3. Acoustic Continua and Phonetic Categories

4. Frequency - Tones

8. Frequency - Complex Sounds

10. Frequency - Vowels Vowels combine acoustic energy at a number of different frequencies Different vowels ([a], [i], [u] etc.) contain acoustic energy at different frequencies Listeners must perform a ‘frequency analysis’ of vowels in order to identify them (Fourier Analysis)

11. Joseph Fourier (1768-1830) Time --> Frequency Amplitude Any function can be decomposed in terms of sinusoidal (= sine wave) functions (‘basis functions’) of different frequencies that can be recombined to obtain the original function. [Wikipedia entry on Fourier Analysis]

12. Frequency - Male Vowels

14. Frequency - Female Vowels

16. Synthesized Speech Allows for precise control of sounds Valuable tool for investigating perception

17. Timing - Voicing

18. Voice Onset Time (VOT) 60 msec

19. English VOT production Not uniform 2 categories

20. Perceiving VOT ‘Categorical Perception’

21. Discrimination Same/Different 0ms 60ms Same/Different 0ms 10ms Same/Different 40ms A More Systematic Test 0ms 20ms 40ms 20ms 40ms 60ms DT D T T D Within-Category Discrimination is Hard

22. Cross-language Differences R L R L

23. Cross-Language Differences English vs. Japanese R-L

24. Cross-Language Differences English vs. Hindi alveolar [d] retroflex [D] ?

25. Russian -40ms -30ms -20ms -10ms 0ms 10ms

26. Kazanina et al., 2006 Proceedings of the National Academy of Sciences, 103, 11381-6

27. Quantifying Sensitivity

28. Response bias Two measures of discrimination –Accuracy: how often is the judge correct? –Sensitivity: how well does the judge distinguish the categories? Quantifying sensitivity –HitsMisses False AlarmsCorrect Rejections –Compare p(H) against p(FA)

29. 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

30. Normal Distribution Mean (µ) Dispersion around mean Standard Deviation A measure of dispersion around the mean. √( ) ∑(x - µ) 2 n Carl Friederich Gauss (1777-1855)

31. 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

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

33. 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)

34. See Excel worksheet sensitivity.xls

35. Quantifying Differences

36. (N ää t ä nen et al. 1997) (Aoshima et al. 2004) (Maye et al. 2002)

37. Normal Distribution Mean (µ) Dispersion around mean Standard Deviation A measure of dispersion around the mean. √( ) ∑(x - µ) 2 n

38. 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

39. 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?

40. 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

41. Standard Error is the Standard Deviation of sample means.

42. 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?