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Quantitative Analysis of “craigsub” HT Subwoofer Ratings

post #1 of 244
Thread Starter 
got bored, wanted to give back, wrote a paper. here is an excerpt:

QUANTITATIVE ANALYSIS OF CRAIGSUB HT SUBWOOFER RATINGS

Publius

\tIn a novel dataset, the craigsub HT subwoofer scores, a small number of readily acquired variables explain the overwhelming majority of variation in home theater subwoofer performance, upwards of 95%. Therefore, quantitative methods may be tremendously valuable in assisting the subwoofer purchaser to sort through all the marketing hoopla that is all too common in the industry. Purchasers should focus on driver diameter, box volume, amplifier power, vented design, extreme linear excursion and possibly number of drivers. All these factors predict higher performance in home theater.

Reason for Inquiry
The craigsub data provide a great start to comparing many popular subwoofers. His stated goal,

The purpose of this information is to help people to quickly look at a variety of subwoofers and get a pair of scores, some performance numbers, and some listening tests describing the characteristics of each subwoofer. Hopefully, this will provide some assistance when researching for a subwoofer purchase.

Obviously, he has achieved his stated goal, but can we learn more? Is there anything that we can generalize from the data that will provide assistance to researching subwoofers that have not been tested. The subwoofer market is huge and highly fragmented. No reviewer can be expected to test them all and subjective scorings vary too much between reviewers (and their listening environments) to provide a sound basis for comparison. Illka subwoofer tests listed on hometheatershack.com are among the growing trend toward objective performance measurement, but such tests tell us nothing about how to generalize subwoofer principals in order to make predictions about subwoofers that have not been tested. This is the first such quantitative analysis of subjective subwoofer data of which the author is aware.

Data
craigsub subwoofer scoring data were gathered from avsforum.com, as of Feb 21, 2008. Manufacturer websites were used for subwoofer specifications where possible. If the model was an old model and no longer on the manufacturers website, a review website that reported specifications was used.


Methods
Multiple linear regression (MLS) methods have been used in a wide variety of fields to tease out relationships that may not be obvious using other quantitative methods. Essentially, MLS is a tried and true method for identifying linear relationships between a dependent variable (subwoofer scores) and a set of independent or explanatory variables (driver diameter, amplifier power, etc.). By transforming data (taking roots, logs, etc.), non-linear relationships in data can also be identified. Dummy variables can be used to determine if binomial variables (such as vented/sealed) are significant.

Variables
craigsub home theater scores (HT) was the independent variable. The variables used to explain the HT score were:

VNT = dummy variable for whether the subwoofer is vented or passive radiator (this variable takes a one for vented or passive radiator, a zero for sealed enclosure).

DRVRS = number of drivers

DRV_DIAM = reported driver diameter (this is typically the diameter of the frame; the actual radiating portion is much smaller)

DxD2 = this is a compound variable that combines the number of drivers and the square of the driver diameter. This variable is a measure of the area of all the drivers.

PWR = reported RMS power of the amplifier.

BOX_VOL = volume of the enclosure. This is often not reported and so has to be estimated. Box volume is roughly the exterior volume, less wall thickness, less volume of amp and subwoofer driver, less internal bracing.

HI_XMAX = extreme xmax capability. This applies to drivers with linear excursion in the +/-35mm range. Dummy variable takes one for extreme excursion subs, zero otherwise.

COI = craigsub conflict of interest variable. Suspicions have been raised about the objectivity of the analysis, as craigsub and the principals at AV123 are known to be good friends and may have business dealings in development. This is another dummy variable that takes on a one for products from AV123.

 

Quantitative Analysis Subwoofers Revised.pdf 157.0439453125k . file

 

source_data.txt 2.8466796875k . file
post #2 of 244
Thread Starter 
Results
First pass regressions. Here HT is regressed on DRVRS, DRV_DIAM, DxD2, PWR, and BOX_VOL.

Regression Analysis: HT versus DRVRS

The regression equation is
HT = 37.3 + 9.07 DRVRS

Predictor Coef SE Coef T P
Constant 37.267 3.901 9.55 0.000
DRVRS 9.067 3.167 2.86 0.008

S = 6.442 R-Sq = 23.3% R-Sq(adj) = 20.4%

Regression Analysis: HT versus DRV_DIAM

The regression equation is
HT = 17.0 + 2.35 DRV_DIAM

Predictor Coef SE Coef T P
Constant 16.953 4.364 3.88 0.001
DRV_DIAM 2.3485 0.3256 7.21 0.000

S = 4.300 R-Sq = 65.8% R-Sq(adj) = 64.6%

Regression Analysis: HT versus DxD2

The regression equation is
HT = 38.6 + 0.0427 DxD2

Predictor Coef SE Coef T P
Constant 38.577 1.694 22.78 0.000
DxD2 0.042694 0.006681 6.39 0.000

S = 4.640 R-Sq = 60.2% R-Sq(adj) = 58.7%

Regression Analysis: HT versus PWR

The regression equation is
HT = 43.4 + 0.00623 PWR

Predictor Coef SE Coef T P
Constant 43.394 1.676 25.89 0.000
PWR 0.006225 0.001723 3.61 0.001

S = 6.038 R-Sq = 32.6% R-Sq(adj) = 30.1%

Regression Analysis: HT versus BOX_VOL

The regression equation is
HT = 36.4 + 2.67 BOX_VOL

Predictor Coef SE Coef T P
Constant 36.443 1.697 21.47 0.000
BOX_VOL 2.6723 0.3525 7.58 0.000

S = 4.159 R-Sq = 68.0% R-Sq(adj) = 66.8%

The t-statistics are all significant and the high r-squared suggest that each of these variables alone help explain subwoofer HT scores. The magnitudes of the r-squareds are striking! Summarizing the results:

Score Variable % of Score Explained by Variable
Increases Number of drivers increases 20.4%
Increases Driver diameter increases 64.6%
Increases Driver total area increases 58.7%
Increases Driver amplifier power increases 30.1%
Increases Driver box volume increases 66.8%
post #3 of 244
Thread Starter 
These results tell us that each of these variables is important and helps explain subwoofer scores, but how to they combine? How does one go about making tradeoffs between the variables? For example, driver diameter by itself explains 64.6% and box volume explains 66.8%. Together, these would sum to over 100%, which can’t be the case. Clearly the two variables have some overlap in their explanatory power. Are they essentially the same thing and so using both adds no value? Or, are there aspects of each variable that contribute independently to explaining performance? These questions will be answered by constructing a multiple regression model.

Second pass regression. In this regression, the multiple regression model construction is begun. Driver diameter (DRV_DIAM) will be the first variable.

Recall:
Regression Analysis: HT versus DRV_DIAM

The regression equation is
HT = 17.0 + 2.35 DRV_DIAM

Predictor Coef SE Coef T P
Constant 16.953 4.364 3.88 0.001
DRV_DIAM 2.3485 0.3256 7.21 0.000

S = 4.300 R-Sq = 65.8% R-Sq(adj) = 64.6%

To that variable, a second variable, box volume (BOX_VOL) is added.

Regression Analysis: HT versus DRV_DIAM, BOX_VOL

The regression equation is
HT = 23.9 + 1.30 DRV_DIAM + 1.61 BOX_VOL

Predictor Coef SE Coef T P
Constant 23.898 4.086 5.85 0.000
DRV_DIAM 1.2967 0.3948 3.28 0.003
BOX_VOL 1.6128 0.4419 3.65 0.001

S = 3.563 R-Sq = 77.4% R-Sq(adj) = 75.7%

R-squared went up from 64.6% to 75.7%. This suggests that there is information in the BOX_VOL variable that is not subsumed in the driver diameter (DRV_DIAM) variable.

Adding a third variable, amplifier power (PWR) improves things further:

Regression Analysis: HT versus DRV_DIAM, BOX_VOL, PWR

The regression equation is
HT = 26.6 + 0.894 DRV_DIAM + 1.67 BOX_VOL + 0.00324 PWR

Predictor Coef SE Coef T P
Constant 26.597 3.525 7.55 0.000
DRV_DIAM 0.8943 0.3521 2.54 0.018
BOX_VOL 1.6740 0.3720 4.50 0.000
PWR 0.0032377 0.0009437 3.43 0.002

S = 2.996 R-Sq = 84.6% R-Sq(adj) = 82.8%

Combining these three variables explains 82.8%% of the variation in subwoofer scores. Yes, in these data, almost 83% of the score could be predicted by knowing just three variables: driver diameter (DRV_DIAM), enclosure volume (BOX_VOL), and amplifier power (PWR).

On to the fourth variable, the vent.

Regression Analysis: HT versus DRV_DIAM, BOX_VOL, PWR, VNT

The regression equation is
HT = 18.7 + 1.35 DRV_DIAM + 1.11 BOX_VOL + 0.00453 PWR + 4.28 VNT

Predictor Coef SE Coef T P
Constant 18.711 4.806 3.89 0.001
DRV_DIAM 1.3467 0.3842 3.51 0.002
BOX_VOL 1.1144 0.4262 2.61 0.015
PWR 0.004526 0.001048 4.32 0.000
VNT 4.277 1.909 2.24 0.035

S = 2.781 R-Sq = 87.3% R-Sq(adj) = 85.2%

The increase in r-squared by adding variables is starting to diminish. However, the model can now explain 85.2% of the variation in scores, which is huge! Now, the number of drivers will be included.

Regression Analysis: HT versus DRV_DIAM, BOX_VOL, PWR, VNT, DRVRS

The regression equation is
HT = 26.2 + 0.897 DRV_DIAM + 1.94 BOX_VOL + 0.00628 PWR + 4.52 VNT - 5.59 DRVRS

Predictor Coef SE Coef T P
Constant 26.202 5.119 5.12 0.000
DRV_DIAM 0.8970 0.3816 2.35 0.028
BOX_VOL 1.9380 0.4889 3.96 0.001
PWR 0.006276 0.001141 5.50 0.000
VNT 4.522 1.705 2.65 0.014
DRVRS -5.593 2.089 -2.68 0.013

S = 2.480 R-Sq = 90.3% R-Sq(adj) = 88.2%

The coefficient on DRVRS is negative. This suggests that after the other four variables are controlled for, increasing the number of drivers has a negative effect on score. This result is the first counterintuitive result thus far and suggests that there may be too few datapoints to estimate this last parameter properly. This result suggests the limits of the predictive model have been reached in this data.

The last remaining variable is the dummy variable for extreme excursion subwoofers. Removing DRVRS and substituting HI_XMAX gives the following:

Regression Analysis: HT versus DRV_DIAM, BOX_VOL, PWR, VNT, HI_XMAX

The regression equation is
HT = 22.7 + 1.02 DRV_DIAM + 1.24 BOX_VOL + 0.00476 PWR + 2.83 VNT
+ 7.09 HI_XMAX

Predictor Coef SE Coef T P
Constant 22.736 2.924 7.77 0.000
DRV_DIAM 1.0182 0.2340 4.35 0.000
BOX_VOL 1.2420 0.2545 4.88 0.000
PWR 0.0047566 0.0006248 7.61 0.000
VNT 2.834 1.157 2.45 0.022
HI_XMAX 7.091 1.061 6.69 0.000

S = 1.656 R-Sq = 95.7% R-Sq(adj) = 94.7%

By explaining 94.7% of the variation, the model is essentially a perfect predictor of subwoofer HT score!
post #4 of 244
You are an advanced member for sure
post #5 of 244
Wow...
post #6 of 244
lol @ that

when I'm bored, I just search for pr0n...
post #7 of 244
I go to joox
post #8 of 244
normally, I would say: "you need a hobby"
post #9 of 244
I am more advanced than LTD. A later model.

--Regards,
post #10 of 244
Will you try to validate this on future craigsub ratings? Mind you, the change in his testing panel may confound the model. May be he should post how many alcohol beverages were consumed during the testing.
post #11 of 244
Quote:
Originally Posted by NewOrlnsDukie View Post

lol @ that

when I'm bored, I just search for pr0n...


hilarious
post #12 of 244
You did this because you were bored?

I pop some popcorn and watch a movie. lol
post #13 of 244
I did the same study a few weeks ago during the intermission of 2001: A Space Odyssey Blu-Ray with similar results.

I just never posted it. :-)

Splotto
post #14 of 244
I thought I left statistics like this behind when I finished graduate school...you're making my head hurt.
post #15 of 244
LTD,

What equipment do you have and did you do any such analysis before buying them?
post #16 of 244
LTD02,

Good post,however it will simply cause mass confusion in many.
post #17 of 244
yea. what he said.
post #18 of 244
LTD02,

This is pretty great, thanks for doing this.

If I'm reading the scores right, the objectivity variable COI has a p-value of ~.77, making it a completely insignificant variable. So even the small coefficient in the model appears to be due to chance. You already cleared craigsub based on the small coefficient, but I'd also mention the fact that the result isn't significant.

One other question: did you try regressing against radiating area, or volume displaced, instead of driver diameter? It looks like you started to with the composite DxD2, and I guess you dropped that after the first pass when diameter did better, but what about just using, say, the area of a single driver? I'd expect a more linear relationship with that.

Anyway, these aren't criticisms; I really enjoyed reading this.
post #19 of 244
Quote:
Originally Posted by SpectralD View Post


One other question: did you try regressing against radiating area, or volume displaced, instead of driver diameter?

That's a good question. The problem would be finding that data. How would you be able get displacement info or x-max info on all these subs?

Another interesting thought to pursue would be to figure out what makes the PB13 and the Castle perform outside the predictor model.
post #20 of 244
sooooo...what is craigsub?
post #21 of 244
I hope you did this at work I can't imagine doing something like this when you could have been listening to your system, searching for your next upgrade, or, of course, searching for pron
post #22 of 244
Couple comments:

Including max excursion into the equation would be a good idea. Driver size/area is only part of the [volume of] air movement formula.

Additional caveat: Analysis assumes no eq, that both the amplifiers and sub woofers are of equal quality, and the box designs are optimized for the driver.
post #23 of 244
Quote:
Originally Posted by veris View Post

and the box designs are optimized for the driver.

Isn't that a safe assumption? Since they are all commercially available subs why wouldn't a manufacturer make the box they want you to listen to
post #24 of 244
I've read that excursion doesn't really have as much significance as most people give it. Something along the lines that high excursion is only utilized in the lowest of frequencies where it does make a major impact.
post #25 of 244
Very entertaining and interesting read.

It would have been nice to validate this model prospectively... It's too bad Craig is shutting down his testing.
post #26 of 244
Quote:
Originally Posted by Chris Schempp View Post

Isn't that a safe assumption? Since they are all commercially available subs why wouldn't a manufacturer make the box they want you to listen to

Sounds logical, Chris, and I'll bet it's what you guys do but I'd also bet that often compromises are made for the sake of coming up with a more compact or sellable package. In case you haven't noticed, not all commercially available subs sound very good.
post #27 of 244
Quote:
Originally Posted by mojomike View Post

Sounds logical, Chris, and I'll bet it's what you guys do but I'd also bet that often compromises are made for the sake of coming up with a more compact or sellable package. In case you haven't noticed, not all commercially available subs sound very good.

LOL...I will concede to that point. The A5-350 could be a bit better in a slightly larger enclosure, but it wouldn't ship FedEx anymore.
post #28 of 244
Quote:
Originally Posted by CADOBHuK View Post

I've read that excursion doesn't really have as much significance as most people give it. Something along the lines that high excursion is only utilized in the lowest of frequencies where it does make a major impact.

Depending on the overall design, excursion can be as important as driver size. Take for example the JL f113. It would be impossible for it to do what it does without it's enormous excursion capability.
post #29 of 244
Quote:
Originally Posted by Chris Schempp View Post

Isn't that a safe assumption? Since they are all commercially available subs why wouldn't a manufacturer make the box they want you to listen to

re: "box designs are optimized for the driver."


Certainly the safest assumption, but an assumption none the less. As with most real world situations I expect there are often "minor" compromises for build efficiency, cost, or shipping.

The assumption also extends to rigidity/bracing of the cabinets. I'm not a cabinet maker, but I'm fairly certain all cabinets aren't built equally.
post #30 of 244
I just read through the PDF. The only other bit missing is the calculated rankings raw data.

Very nice.

BTW I'm not suggesting you add it unless it is readily available. You've already spend a lot of time on it.
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