Acoustic Continua and Phonetic Categories Frequency - Tones Frequency - Tones Frequency - Tones Frequency - Tones Frequency - Complex Sounds Frequency - Complex Sounds 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) 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] Time --> Amplitude Frequency Joseph Fourier (1768-1830) Frequency - Male Vowels Frequency - Male Vowels Frequency - Female Vowels Frequency - Female Vowels Synthesized Speech •Allows for precise control of sounds •Valuable tool for investigating perception Timing - Voicing Voice Onset Time (VOT) 60 msec English VOT production • Not uniform • 2 categories Perceiving VOT ‘Categorical Perception’ Discrimination Same/Different 0ms 60ms Same/Different 0ms 10ms Same/Different 40ms 40ms A More Systematic Test D 0ms 20ms D D 20ms 40ms T T 40ms 60ms T Within-Category Discrimination is Hard Cross-language Differences R R L L Cross-Language Differences English vs. Japanese R-L Cross-Language Differences English vs. Hindi alveolar [d] retroflex [D] ? Russian -40ms -30ms -20ms -10ms 0ms 10ms Kazanina et al., 2006 Proceedings of the National Academy of Sciences, 103, 11381-6 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 False Alarms Misses Correct Rejections – Compare p(H) against p(FA) 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 Normal Distribution Dispersion around mean Standard Deviation A measure of dispersion around the mean. Mean (µ) Carl Friederich Gauss (1777-1855) √( ∑(x - µ)2 n ) 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 Normal Distribution Standard deviation = 2.5 inches Heights of American Females, aged 18-24 Mean (µ) 65.5 inches 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) See Excel worksheet sensitivity.xls Quantifying Differences (Näätänen et al. 1997) (Aoshima et al. 2004) (Maye et al. 2002) Normal Distribution Dispersion around mean Standard Deviation A measure of dispersion around the mean. Mean (µ) √( ∑(x - µ)2 n ) 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 • 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?