] “water”[pal] “big”[s\ul] “Seoul”[ilkop] “seven”[ipalsa] “barber”

#3 - What, no minimal pairs?

Stager & Werker, 1997

A Learning Theory…

• How do we find out the contrastive phonemes of a language?

• Minimal Pairs

Word Learning

• Stager &Werker 1997

‘bih’ vs. ‘dih’and‘lif’ vs. ‘neem’

QuickTime™ and aVideo decompressor

are needed to see this picture.

PRETEST

QuickTime™ and aCinepak decompressor


QuickTime™ and aCinepak decompressor


HABITUATION

TEST

SAME SWITCH

Word learning results

• Exp 2 vs 4

Why Yearlings Fail on Minimal Pairs

• They fail specifically when the task requires word-learning

• They do know the sounds

• But they fail to use the detail needed for minimal pairs to store words in memory

• !!??

One-Year Olds Again

• One-year olds know the surface sound patterns of the language

• One-year olds do not yet know which sounds are used contrastively in the language…

• …and which sounds simply reflect allophonic variation

• One-year olds need to learn contrasts

Maybe not so bad after all...

• Children learn the feature contrasts of their language

• Children may learn gradually, adding features over the course of development

• Phonetic knowledge does not entailphonological knowledge

Roman Jakobson, 1896-1982

Werker et al. 2002

14 17 20

14 months 17 months 20 months

0 60 300 600

Swingley & Aslin, 2002• 14-month olds did recognize mispronunciations of familiar

words

Dan Swingley, UPenn

Alternatives to Reviving Jakobson

• Word-learning is very hard for younger children, so detail is initially missed when they first learn words

• Many exposures are needed to learn detailed word forms at early stages of word-learning

• Success on the Werker/Stager task seems to be related to the vocabulary spurt, rapid growth in vocabulary after ~50 words

Questions about Development

6-12 Months: What Changes?

Structure Changing

Patricia KuhlU. of Washington

Structure Adding

• Evidence for Structure Adding(i) Some discrimination retained when sounds presented close together (e.g. Hindi d-D contrast)(ii) Discrimination abilities better when people hear sounds as non-speech(iii) Adults do better than 1-year olds on some sound contrasts

• Evidence for Structure Changing(i) No evidence of preserved non-native category boundaries in vowel perception

Sources of Evidence

• Structure-changing: mostly from vowels

• Structure-adding: mostly from consonants

• Conjecture: structure-adding is correct in domains where there are natural articulatory (or acoustic) boundaries [cf. Phillips 2001, Cogn. Sci., 25, 711-731]

So how do infants learn…?

• Surface phonetic patterns

• Tests of experimentally induced changes…

[2003, Proceedings of the National Academy of Sciences]

5 hours’ exposure to Mandarin± human interaction

Alveo-palatal affricate vs. fricative contrast

fricativeaffricate

Alveo-palatals

Jessica Maye, Northwestern U.

• Infants at age 6-8 months are still ‘universal listeners’, cf. Pegg & Werker (1997)

• Infants trained on bi-modal distribution show ‘novelty preference’ for test sequence with fully alternating sequence

• How could the proposal scale up?

0

10

20

30

40

50

60

0 50 100 150 200 250 300 400

E

ee

0

10

20

30

40

50

60

70

0 50 100 150 200 250 300 400

E

ee

sum

p(a) = p(b) p(a) = 2 x p(b)

1.0

.5

.25

.1

(Jusczyk 1997)

Invariance

Training on [g-k] or [d-t], generalization across place of articulation.(Dis-)habituation paradigm.

[Maye & Weiss, 2003]

So how do infants learn…?

• Phoneme categories and alternations

– Perhaps more like a phonologist than like a LING101 student - look directly for systematic relations among phones

– Gradual articulation of contrastive information encoded in lexical entries

– Much remains to be understood

Abstraction in Infant Speech Encoding

• From a very early age infants show great sensitivity to speech sounds, possibly already with some ‘category-like’ structure

• Although native-like sensitivity develops early (< 1 year), this should be distinguished from adult-like knowledge of the sound system of the language– Children still need to learn how to efficiently encode words (phoneme

inventory)

– Children presumably still need to learn how to map stored word forms onto pronunciations (phonological system of the language)

• Popular distributional approaches to learning the sound system address rather non-abstract encodings of sounds, at best

quantifying sensitivity

Documents

mean score

standard scorein zscore

sensitivity score d

standard deviation of

empirical rule1

units of standard deviations

inchesstandard deviation

data point