Statistical analysis of multiple REW measurements - Home Theater Forum and Systems - HomeTheaterShack.com

Old 05-03-13, 03:27 PM Thread Starter
Shackster
Mark

Join Date: Feb 2013
Location: UK
Posts: 13
My System
Statistical analysis of multiple REW measurements

I've been using REW to try to measure transmission losses of several samples of material, hoping one (or more) will be good enough to use as an acoustically transparent projector screen.

During my last test I took 3 microphone-only measurements and the results varied from test to test by a few db so I'm thinking of repeating my tests and taking 7 measurements for each fabric and microphone-only.

My questions is: does anyone know which statistical test I should use to "analyse" the results? Can I use a simple conversion to intensity (i = 10^(dB/10)), average the intensities and convert this average back to dB (dB = 10 log i)?

It's been 20 years since I've done any stats and while I know the accuracy of my tests is limited before I start by the equipment (laptop, Anthem mic) I'd like to follow best practice to analyse the results so I can hopefully see if any of the fabrics are good enough to use as an AT screen.

These are 3 of the graphs from my test, the 3 purple lines are the microphone-only measurements:

Thanks

The images don't seem to be showing up, here are the links for anyone interested:

http://inagoodlight.com/images-for-f...bric-test2.png
http://inagoodlight.com/images-for-forums/104hz.png
http://inagoodlight.com/images-for-forums/240hz.png

Last edited by mhuk; 05-03-13 at 04:27 PM.
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Old 05-03-13, 04:30 PM
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John

Join Date: Apr 2006
Location: UK
Posts: 6,306
Re: Statistical analysis of multiple REW measurements

When comparing the measurements you should ignore areas where there are sharp dips, such room effects will be highly dependent on exact positioning of mic and source, even a few mm variation in position can alter the results significantly.
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Old 05-03-13, 04:38 PM Thread Starter
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Mark

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Re: Statistical analysis of multiple REW measurements

I did wonder about room effect and I'm sure the patent-pending AT material holding device (a cardboard box with a cut-out for the fabric to be taped on, mounted on a lighting stand) moved a bit between measurements.

Would I be better off smoothing at a higher smoothing "rate" or just look at the frequencies that are typically stated for absorption coefficients of acoustic material?

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Old 05-03-13, 04:43 PM
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John

Join Date: Apr 2006
Location: UK
Posts: 6,306
Re: Statistical analysis of multiple REW measurements

I wouldn't use smoothing as that would smear the effect of room-related dips and peaks across nearby frequencies. Probably best ignoring frequencies where there are significant dips in the response and treating any measurement runs of the same material that showed significant deviation (outside those dips) as suspicious and rerun the test. It would be worth your while to find some literature on the methods used to measure the acoustic properties of materials, however.
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Old 05-03-13, 06:43 PM Thread Starter
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Mark

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Re: Statistical analysis of multiple REW measurements

Quote:
It would be worth your while to find some literature on the methods used to measure the acoustic properties of materials,
I've been trying but all the google links I've found lead to pages selling test methodology (ASTM, ISO etc) that may or may not be relevant, and finding anything related specifically to testing acoustic transparency of fabric hasn't been successful. Any tips on googling better terminology would be much appreciated
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Old 05-03-13, 06:52 PM
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Wayne Myers

Join Date: Jun 2012
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Re: Statistical analysis of multiple REW measurements

Quote:
mhuk wrote: View Post
My questions is: does anyone know which statistical test I should use to "analyse" the results? Can I use a simple conversion to intensity (i = 10^(dB/10)), average the intensities and convert this average back to dB (dB = 10 log i)?
I do not know the answer to your question for certain, but you got me thinking. Wouldn't averaging intensity give stronger weighting to the higher SPL measurements? And since our hearing sensitivity is pretty logarithmic (or at least more logarithmic than linear), it seems to like simply averaging SPLs would be the valid approach.
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Old 05-04-13, 05:09 AM Thread Starter
Shackster
Mark

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Re: Statistical analysis of multiple REW measurements

The equations I posted were the ones I found when I googled how to average dB readings so I'm not sure.

If I have 3 dB measurements: 57, 55 and 53:

the arithmetic mean is 55

the geometric mean is 54.98

the harmonic mean is 54.95

the average intensity back to dB is 55.3 (which supports the weighting of higher SPL to affect the average).

There's not a huge difference between the means for my example dB but which one is the correct method to use I don't know, although experimental error would seem to be statistically significant and render any calculations worthless?

calculators: http://easycalculation.com/statistic...etric-mean.php

Last edited by mhuk; 05-04-13 at 05:17 AM.
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Old 05-04-13, 05:21 PM
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Wayne Myers

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Re: Statistical analysis of multiple REW measurements

Quote:
mhuk wrote: View Post
There's not a huge difference between the means for my example dB but which one is the correct method to use I don't know, although experimental error would seem to be statistically significant and render any calculations worthless?
Again not speaking authoritatively, it seems like the desired result is that which correlates most closely to the way we hear, which to me sounds like the arithmetic mean of the SPL readings. With the small differences you will be encountering, we are probably splitting hairs. Arithmetic Mean gets my vote for (1) simplicity, and (2) as far as I can tell, representing the way we hear.
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Old 05-04-13, 10:42 PM
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jamin

Join Date: Jun 2006
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Re: Statistical analysis of multiple REW measurements

RMS of the Pressure works out to averaging the intensity and is the method used for spatial averaging. As noted, this method gives less weight to lower measures.

Imagine 4 measurements with one of them 20 dB down from the other 3. Straight averaging of the dB would yield a measure -5 dB below the 3 overlays. An RMS, read as intensity average, yields a decrease of only ~-1.23 dB.

The flip side is to imagine 1 of the 4 measures being say 6dB above the other 3. With RMS this leads to an increase of ~2.4 dB whereas the straight average in dB yields an increase of 1.5 dB.

I tend to come down on the side of the established RMS calculation.

IMHO, FWIW, etc.

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Old 05-05-13, 02:08 AM
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jamin

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Re: Statistical analysis of multiple REW measurements

Quote:
jamin wrote: View Post
RMS of the ...../snip...
An RMS, read as intensity average, yields a decrease of only ~-1.23 dB..../snip..
Arrgh--
Decrease of 1.23 dB
Fingers moving too fast!

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