Experimental analysis problem

Hi,

I conducted a series of experiments into the effect of inter-aural 
signal differences on the perception of sound direction.  I change two 
variables (the inter-aural time difference ITD, and inter-aural level 
difference ILD) and measure the human directional response.  I change 
ITD by inserted blank samples to the beginning of one channel, then I 
change the ILD by multiplying all samples in one channel by a number 
smaller than 1.  I then need to plot the combined effect of ILD and ITD 
against the perceived direction.

But what, mathematically, have I done?

Based on intuition I normalised the two to give them equal weighting and 
then added them together.  This gives me the lovely straight line I am 
looking for.  I am having a hard time justifying this in my mind.

Any comments would be most welcome.

Richard

I would first plot ILD and ITD seperalty against perceived direction
instead of trying to normalize and combine  them together.

Mark

Mark wrote:
> I would first plot ILD and ITD seperalty against perceived direction
> instead of trying to normalize and combine  them together.
> 
> Mark
> 

Thanks for your reply Mark.  That was a seperate part of the experiment. 
  I performed trials in which I varied the ITD and ILD seperately in 
which I plotted them against perceived direction.

Then I there were trials where I varied both at once in order to find 
how they interact.  For these trials if I plot the ILD or ITD alone 
against direction I get a very broad envelope but if I add the two 
together I get exactly what i'm looking for, a linear relationship 
between the sum of ILD and ITD against the direction.

I have read sources saying that the ITD and ILD are multiplied to 
localize sound.  I tried multiplying the ILD and ITD values together and 
the result is a mess.  But then maybe that is a meaningless thing to do 
in the context of how I combined them, or maybe adding them is and its 
coincidence.  Which comes back to my question.  If I add some samples 
and then multiply all the samples by some number, what function have I 
performed?

Any further thoughts?

Richard

Richard wrote:

> Hi,
> 
> I conducted a series of experiments into the effect of inter-aural 
> signal differences on the perception of sound direction.  I change two 
> variables (the inter-aural time difference ITD, and inter-aural level 
> difference ILD) and measure the human directional response.  I change 
> ITD by inserted blank samples to the beginning of one channel, then I 
> change the ILD by multiplying all samples in one channel by a number 
> smaller than 1.  I then need to plot the combined effect of ILD and ITD 
> against the perceived direction.
> 
> But what, mathematically, have I done?
> 
> Based on intuition I normalised the two to give them equal weighting and 
> then added them together.  This gives me the lovely straight line I am 
> looking for.  I am having a hard time justifying this in my mind.
> 
> Any comments would be most welcome.
> 
> Richard

Please can anyone else add anything to this thread?

Come on, seriously, this could be the difference between me getting a 
1st and a 2:1 in my degree.  Can you live with that on your conscience ;-) ?

Richard

Richard skrev:
> Richard wrote:
>
> > Hi,
> >
> > I conducted a series of experiments into the effect of inter-aural
> > signal differences on the perception of sound direction.  I change two
> > variables (the inter-aural time difference ITD, and inter-aural level
> > difference ILD) and measure the human directional response.  I change
> > ITD by inserted blank samples to the beginning of one channel, then I
> > change the ILD by multiplying all samples in one channel by a number
> > smaller than 1.  I then need to plot the combined effect of ILD and ITD
> > against the perceived direction.
> >
> > But what, mathematically, have I done?
> >
> > Based on intuition I normalised the two to give them equal weighting and
> > then added them together.  This gives me the lovely straight line I am
> > looking for.  I am having a hard time justifying this in my mind.
> >
> > Any comments would be most welcome.
> >
> > Richard
>
> Please can anyone else add anything to this thread?
>
> Come on, seriously, this could be the difference between me getting a
> 1st and a 2:1 in my degree.  Can you live with that on your conscience ;-) ?

You don't want me start ranting along those lines, believe me!

I don't know much about your particular field of work, but having
worked a bit with experimental data, I prefer somebody who
presents some result, explains how he got there and then
expresses whatever doubts or reservations he might have,
over somebody who express "perfect" results as if there were
no problems whatsoever.

>From your phrasing of the problem, I suspect I know how you think
about such matters. You would have to search out what your
supervisor thinks about the matter, and depending on what you
find, think very carefully about how you want to play the game.

A cleared-out consciousness is one thing. A cleared-out bank
account might be far more serious.

Rune

Hi Richard,

ILD is mostly responsible for sound localization at high frequencies
(say 2> KHz, not sure exactly).
While ITD is mostly responsible for sound localization of low frequency
sources.

So if you want to study their coupled effects you *must* take into
account the frequency of the source that you are using and you can't
really assume the ILD and ITD are independent of one another...

It seems like you can do an analysis of variance (ANOVA) of your data
with an interaction term for ITD and ILD, as long as you have varied
these parameters independent of one another. This is essentially a
multi-regression on ITD, ILD and their interaction.

Keep in mind that there is a frequency effect here and that you might
miss non-linear relationships here...you will need to hold the
frequency constant to simplify the experiment.

Hi Ikaro, thanks for your reply

Ikaro wrote:

> Hi Richard,
> 
> ILD is mostly responsible for sound localization at high frequencies
> (say 2> KHz, not sure exactly).
> While ITD is mostly responsible for sound localization of low frequency
> sources.
> 
> So if you want to study their coupled effects you *must* take into
> account the frequency of the source that you are using and you can't
> really assume the ILD and ITD are independent of one another...
> 

Whilst this is true, my research and experience suggests it is only 
partially true.  The brain does not consider the ITD for sounds above 
about 1.5khz.  In the real world there is very little ILD for sounds 
below 1.5khz because the wavelength is larger than the width of the head 
so there is almost perfect diffraction.  However, I have shown that the 
brain will use an ILD if it exists for those sounds (and I am putting it 
in artificially).  However, as a result the brain is very sensitive to 
the ILD at low frequencies and it is therefore a very frequency 
dependant cue as you point out.

The sounds that I am using have very little content above 1500hz.

I am not assuming they are independent at all.  It is the way the two 
interact that I am trying to determine.  It seems that sometimes the 
brain follows ITD, occasionally it follows ILD, and most of the time it 
finds some point somewhere between where the ITD and ILD says it is.

> It seems like you can do an analysis of variance (ANOVA) of your data
> with an interaction term for ITD and ILD, as long as you have varied
> these parameters independent of one another. This is essentially a
> multi-regression on ITD, ILD and their interaction.
> 

I performed logistic regression on the trials in which I varied only one 
of them.  In the trials where I varied both at once I considered trying 
perform some regresson test that took both into account but could not 
find the correct way to do it.  Is an ANOVA appropriate in this case?

> Keep in mind that there is a frequency effect here and that you might
> miss non-linear relationships here...you will need to hold the
> frequency constant to simplify the experiment.
> 

I am using a single sound for all experiments, that of a snare drum 
beat.  It has large frequency content between 150 and 400hz and 
significant content up to about 1000hz but not much above that.  This is 
the main reason I chose the sound.  Is this what you mean?

Thanks again

Rune Allnor wrote:

> Richard skrev:
> 
>>Richard wrote:
>>
>>Please can anyone else add anything to this thread?
>>
>>Come on, seriously, this could be the difference between me getting a
>>1st and a 2:1 in my degree.  Can you live with that on your conscience ;-) ?
> 
> You don't want me start ranting along those lines, believe me!

:-)

> 
> I don't know much about your particular field of work, but having
> worked a bit with experimental data, I prefer somebody who
> presents some result, explains how he got there and then
> expresses whatever doubts or reservations he might have,
> over somebody who express "perfect" results as if there were
> no problems whatsoever.

I try, perfect results are after all rather dull.  Having said that I 
don't want to present an analysis of my results from which I conclude 
what I can, only to then discover later that my analysis is simply wrong 
and I fail for it.

> 
> From your phrasing of the problem, I suspect I know how you think
> about such matters. You would have to search out what your
> supervisor thinks about the matter, and depending on what you
> find, think very carefully about how you want to play the game.
> 

My impression is he's pretty sharp on signal processing.  Having said 
that he knows very little about psychology which is the focus of the 
experiment.

> A cleared-out consciousness is one thing. A cleared-out bank
> account might be far more serious.
> 
> Rune
> 

Do you mean a cleared out concience?  I haven't had one of them for 
years.  If you do mean what you wrote then I am planning to clear out my 
bank account in order to clear my consciousness just as soon as I hand 
this report in.  Mmmmmm Whiskey!

Richard

>I performed logistic regression on the trials in which I varied only one
>of them.  In the trials where I varied both at once I considered trying
>perform some regresson test that took both into account but could not
>find the correct way to do it.  Is an ANOVA appropriate in this case?

Not if you are varying ILD and ITD dependently. In this case you
*might* go by using ANCOVA, and setting one of the stimulus as a
covariate variable.

But the best way would be to add independent noise (pertubations) to
both stimulus (note that you will need 2 independent noise sources).
And see how these pertubations affect the accuracy, either by doing
ANOVA as mentioned here, or an analysis of perceptual weights for human
observers. Check the following paper for an implementation of that:

Berg, B. G. (1989). "Analysis of weights in multiple observation
tasks," J. Acoust. Soc. Am. 86, 1743-1746

The key point is that the predictors in your model should be varied
independtly of each other.

>I am using a single sound for all experiments, that of a snare drum
>beat.  It has large frequency content between 150 and 400hz and
>significant content up to about 1000hz but not much above that.  This is
>the main reason I chose the sound.  Is this what you mean?

No. Ideally it would be best if the sounds were within one critical
band of the auditory system . Since you stimulus goes across several
critical bands, its possible that the subject weigth the cues
differently across the critical bands. Not to mention that they might
switch listening strategies... all of which would complicate
investigation of the perceptual weights given to ILD and ITD (as well
as their interactions).

Richard skrev:
> Rune Allnor wrote:
>
> > Richard skrev:
> >
> >>Richard wrote:
> >>
> >>Please can anyone else add anything to this thread?
> >>
> >>Come on, seriously, this could be the difference between me getting a
> >>1st and a 2:1 in my degree.  Can you live with that on your conscience ;-) ?
> >
> > You don't want me start ranting along those lines, believe me!
>
> :-)
>
> >
> > I don't know much about your particular field of work, but having
> > worked a bit with experimental data, I prefer somebody who
> > presents some result, explains how he got there and then
> > expresses whatever doubts or reservations he might have,
> > over somebody who express "perfect" results as if there were
> > no problems whatsoever.
>
> I try, perfect results are after all rather dull.

Most certainly agreed.

>  Having said that I
> don't want to present an analysis of my results from which I conclude
> what I can, only to then discover later that my analysis is simply wrong
> and I fail for it.

With real-life experiments, one can never do more than one's
best. If there is a "truth" out there, I have never found it. If your
supervisor is worth his salary, he will look at the arguments
you present and see if you make sense of them. There will always
be one more argument to present, but one have to stop somewhere.

After all, one have only so much time available.

> > From your phrasing of the problem, I suspect I know how you think
> > about such matters. You would have to search out what your
> > supervisor thinks about the matter, and depending on what you
> > find, think very carefully about how you want to play the game.
> >
>
> My impression is he's pretty sharp on signal processing.  Having said
> that he knows very little about psychology which is the focus of the
> experiment.

Is he good with experimental work?

> > A cleared-out consciousness is one thing. A cleared-out bank
> > account might be far more serious.
> >
> > Rune
> >
>
> Do you mean a cleared out concience?

Yep. as you might have noticed, orthography is not among
my stronger sides...

> I haven't had one of them for
> years.  If you do mean what you wrote then I am planning to clear out my
> bank account in order to clear my consciousness just as soon as I hand
> this report in.  Mmmmmm Whiskey!

Laphroaigh is my favourite... made a lasting impression.

Bad jokes aside: I meant that some people want your results to
correspond to their truths. If you encounter any of those, you
will have some pretty far-reaching decisions to make; most of
which affect the in-flux side of your bank account.

Rune