# T-Test and F-Test Equality

Six Sigma – iSixSigma Forums Old Forums General T-Test and F-Test Equality

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• #36064

New BB
Participant

This question is for the six sigma experts. Darth and Trev
said to post it as a separate post and I would get an
answer very quickly. How does a simple t-test for two
groups with equal variances equate to the F test?
Assuming there is a statistical relationship then why do
we use an Xbar and S chart instead of an F chart since
both are designed to detect changes in mean location? I
ask this question because I was told that an on-going
cumulative one way analysis of variance could be plotted
on a chart and it would tell me the same thing as an Xbar
and S chart. Help???

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#102879

Darth
Participant

Sorry, never heard of an F chart.  Furthermore, the use of control charts is different than that for Hypothesis Testing.  Not sure who is telling you these things but it sounds strange.  If you have a cited source for this wisdom please share it.  Hopefully, my response to your other post clarified the relationship between the 2 sample t and F tests.

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#102915

Participant

This is the first time I will hear about F- Chart. However, if it exist, then i will be interested in knowing the principle behind it.

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#102960

Sigmordial
Member

You asked: “How does a simple t-test for two groups with equal variances equate to the F test?”
The square of the t-statistic for the 2 group test will equal the F statistic if you ran a 1-Way ANOVA for the same dataset.
Your next question is a bit confusing — are you looking for relationships between the CUSUM and the X-bar & s charts?

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#103024

Jonathon L. Andell
Participant

Unless I misunderstood the question:
A t-test determines whether two means differ, to some level of confidence (usually 95%). An F-test is used to determine whether two variances differ.
When comparing three or more means, a procedure called Analysis of Variance (ANOVA) builds an F-statistic. Too complex to explain briefly, but here’s the “elevator speech” for ANOVA: uses sums of squares and degrees of freedom to compare variance between groups vs. variance within groups, using the F statistic.
Hope this helps.
PS – Never heard of an F chart.

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#103025

Swaggerty
Participant

I’m not sure what the *real* question is, so I’ll answer a different one than has been answered so far:  When do you use a t-Test vs an F-Test (ANOVA) or What’s the difference between the two?
All statistical tests are based on distributions.  The t-Test allows you to use a small number of observations or cases, like 4 or 5 – but you can only test 2 groups.  When the number of cases gets to about 25 to 30, the t-distribution starts to look like the F-distribution.   The ANOVA is a more robust analysis and allows more than 2 groups of data to be analyzed at a time.   So, specific tools for specific situations.  The t-Test and ANOVA will yield identical results when there are two groups, and the number of cases exceeds about 30.

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#103049

Jamie
Participant

To answer the question as simple as possible…”How does a simple t-test for two groups with equal variances equate to the F test?”
They are equivelent to each other. Try a sample dataset and you will see you get the exact same P-value. Though ANOVA will allow you to test the differences between 2 or more group means where 2 sample t-test is limited to only 2 groups.
Jamie

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#103054

Reigle Stewart
Participant

New BB: What Jamie says is so true, but often
overlooked by many practitioners. Given the statistical
relationship between the t-test, F-test and ANOVA, one
can easily and confidently conclude that any given
difference between two or means can be mathematically
equated to a ratio of the variances. In short, a mean shift
can be calibrated to an expansion of the standard
deviation. This relation is exploited in Six Sigma work,
specifically related to the “Six Sigma Model.” For
example, if we set Cpk = Pp, then we algebraically
determine that k = 1  (1 / c), where c = S.lt / S.st and S.lt
is the long-term standard deviation and S.st is the short-
term standard deviation. By some more simple algebra, it
can be demonstrated that the equation k = 1  (1 / c) can
be further reduced to Z.shift = Z.st  Z.lt. So, for the Six
Sigma model, we observe that Z.shift = Z.st  Z.lt. = 6.0 –
4.5. = 1.5. Remember, this is a “model” and not an
absolute. Regards, Reigle Stewart

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#103070

Darth
Participant

Hey Reigle, nice pitch for the old 1.5 shift again.  But, the original question was whether he can create an “F chart”, that is, a “control chart” of F values to pick up a shift in the mean in lieu of an Xbar/s/r chart.  NewBB hasn’t gotten back yet how he would propose to do such a thing or the statistical foundation for doing it instead of using a more classical Shewhart approach.  He initially asked about the difference between the 2 sample t-test and ANOVA and whether the F value in Anova was equivalent to the t value.  We have already established that they are related for a 2 sample test.  I am puzzled how and why he proposes to use the F value and some sort of CI to approximate a control chart for means.

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#103072

Sigmordial
Member

george wrote: “When the number of cases gets to about 25 to 30, the t-distribution starts to look like the F-distribution.”
Though this does sound rather statistical, it is not true.  There is a relationship between the t and F distributions, but this is not it.
george, if interested in learning more about distributions and their relationships, there is a book titled Statistical Distributions. JASA and JQT provides favorable reviews.

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#103075

Mikel
Member

Here we go again – what BS

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#103076

Darth
Participant

Hey Sigy, if I recall correctly, the t distribution will be normal in appearance and the f distribution will be skewed in appearance so they don’t “look alike” do they? although, as you explained there is a relationship.

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#103077

Darth
Participant

Hey Stan, I assume u were referring to the post I responded to and not mine.  Give the guy a break…he is warming up for the big talk-off and found someone who hadn’t participated in the previous discussions about the “you know what”.

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#103078

why, oh, why?
Member

Stan and Darth, since you mentioned the ‘big talk off’ on July 29th , do you {Stan} have a second just in case of a last minute groin injury, or something more spectacular?
Do you suppose that master of the magic wand, the king of conjure, the one and only Praveen G. may be available to assist in the event of misfortune? Afterall, the show must go on…..

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#103079

Mikel
Member

Of course I was not talking about you. I don’t do that (not on this forum anyway). ;-)
Actually someone commended him for giving real advice (although it was very poor advice based on ignorance) and he has gone back to Mikel worship and quoting verse and chapter from the book of Mikel.
The boy obviously doesn’t have a mind of his own.

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#103080

Mikel
Member

Paper submitted and no response for weeks now. The whole thing is a sham.
I do have a list of technical errors in the book, I wonder if they even know what they are.

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#103095

Reigle Stewart
Participant

Stan: As of today, Mr. Jeff Goss or Dr. Montgomery at
ASU has NOT received any type of white paper or
communication from you. Their e-mail addresses have
been posted several times for your convienence. The
stage is set, the parties are ready, the referees await your
position paper. Respectfully, Reigle Stewart

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#103160

Reigle Stewart
Participant

Stan: To reconfirm the status of your paper, I contacted
ASU today and nobody including Jeff Goss or Dr.
Montgomery have received a white paper from you, nor
have they had any communication with you concerning
business on July 15, 2004. If you really did send the
paper, then immediately respond to me with the person’s
name and address. Perhaps we can track in down
through this person. Recall that I previously posted that
your paper must be sent to the e-mail address of Mr. Jeff
Goss or Dr. Montgomery. Since you stated the paper has
been completed, I recommend that you re-send it today
(to either of these two gentlemen). I look forward to your
reply on this issue. Respectfully, Reigle Stewart

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#103164

debate tension builds…
Participant

Dun Da Dun Dun Dunnn,…. …

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#103166

Darth
Participant

Dumb, Da Dumb Dumb Dumbbbbbb might be more appropriate :-).

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#103168

debate tension builds…
Participant

a good response on many levels

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#103175

Reigle Stewart
Participant

Stan: I know you like to be a little controversial and that is
OK by me … to each his own, and rightfully so. However,
some have invested a fair amount work (and personal
expense) to put this debate together. Various key people
have organized their calendars to make their contribution
possible. These individuals (and myself) would greatly
appreciate some cooperation and information from you.
As you previously indicated, your white paper was
completed and sent to ASU (per one of your recent posts).
As of this afternoon, there is still no paper present at ASU
and no communication with ASU. People are beginning
motives). Without any form of judgment, we kindly ask if it
is still your intent to: a) submit a white paper on the
defined topic and b) attend the debate. Please, lets
practice some basic professional courtesies. If you do not
intend to provide a white paper and participate in the
debate, then please, say so now. There is no point in
being disruptive to others time and resources. Thank you
for your immediate post concerning this issue. Reigle
Stewart

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#103177

Shakespear’s Descendent
Member

“All the world’s a stage and each one of us are actors..”, My kudos to Dr. Harry on this brilliant piece of scripted Salesmanship.

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#103178

dismayed
Participant

I hope you are not suggesting hidden agendas, ulterior motives, and thinly veiled attempts at crass commercialism are at play here.   If so, I am shocked, disappointed, and utterly dismayed.  What happened to science based intellectual inquiry?   Is this to be a debate on the technical merits of the 1.5 sigma shift or exploitation?

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#111755

Darth
Participant

There is nothing like a little retro now and then.  Let’s dredge this one up if we are hard up for new threads.

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#111758

Mikel
Member

Ha! I knew it all along. Darth and Reigle are the same person.

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#111761

Darth
Participant

Well, that would end the debate that I am really one of the Stans.  Regards to the little Stans, Helga and the Killer Dog.
Wasn’t Mr. Berlin a real putz today????  There goes our UM/UF bet.

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#111787

Mikel
Member

Berlin was always a putz. Grossman has already been making millions for two years warming a bench and Berlin is still trying to prove he was the better quarterback coming out of high school. I wonder if a DFSS project on pricing would help him?

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#111794

Darth
Participant

Should be fun at the Peach Bowl when he is playing in front of his former classmates.  Congrats on your new coach.  His record is impressive.  Possibly next year you might actually win a beat with me.

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#111795

Mikel
Member

No, they will fire him next year for only going 10 – 1 when he loses to Vanderbilt.

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