# B vs C

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• #38922

Chelle
Participant

i have read some references on b vs c study… i have trouble understanding how to interpret its result… what is the criteria or rule that i should follow in interpreting result of a b vs c study…thanks!

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#117232

Mikel
Member

The rules are called Tukey end counts – look it up.

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#117246

Iain Hastings
Participant

Chelle,
A couple of references for applying Tukey’s end count
1) The book “World Class Quality” by Bothe and Bothe.
2) On the web: recently (beginning of March) a poster linked to a Shainin Manual that he had prepared. Attached link should take you to the correct place.
http://www.shainin-manual.nl/english/selectlikelycausesPairedpartscomparisonSlide/index.html

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#117258

Reigle Stewart
Participant

Many years ago, Mr. Dorian Shannin introduced the B vs C test as a methodology to statistically contrast two groups (in much the same vain as the classical t-test).  The primary advantage was the ability to use fewer samples for the experimental condition.  To clarify this notation, we must first understand that C stands for the control condition and B signifies the better condition (or at least what is expected to be better).

At the extreme end of things, the B vs C test allows us to statistically examine an experimental condition with only one sample!  However, the control condition always requires more than one sample.  Also note that many would argue that a balanced condition (equal number of Bs and Cs) is usually superior (for a variety of theoretical reasons).  Nonetheless, some practical applications will not allow for such an ideal balance — like whenever expensive destructive testing is at hand.  Hence, the pragmatic value of the B vs C test as compared to a standard t-test or one-way anova (two group).

To illustrate, let us consider a simple case.  For example, suppose an engineer wanted to test the effect of some coating on the strength of a certain material.  Lets say three samples were randomly selected from the general population of existing parts (standard coating) and tested for strength.  In this fashion, the C group was formed and the resultant dependent variable measurements were properly recorded.

Next, three other parts were randomly selected; however, they were treated with the new coating.  After application of the experimental coating, the strength of all three components was individually assessed and duly recorded.  In this manner, the B group was formed.

At this point in the methodology, all N=6 parts were rank ordered in terms of the dependent variable called strength.  In this case, it was noted that all of the Bs outranked all of the Cs.  Consequently, the engineer accepted the alternate hypothesis (Ha) and concluded that the new coating makes a statistically significant difference in strength.  Why?

Namely because the engineer used 3 parts for the C condition and 3 parts for the B.”  This means there existed 20 possible outcomes (in terms of potential rankings).  Hence, the random chance event of seeing all Bs outrank all of the Cs would be 1 / 20 = .05, or about 5%.  Thus, by selecting C = 3 and B = 2 (for a total of N = 6), the engineer had 100% – 5% = 95% statistical confidence.  But this is only one part of the total problem!  Let us now move on to the less obvious portion of our discussion.

We will now say that the engineer began this exercise by declaring that she must observe a 3 sigma change (or greater) in the universe mean (in terms of strength) if switching over to the new coating was to be justifiably implemented.

To help with this part of the problem, Dorian Shannin set forth a table of KS values, where K symbolizes the number of standard normal deviates ( Z ) and S represents the pooled standard deviation.  For example, his table of KS values shows that for the case of B = 3 and C = 3 (i.e., N = 6) with a Power of 95% (i.e., a beta risk of 5%), then KS = 3.3.  So how did he arrive at these values?  Where did he get K”?

Without a drawn out theoretical explanation, consider the application equation: =(NORMSINV(P^(1/(N-1))))*SQRT(V.B + V.C), where P is the power of test, N is the total sample size, and V is the variance.  To understand how this equation is applied, consider the following inputs.

Bs = 3
Cs = 3
P = .95
V.B = 1.0
V.C = 1.0

Thus, we compute KS =(NORMSINV(.95^(1/(6-1))))*SQRT(2) = 3.28, or 3.3.  This says that for the case of N = 6 and a detection power of 95%, the decision threshold would be a mean difference of 3.3 sigma, but only if all Bs outrank all Cs.  Of course, for a given value of N, the alpha risk will vary depending of the specific number of Bs and Cs.  Note also that the KS value is not dependent upon the total combinations; however, it is dependent upon the total sample size and selected beta risk.

In other words, if all 3 Bs outrank all 3 Cs, then the B vs C test would be capable of detecting a mean difference of at least 3.3 sigma with a detection power of 95%.  So, if N = 6 samples are prepared ( B = 3 and C =3) and the engineer observes that all Bs outrank all of the Cs, then there would exist P = 95% certainty of detecting a 3.3 sigma change if such a magnitude of change was really there to be detected!

Using the equation listed above, you will be able to construct your own table of KS values — beyond those published by Dorian Shannin.

I hope this helps you in your understanding of the B vs C test and resolves some of the mystery around the infamous KS value.

Respectfully,

Reigle Stewart

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#117260

Mikel
Member

Mr. Reigle my friend.
Glad to see you have not changed – a 30 minute answer to a 10 second question.

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#117266

Reigle Stewart
Participant

Mr Stan:
It is most unfortunate that I was not blessed with a spot of simplistic genius or marked by the powers of extraordinary communication.  I humbly aplogize for being somewhat wordy in my explaination of the B vs C test.
Perhaps you could grace us with a definitive 10 second explaination of how to account for beta risk when using the method of end-counts.  Please enlighten us to this knowledge for a selected range of required improvement.
It is always good to hear from such an accomplished practitioner.
Reigle Stewart

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#117269

Mikel
Member

Mr. Reigle,
Good to see you are alive and kicking and asking non relevant questions as a way to divert a discussion. Some things never change.
Any good Mikel quotes for us today?

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#117271

Dayton
Member

Dr. Mikel Harry suddenly contracted the dreaded disease kurtosis. Not only was this disease severely debilitating but he had the most virulent strain called leptokurtosis. A close friend told him his only hope was to see a statistical physician who specialized in this type of disease. The man was very fortunate to locate a specialist but he had to travel 800 miles for an appointment.
After a thorough physical exam, the statistical physician exclaimed, “Sir, you are indeed a lucky person in that the FDA has just approved a new drug called mesokurtimide for your illness. This drug will bulk you up the middle, smooth out your stubby tail, and restore your longer range of functioning. In other words, you will feel “NORMAL” again!”
Vinny
Oopps. you said Dr. Harry quotes and I thought you said Dr. Harry jokes Sorry!

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#117272

Mikel
Member

Just change the doctor’s name to Joe Smuckatelli and it could be a Mikel quote as well.
(that was a good Mikel joke by the way)

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#117273

Savage
Participant

Now that was funny.  Thanks.

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#117289

Markert
Participant

Vinny, you failed to mention that the specialist was located in Paris and on that same trip Dr. H  had made dinner plans involving a famous restaurant that served a delicous rabbit pie. This particular restaurateur had a reputation for being able to obtain rabbits when other gourmet establishments were unable to do so. And this was one such time when there was short supply in the market.
One of Dr. H’s dinner aquaintances, a local Parisian, stopped the restaurateur briefly while he was going table to table greeting his guests, and it just happened that his and Dr. H’s dinner had arrived; each had ordered the house specialty.
Dr. H’s dinner guest asked the restaurateur if there was any truth to the talk that he was stretching the rabbit supply by adding horse meat. The restaurateur paused, and quietly admitted ‘yes, a little.’
‘How much horse meat?’ asked the local to the restaurateur.
‘It’s about 50-50,’ came the response.
Dr. H, statistically evaluating the response of 50-50 and considering the mystery of the 1.5 sigma shift versus the size of the hot, appealing portion in front him, which was rapidly cooling, and analyzing the potential probability of equus caballus content in his dinner, thought for a moment.
Satisfied, he plunged his fork into the pie and began eating, enjoying each forkful whole heartedly.
His dinner aquaintance, a worldly local, thought briefly too, and while the restaurateur was giving instructions to a employee while still at their table, waited to resume the conversation with the restaurateur as Dr. H completed most of this extra-large sized meal entre.
As the restaurateur finished giving instructions to the staff, the local aquaintance reminded the restaurateur of the topic they had been discussing several minutes before.
‘You said, 50-50; what does that mean?’
The restaurateur replied candidly, ‘One rabbit and one horse.’
HI HO Silver!!!!

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#117291

Dayton
Member

Phil,

Not just a statistically significant response on your part but one that has its basis in proportional significance.  Well done.

I look forward at some point to co-hosting a statistically based game show with you.    We could call it Degrees of Freedom and pattern it after the Chuck Barris Gong Show.     I can just see the audience exploding in appreciative frenzy as we unexpectedly run little One and Two-Tailed Tests out on the stage closing with a weekly tribute to a highly contributory dead mathematician.

If youre interested Ill have my people contact your people and setup a power lunch at a Whataburger of your choice.   Whata ya say?
Vinny

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#117294

Markert
Participant

Vinny, and by indirect mention, Stan and Darth,
Teriffic idea. Vern, our oftmentioned storyboard guy, will be awaiting a call from a representative of your organization. But please be advised, Vern is a very emotional guy and prone to fits of excessive emotional behavior. You may remember that when he heard you had responded after last fall’s “never to return post,” he was so excited he spilled soft drinks on our pants and nobody could stand up without being embarassed until it dried.
Unfortunately, our staff has three folks who don’t speak like Teller, of Penn and Teller, and our temps the Town Idiot and the Zoo’s monkey, both of which serve on the JO club nominating committee, can’t communicate well enough to recieve your call, so Vern it must be. I don’t like talk back, and prefer to employ those who lack the power of push-back in our group.
I will be out for a while, having enjoyed two of Burger King’s newest creation, the Big Friggen Omlet breakfast daily since its introduction and at least two-a-day of Hardee’s Super Jumbo \$6, 1500-calorie sandwich, likely made with horse meat, for lunch and dinner.
My absence, not to make light of a bad situation likely utilizes several of the products manufactured by your day-job’s fine medical products organization, and will ultimately result in an implant and a 12volt DieHard battery which I will need to trolley around on my 4-wheel drive Rascal. Lucky none of them contain RFID tags so we won’t need to get rid of the microwave here in HQ.
I believe that the game show idea is a fine one. Perhaps it can be a main stage event area at the proposed “Famous Dead Mathematicians and Statisticians of History — Field of Dreams Amusement Park” discussed a short time ago. Remember, if you build it, they will come.
Perhaps another main stage event can be the Reality Stage in Six Sigma, an offshoot of the idea tested last year. We can have Stan, Darth, Mjones, Carnell, and other contributers lined up to do a project on the spot, using whatever they have on hand. An example:
Stan: Modify this device to make it Single Minute Exchange of Die using this bag of rubber bands, a hammer, and this half of a turkey sandwich. {I’ll bet Helga can do it, but Olde Stan won’t be able to.}
Maybe as a result of success or failure, Stan will be forced to take on a couple of the dead math/stat’s guy mano-a-mano in a ring we set up specifically for the outcome round. This will appeal to the GenX males that only are interested in sports and adult entertainment on cable. Add a couple full-arm tatoo’s on Stan, and he can be a brand new generational icon for these guys, already starved for adult supervision.
Perhaps we can have Darth entertaining in another area with other simularly attired Empire Clad entertainers doing a song and dance number. You know the kind of family entertainment found in Las Vegas. Darth, what kind of singing voice do you have, and can you quickly learn to Moonwalk before Michael Jackson gets carted off to jail?
What do you all think?

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#117297

Darth
Participant

Phil, as usual, a witty well thought out post.  I think you have some great ideas.  Unfortunately, my singing range is soprano or better yet falsetto.  This, as a result, of the really tight black pants and cup I am required to wear while onboard the Death Star.  The accidental kneeing by Babe of  a Sister didn’t help either.  But, I would be glad to handle the family entertainment booth along with the red wine in a Coke can concession.
I believe the Town Idiot and Zoo Monkey may have a new J.O. candidate to nominate.  Please see the brilliant post on Standard Deviation whereby I was called a nasty name by the obviously literary challenged poster.

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#117329

Markert
Participant

Darth:
Missed the events of earlier today. However, the nominating committee indicates that pursuant to article IV, section 8, paragraph 19, line 6 nominees must “show habitual inablity and frequent lack of intellectual capabiltiy in Six Sigma, as well as not having a made-up name.”
Therefore if Yak-el ratchets it up a notch, and keeps at it using an ordinary name, he’s got potential.
Like the idea of the combo of the tight pants and the cup. Think there is some great potential for adding these items to the Six Sigma Forum Spring Catalog. How about the really tight pants and cup/coffee mug for the Six Sigma professional on the go. Fly into a remote plant in the middle of no-where and have all the gear you’ll need for a 72-hour trip. Laptop with spell-check, briefcase, aerodynamic tight Michael Jackson like pants, white socks and Sonny Crocket turned up collar, and your own cup/coffee mug ready to stash/unstash as necessary. Even more helpful if you need to cross union picket lines on your way inside the plant.
Since there was some talk about spooning the other day in Mike J’s court case, perhaps even a line of specialty spoons may be popular. Maybe with cast-profiles of the numerous dead mathematicians and statisticans that Vinny is always noting in his post. Come to think of it, it has been a while since he provided us with a new profile and bio on the 500 year old ‘Masters of Math?’
Perhaps we can also use you to pre-record some of your favorite tunes using that falsetto voice to provide significant “scared straight” reinforcment to our yellow-belts.Another Spring promo item.
“You guy’s better shape up or it’ll be back in the closet listening to Darth sing “Having My Baby” with those headphones, again.” ‘Oh, no not that again. Please give me one more chance?’
Corporate HR departments everywhere will order cases of them to assure high performance in their implementations. In fact, this may be an idea for a turning point for failing implementations……Just a thought.

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#117333

Darth
Participant

Excellent recommendations.  But I caution on the cup/coffee mug.  There are few people who can consume that large a quantity of coffee.  Of course I assume you intended to do a personal casting for the sake of reality.
I apologize for missing the fine print in the J.O. Guide to Membership.  Of course, one stupid posting does not a J.O. make.  But we must do something about the fake poster using the hallowed name of Darth.  Obviously a great worshiper since imitation is the highest form of flattery or flatulance, I can never remember which.  Reposting my post multiple times is not very creative and is not worthy of such a being as Fake Darth.  Shape up Buckeroo.

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#117334

Darth
Participant

Excellent recommendations.  But I caution on the cup/coffee mug.  There are few people who can consume that large a quantity of coffee.  Of course I assume you intended to do a personal casting for the sake of reality.
I apologize for missing the fine print in the J.O. Guide to Membership.  Of course, one stupid posting does not a J.O. make.  But we must do something about the fake poster using the hallowed name of Darth.  Obviously a great worshiper since imitation is the highest form of flattery or flatulance, I can never remember which.  Reposting my post multiple times is not very creative and is not worthy of such a being as Fake Darth.  Shape up Buckeroo.

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