Lecture 10

Experiment 2

Martin Giese

What you should remember

1. Function of the middle ear

2. Traveling wave theory

3. Audibility function

4. Loudness perception

5. Masking

What you should learn today

1. Programming of stimuli in MATLAB

2. Data analysis

3. Details about the experiments

Programming the Experiments

Playsound

“High-level” function that plays a sinusoidal sound :

Playsound(f, A, t) plays sinusoidal tone with

frequency with frequency f and amplitude A for t seconds

Playsound(f, A, t, An, fn, Bn) plays sinusoidal tone with band pass background noise with mid frequency fn and band width +/-Bn

Randomization

Example: Randomize conditions for 3 different frequencies (f1, f2, f3) and 2 different amplitudes Aij per frequency

Systematic proceeding:

1. Design matrix: 2 x 3

f1 f2 f3

A11

A12

A21

A22

A31

A32

Randomization

2. Build equally shaped matrices for A and f

f1 f2 f3

Mf = f1 f2 f3

MA = A31

A32

A21

A22

A12

A12

Randomization

3. Cast matrices into vectors:

Mf = Mf(:); MA = MA(:);

4. Build a random integer vector with # of conditions:

cond_index = randperm(length(Mf));

Randomization

5. Address MA and Mf through this index: MA(cond_index(n)) (Amplitude of trial n)

Mf(cond_index(n)) (Frequency of trial n)

6. Loop over all trials:

for n=1:length(cond_index), ….. some function dependent on MA(cond_index(n)) and Mf(cond_index(n)) …..end;

Reading In Key Presses

Example:

Check whether the key “a” or “l” has been pressed. If yes, print the letter, otherwise

ignore the key press.

Reading In Key Presses

function key_demo(); % initializationret_strg = ‘‘;

% wait for a valid key presswhile strcmp(ret_strg, {'a', 'l'}) == 0, disp('Enter String.‘); ret_strg = getchar;end; % actions for admissible letters a and l if strcmp(ret_strg, 'a') == 1, disp('A');elseif strcmp(ret_strg, 'l') == 1, disp('L');end;

Simple example function

Data Analysis

Data Analysis

• Thresholds from probability data: – 50% threshold – Cool (optional): fit logistic threshold function

• Thresholds directly from adjustment methods / stair case

• Statistics for comparing thresholds: – t-test (pairwise comparisons) if enough items;

watch for (de)pendent measures !– non-parametric test for few items– ANOVA (next lecture)

• Extremely cool (idea for final project):run 2AFC experiment and estimate d’

Data Analysis

Correction of the level

• Problem: test difference between 2 AFs • Given: N threshold values for K values

of the frequency {Akn} and {Akn}• Possibilities:

– t-test (pairwise comparisons) K independent tests

– Better: ANOVA (next lecture !)

How can we combine the results from K independent tests?

Data Analysis

P(single test significant even though H0 true) <

P(single test non-significant if H0 true) >= 1-

Tests independent

P(all K tests non-significant if H0 true) >= (1- K

P(at least one out of the K tests significant if H0 true)

< 1 - (1- K = eq

Data Analysis

Equivalent significance level for K independent tests:

eq = 1 - (1- K

= 1 - (1- eq1/K

For large K:

eqK (“Bonferoni correction”)

Example:

K = 4eq = 5 % = 1.27 %

Experiments

Method of Constant Stimuli

• Frequencies: 30, 500, 2k, 10k, 18k Hz

• Pilot: for each frequency regime find out approximately the threshold and set up 5 amplitudes around this value

• 20 repetitions

Method of Limits

• Frequencies: 30, 500, 2k, 10k, 18k Hz

• Pilot: for each frequency regime find out approximately the threshold

• Ascending block: Start always with a stimulus that Ss don’t hear; increase by factor 1.2 until they hear; store result and start next trialDescending block: start with stimulus that Ss hear a decrease by factor 1.2 until they don’t hear stimulus any more

• 10 repetitions

Staircase Method

• Frequencies: 30, 100, 200, 500, 1k, 2k, 5k, 10k, 15k, 18k Hz

• Pilot: for each frequency regime find out approximately the threshold

• Steps; multiply / divide by 1.2

• Cross threshold 8 times before next trial starts

• 5 repetitions

Equal Loudness Contours

• Frequency of reference stimuli: 1000 Hz

• Test frequencies: 50, 100, 200, 500, 1k, 3k, 5k, 10k Hz

• 3 different amplitudes of the reference: low / medium / high

• Adjust amplitude of the test stimulus as to match loudness of reference

• 5 repetitions

Difference Thresholds

• Frequency of reference stimulus: 200 Hz

• Test 5 different amplitudes of the reference in the regime between very low and (conveniently) high amplitudes

• Measure for each amplitude difference thresholds using a method of constant stimuli

• 15 repetitions for the method of constant stimuli

Masking I

• Mask: narrowband noise with frequency 400 +/- 45 Hz

• Test frequencies: 100, 250, 400, 1k, 2k Hz

• Method of constant stimuli

• Trials with and without mask

• No time delay !

• 15 repetitions per condition

Masking II

• Mid frequency of mask and test tone 400 Hz; bandwidth +/- 45 Hz

• 5 different time delays: 0, 50, 100, 200 ad 500 ms

• Method of constant stimuli

• Trials with and without mask

• 15 repetitions per trial