Quantifying Sensitivity
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Transcript of Quantifying Sensitivity
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Quantifying Sensitivity
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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)
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Quantifying Sensitivity
• 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
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Normal Distribution
Mean (µ)
Dispersionaround mean
Standard DeviationA measure of dispersionaround the mean.
√( )∑(x - µ)2
n
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The Empirical Rule
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
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Quantifying Sensitivity
• 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)
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See Excel worksheet
sensitivity.xls
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Quantifying Differences
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(Näätänen et al. 1997)
(Aoshima et al. 2004)
(Maye et al. 2002)
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Normal Distribution
Mean (µ)
Dispersionaround mean
Standard DeviationA measure of dispersionaround the mean.
√( )∑(x - µ)2
n
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The Empirical Rule
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
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Normal Distribution
Mean (µ)65.5 inches
Standard deviation = 2.5 inches
Heights of AmericanFemales, aged 18-24
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• 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?
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• 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
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• Standard Error
is the Standard Deviation of sample means.
€
n
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• 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?
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Development of Speech Perception in Infancy
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Voice Onset Time (VOT)
60 msec
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Perceiving VOT
‘Categorical Perception’
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Discrimination
Same/Different0ms 60ms
Same/Different0ms 10ms
Same/Different40ms 40ms
A More Systematic Test
0ms
20ms
40ms
20ms
40ms
60ms
D T
D
T T
D
Within-Category Discrimination is Hard
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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
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Three Classics
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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
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Developmental Differentiation
0 months 6 months 12 months 18 months
UniversalPhonetics
Native Lg.Phonetics
Native Lg.Phonology
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#1 - Infant Categorical Perception
Eimas, Siqueland, Jusczyk & Vigorito, 1971
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Discrimination
Same/Different0ms 60ms
Same/Different0ms 10ms
Same/Different40ms 40ms
A More Systematic Test
0ms
20ms
40ms
20ms
40ms
60ms
D T
D
T T
D
Within-Category Discrimination is Hard
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high amplitude suckingnon-nutritive sucking
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English VOT Perception
To Test 2-month olds
High Amplitude Sucking
Eimas et al. 1971
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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]
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Universal Listeners
• Infants may be able to discriminate all speech contrasts from the languages of the world!
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How can they do this?
• Innate speech-processing capacity?
• General properties of auditory system?
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What About Non-Humans?
• Chinchillas show categorical perception of voicing contrasts!
PK Kuhl & JD Miller, Science, 190, 69-72 (1975)
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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
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#2 - Becoming a Native Listener
Werker & Tees, 1984
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When does Change Occur?
• About 10 months
Janet Werker
U. of British ColumbiaConditioned Headturn Procedure
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When does Change Occur?
• Hindi and Salishcontrasts testedon English kids
Janet Werker
U. of British ColumbiaConditioned Headturn Procedure
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What do Werker’s results show?
• Is this the beginning of efficient memory representations (phonological categories)?
• Are the infants learning words?
• Or something else?
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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”
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#3 - What, no minimal pairs?
Stager & Werker, 1997
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A Learning Theory…
• How do we find out the contrastive phonemes of a language?
• Minimal Pairs
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Word Learning
• Stager &Werker 1997
‘bih’ vs. ‘dih’and‘lif’ vs. ‘neem’
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PRETEST
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HABITUATION
TEST
SAME SWITCH
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Word learning results
• Exp 2 vs 4
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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
• !!??
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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
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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
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Werker et al. 2002
14 17 20
14 months 17 months 20 months
0 60 300 600
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Swingley & Aslin, 2002• 14-month olds did recognize mispronunciations of familiar
words
Dan Swingley, UPenn
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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
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Questions about Development
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6-12 Months: What Changes?
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Structure Changing
Patricia KuhlU. of Washington
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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
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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]
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So how do infants learn…?
• Surface phonetic patterns
• Tests of experimentally induced changes…
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[2003, Proceedings of the National Academy of Sciences]
5 hours’ exposure to Mandarin± human interaction
Alveo-palatal affricate vs. fricative contrast
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fricativeaffricate
Alveo-palatals
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Jessica Maye, Northwestern U.
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• 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?
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0
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p(a) = p(b) p(a) = 2 x p(b)
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1.0
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(Jusczyk 1997)
Invariance
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Training on [g-k] or [d-t], generalization across place of articulation.(Dis-)habituation paradigm.
[Maye & Weiss, 2003]
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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
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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
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