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# Quantifying Sensitivity - PowerPoint PPT Presentation

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 Misses False Alarms Correct Rejections

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### 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 extremesz-scores

Dispersionaround mean

Mean (µ)

√( )

∑(x - µ)2

n

Normal Distribution

Standard Deviation

A measure of dispersionaround the mean.

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

2 s.d. from mean: 95% 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)

### Quantifying Differences

(Näätänen et al. 1997)

(Aoshima et al. 2004)

(Maye et al. 2002)

Dispersionaround mean

Mean (µ)

√( )

∑(x - µ)2

n

Normal Distribution

Standard Deviation

A measure of dispersionaround the mean.

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

2 s.d. from mean: 95% of data

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

Standard deviation

 = 2.5 inches

Heights of American

Females, aged 18-24

Mean (µ)

65.5 inches

• If we observe 2 people, how likely is it that they is at least 2 s.d. from the mean?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 at least 2 s.d. from the mean?is the Standard Deviation of sample means.

### Development of Speech Perception in Infancy mean by 2 s.e., how likely is it that this group was drawn from the same population?

Voice Onset Time (VOT) mean by 2 s.e., how likely is it that this group was drawn from the same population?

60 msec

Perceiving VOT mean by 2 s.e., how likely is it that this group was drawn from the same population?

‘Categorical Perception’

Discrimination mean by 2 s.e., how likely is it that this group was drawn from the same population?

A More Systematic Test

Same/Different

D

D

0ms 60ms

0ms

20ms

D

T

20ms

40ms

Same/Different

0ms 10ms

T

T

40ms

60ms

Same/Different

Within-Category Discrimination is Hard

40ms 40ms

Abstraction mean by 2 s.e., how likely is it that this group was drawn from the same population?

• 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 mean by 2 s.e., how likely is it that this group was drawn from the same population?

Development of Speech Perception mean by 2 s.e., how likely is it that this group was drawn from the same population?

• 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 mean by 2 s.e., how likely is it that this group was drawn from the same population?

UniversalPhonetics

Native Lg.Phonology

Native Lg.Phonetics

0 months

6 months

12 months

18 months

### #1 - Infant Categorical Perception mean by 2 s.e., how likely is it that this group was drawn from the same population?

Eimas, Siqueland, Jusczyk & Vigorito, 1971

Discrimination mean by 2 s.e., how likely is it that this group was drawn from the same population?

A More Systematic Test

Same/Different

D

D

0ms 60ms

0ms

20ms

D

T

20ms

40ms

Same/Different

0ms 10ms

T

T

40ms

60ms

Same/Different

Within-Category Discrimination is Hard

40ms 40ms

high amplitude sucking mean by 2 s.e., how likely is it that this group was drawn from the same population?

non-nutritive sucking

English VOT Perception mean by 2 s.e., how likely is it that this group was drawn from the same population?

To Test 2-month olds

High Amplitude Sucking

Eimas et al. 1971

General Infant Abilities mean by 2 s.e., how likely is it that this group was drawn from the same population?

• 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 mean by 2 s.e., how likely is it that this group was drawn from the same population?

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

How can they do this? mean by 2 s.e., how likely is it that this group was drawn from the same population?

• Innate speech-processing capacity?

• General properties of auditory system?

What About Non-Humans? mean by 2 s.e., how likely is it that this group was drawn from the same population?

• Chinchillas show categorical perception of voicing contrasts!

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

Suitability of Animal Models mean by 2 s.e., how likely is it that this group was drawn from the same population?

More recent findings…

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

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

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

Some differences in vowel sensitivity…

Joan Sinnott, U. of S. Alabama

### #2 - Becoming a Native Listener mean by 2 s.e., how likely is it that this group was drawn from the same population?

Werker & Tees, 1984

When does Change Occur? mean by 2 s.e., how likely is it that this group was drawn from the same population?

Janet Werker

U. of British Columbia

When does Change Occur? mean by 2 s.e., how likely is it that this group was drawn from the same population?

• Hindi and Salishcontrasts testedon English kids

Janet Werker

U. of British Columbia

What do Werker’s results show? mean by 2 s.e., how likely is it that this group was drawn from the same population?

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

• Are the infants learning words?

• Or something else?

Korean has mean by 2 s.e., how likely is it that this group was drawn from the same population?[l] & [r]

[rupi] “ruby”

[saram] “person”

[irumi] “name”

[mul] “water”

[pal] “big”

[s\ul] “Seoul”

[ilkop] “seven”

[ipalsa] “barber”

### #3 - What, no minimal pairs? mean by 2 s.e., how likely is it that this group was drawn from the same population?

Stager & Werker, 1997

A Learning Theory… mean by 2 s.e., how likely is it that this group was drawn from the same population?

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

• Minimal Pairs

Word Learning mean by 2 s.e., how likely is it that this group was drawn from the same population?

• Stager &Werker 1997‘bih’ vs. ‘dih’and‘lif’ vs. ‘neem’

PRETEST mean by 2 s.e., how likely is it that this group was drawn from the same population?

HABITUATION mean by 2 s.e., how likely is it that this group was drawn from the same population?

TEST

SAME

SWITCH

Word learning results mean by 2 s.e., how likely is it that this group was drawn from the same population?

• Exp 2 vs 4

Why Yearlings Fail on Minimal Pairs mean by 2 s.e., how likely is it that this group was drawn from the same population?

• 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 mean by 2 s.e., how likely is it that this group was drawn from the same population?

• 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... mean by 2 s.e., how likely is it that this group was drawn from the same population?

• 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 mean by 2 s.e., how likely is it that this group was drawn from the same population?

14 months

17 months

20 months

14

17

20

60

300

600

0

Swingley & Aslin, 2002 mean by 2 s.e., how likely is it that this group was drawn from the same population?

• 14-month olds did recognize mispronunciations of familiar words

Dan Swingley, UPenn

Alternatives to Reviving Jakobson mean by 2 s.e., how likely is it that this group was drawn from the same population?

• 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 mean by 2 s.e., how likely is it that this group was drawn from the same population?

6-12 Months: What Changes? mean by 2 s.e., how likely is it that this group was drawn from the same population?

Structure Changing mean by 2 s.e., how likely is it that this group was drawn from the same population?

Patricia KuhlU. of Washington

Structure Adding mean by 2 s.e., how likely is it that this group was drawn from the same population?

• 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 mean by 2 s.e., how likely is it that this group was drawn from the same population?

• Structure-changing: mostly from vowels

• 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…? mean by 2 s.e., how likely is it that this group was drawn from the same population?

• Surface phonetic patterns

• Tests of experimentally induced changes…

5 hours’ exposure to Mandarin mean by 2 s.e., how likely is it that this group was drawn from the same population?

± human interaction

Alveo-palatal affricate vs. fricative contrast

[2003, Proceedings of the National Academy of Sciences]

Alveo-palatals mean by 2 s.e., how likely is it that this group was drawn from the same population?

affricate

fricative

Jessica Maye, mean by 2 s.e., how likely is it that this group was drawn from the same population?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?

p listeners’, cf. Pegg & Werker (1997)(a) = p(b)

p(a) = 2 x p(b)

1.0 listeners’, cf. Pegg & Werker (1997)

.5

.25

.1

Invariance listeners’, cf. Pegg & Werker (1997)

(Jusczyk 1997)

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

[Maye & Weiss, 2003]

So how do infants learn…? articulation.

• 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 articulation.

• 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