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Quantifying Sensitivity

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

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  1. Quantifying Sensitivity

  2. 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)

  3. 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 extremesz-scores

  4. Dispersionaround mean Mean (µ) √( ) ∑(x - µ)2 n Normal Distribution Standard Deviation A measure of dispersionaround the mean.

  5. 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

  6. 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)

  7. See Excel worksheetsensitivity.xls

  8. Quantifying Differences

  9. (Näätänen et al. 1997) (Aoshima et al. 2004) (Maye et al. 2002)

  10. Dispersionaround mean Mean (µ) √( ) ∑(x - µ)2 n Normal Distribution Standard Deviation A measure of dispersionaround the mean.

  11. 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

  12. Normal Distribution Standard deviation  = 2.5 inches Heights of American Females, aged 18-24 Mean (µ) 65.5 inches

  13. 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?

  14. 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

  15. Standard Erroris the Standard Deviation of sample means.

  16. 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?

  17. Development of Speech Perception in Infancy

  18. Voice Onset Time (VOT) 60 msec

  19. Perceiving VOT ‘Categorical Perception’

  20. Discrimination 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

  21. 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

  22. Three Classics

  23. 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

  24. Developmental Differentiation UniversalPhonetics Native Lg.Phonology Native Lg.Phonetics 0 months 6 months 12 months 18 months

  25. #1 - Infant Categorical Perception Eimas, Siqueland, Jusczyk & Vigorito, 1971

  26. Discrimination 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

  27. high amplitude sucking non-nutritive sucking

  28. English VOT Perception To Test 2-month olds High Amplitude Sucking Eimas et al. 1971

  29. 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]

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

  31. How can they do this? • Innate speech-processing capacity? • General properties of auditory system?

  32. What About Non-Humans? • Chinchillas show categorical perception of voicing contrasts! PK Kuhl & JD Miller, Science, 190, 69-72 (1975)

  33. Suitability of Animal Models 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

  34. #2 - Becoming a Native Listener Werker & Tees, 1984

  35. When does Change Occur? • About 10 months Janet Werker U. of British Columbia Conditioned Headturn Procedure

  36. When does Change Occur? • Hindi and Salishcontrasts testedon English kids Janet Werker U. of British Columbia Conditioned Headturn Procedure

  37. What do Werker’s results show? • Is this the beginning of efficient memory representations (phonological categories)? • Are the infants learning words? • Or something else?

  38. 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”

  39. #3 - What, no minimal pairs? Stager & Werker, 1997

  40. A Learning Theory… • How do we find out the contrastive phonemes of a language? • Minimal Pairs

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

  42. PRETEST

  43. HABITUATION TEST SAME SWITCH

  44. Word learning results • Exp 2 vs 4

  45. 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 • !!??

  46. 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

  47. 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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