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Two Sample T or One Way Analysis of Variance

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  • #29487

    Nwajei
    Participant

    What is the difference between the two tests?
    We have the following levels of details:
    Time1:  20 Seconds
    Time2:  30 Seconds
    Time3: 40 Seconds
    The above items are the components of the total time per call:  90 Seconds
    We want to determine if 1 person who works a phone call is different from the next person.  Should I compare the total time of the calls or the components fo the call?  Which test should I use?

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    #75646

    Monte Bainter
    Participant

    Which are you interested in? – probably total call time, so use that data.  Collect several measurements of total call time of Person 1 and several measurements of total call time of Person 2.  Then compare the two samples using T and F tests.  ANOVA by conversation subparts will alarm is any cell seems different from the “norm” established by all the cells;  so if a part of the call typically takes less time than another, that part would be indicated as “different” and the ANOVA would fail.  You probably want to establish “control limits” characterizing your group of call handlers (as though setting up a control chart).  Then you could chart each individual compared to those control limits.  Call handlers falling outside those limits would be recognizable as significantly outperforming or underperforming when compared to the group.  HOWEVER, I strongly encourage you to read Deming, Pgs 70-75;  there is likely more at stake than the length of the call, particularly if these calls involve your customers.  Apply statistics to people wisely;  they are not machines.

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    #75649

    RR Kunes
    Member

    If you have only two groups you use the t-test. It is a form of the ANOVA.
    More germaine to your request is what are you trying to compare? In a call center you have various components of a call, you also have various types of calls. So to assure your comparison is usable you must first baseline the type of call. I would suggest scripting a call and calling the various call reps to obtain your data.
     

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    #75650

    Gabriel
    Participant

    RR:
    Correct me if I am wrong. But t-test is not a form of the ANOVA.
    t-test is averages comparison.
    ANOVA = ANalysis Of VAriance, i.e. variances comparison, i.e. F-test.
    F-test and t-test are two different ways of yipotesis testing.

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    #75654

    James Shortt
    Participant

    ANOVA uses variance to test means (it does not test variance). The 2 sample t-test is a simplified case of ANOVA with only 2 groups. I don’t think there is any difference between the 2 tests (assuming equal variances within groups). Consider the following data sets…
    y1, y210, 79, 812, 1111, 913, 79, 1011, 88, 912, 614, 10
    Y1 and Y2 are both reasonably normal (ie they pass Anderson-Darling test for normality and the histograms appear normal considering only 10 data points). They are have similar variances. (i.e. Bartlett’s test of equal variance does not show a difference). So we can either run an ANOVA or 2 sample t-test. If we do we get a p value of .007 regardless of whether we run ANOVA or 2 sample t. Try it.
    Jamie
     

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    #75655

    James Shortt
    Participant

    The data sets posted strange. Let me repost them….
    y1=10,9,12,11,13,9,11,8,12,14
    y2=7,8,11,9,7,10,8,9,6,10
    Hope this is easier to read.
    Jamie
     

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    #75656

    Ropp
    Participant

    Gabriel –
    I’m afraid both you and RR are somewhat misstating the case.
    Both a t-test and the ANOVA technique test for equality of means. They are not anything alike other thsn both test means.
    The t-test is used when only two groups exist. It tests the differences between the means (or paired observations in the case of a paired t-test) to a reference distribution i.e. the Student’s “t” distribution with the correct degrees of freedom.
    If we try to do multiple sequential t-tests on more than two groups, the alpha risk is inflated.
    That is why we use ANOVA which has a single alpha risk for any number of comparisons.
    The ANOVA as one author; Tom Barker,somewhat tougue in cheek has said, should properly be named ANOMEBUSVA as acronym for ANalysis Of MEans By USing VAriances. But it would be impossible to say.
    The ANOVA does not say that the groups in question have unequal variances. Although it is usually assumed that they do have the same variance to reduce the alpha risk, the technique is not really very sensative to this requirement.
    ANOVA tests wheter the overall or between groups variation exceeds what would be expected by the within group variances summed. The conclusion if it does is that the means are the source of the difference.
    The “F” ratio used as the test statistic in ANOVA does test the equality of variance of the between to the within factors, not the factor to factor variance.
    The “F” ratio test itself tests variances of two groups, nothing else. It is not a test of means in any way.
    Hope that helps.

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    #75657

    Gabriel
    Participant

    Dave:
    Yes, it helped. I was wrong and now I now I was. Thanks.
    Gabriel

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    #75661

    Ex MBB
    Participant

    There is an interesting relationship between the t and F statistics for this scenario and this scenario only (2 sample t-test and 1-way ANOVA).  The square of the t-statistic is equal to the F-statistic. 
    I have attached the Minitab output for the data from James Short.  The t-statistics is 3.06 and the F-statistic is 9.36.  Neat stuff…
    MINITAB Output:
    Two-Sample T-Test and CI: first, second
     
    Two-sample T for first vs second
    N Mean StDev SE Mean
    first 10 10.90 1.91 0.60
    second 10 8.50 1.58 0.50
    Difference = mu first – mu second
    Estimate for difference: 2.400
    95% CI for difference: (0.745, 4.055)
    T-Test of difference = 0 (vs not =): T-Value = 3.06 P-Value = 0.007 DF = 17
     
    One-way ANOVA: first, second
    Analysis of Variance
    Source DF SS MS F P
    Factor 1 28.80 28.80 9.36 0.007
    Error 18 55.40 3.08
    Total 19 84.20
     

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    #75662

    Jay Fleischmann
    Participant

    one way ANOVA is a 2 sample t-test with more than two sets of data.2 sample t test null hypothesis:  u1 = u2 one way ANOVA null hypothesis:  u1=u2=u3=un

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    #75684

    Robert Butler
    Participant

    Actually, the point made concerning the relationship between the t and the F statistic goes much deeper.
     “The distribution of a unit normal deviate to the square root of an independent Chi square with f degrees of freedom, divided by f, is the t distribution with f degrees of freedom.  The ratio of Chi square(f)/f tends to 1 as f tends to infinity. Thus the t distribution with infinite degrees of freedom is identical with the standardized normal distribution.
      The t distribution is related to the F distribution because if we made the degrees of freedom =1 for the numerator of the F test we will have
    F(1,f2)  = t**2(f2)
      For example F.95(1,12) = 4.75 = 2.179**2 = [t.975(12)]**2″
      The above is from Brownlee, 2nd Edition pp.289=290.

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    #75712

    Mike Carnell
    Participant

    Frank,
    When I look at the way you structured the question I am assuming that the 20/30/40 are the break up of a 90 second phone call. It seems that it is really just a multi level Pareto. If you want to take a first cut you check for total time. If you are trying to understand why one gets different results then the analysis needs to be at the 20/30/40 breakdown level.
    It would seem there should be more to the question than just time. We had a guy working a call center that had a time per call metric. The consultant that was on the job saw a guy take a call and spent about 3 times longer on the call than he was allowed but he did resolve the customers issue. When he hung up the consultant asked if he would be in trouble. The guy just connected a call and then dropped it in just seconds. His average time per call came back in spec and there was one satisfied customer and one angry customer. In that case analyzing the variance would flag that type of behavior or something like a time series analysis might show the long call folled by a short call behavior. The real issue is whethter or not time per call is the correct metric? Where is the secondary metric that measures the quality of the call? I understand when you have call center activity that managing time per call has a large effect on staffing but the purpose of the center is to deliver service.
    Just a quick note on your analysis method. You got a very good answer in the string that talked about the effect on the alpha error if you use multiple t tests. You should also stay very aware of your sample size. Both methods, t tests and ANOVA, are affected by the sample size. You really need to make sure you understand the sensitivity of your test.
    You should also understand what is going on with the distribution (normal or not normal) because it could be that testing medians is a better test. You also need to analyze the variace – if you are doing t tests you need to select the correct formula and the effect of unequal variances on ANOVA.
    Good luck.

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    #75744

    Baker
    Participant

    When you say “read Deming, pgs 70-75”, what book of Deming’s is that ?

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    #75757

    Monte Bainter
    Participant

    Deming, “Out Of the Crisis” Pgs. 70-75

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    #75795

    Savage
    Participant

    As Mike Said you got a lot of good feedback. But don’t run before you can walk. Normality was mentioned in the message thread but maybe not made as clear as it should have been.
    Before performing your analysis first check for NORMALITY (Aderson-Darling)as the t-test will be affected if you are using non-normal data.
    The anova method is more robust to non-normal data.

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    #75799

    Chris Seider
    Participant

    Jamie,
    I agree with your clarification except I believe one further point of discussion is warranted.  Because the ANOVA is an analysis of means and if the numbers you posted are means of samples, the Central Limit Theorem allows you to assume normality to use an ANOVA.  However, for the t-tests, the analysis requires you to determine with Bartlett’s test (after confirming normality assumption with Anderson-Darling or other) whether the variances are equal.

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    #75800

    Mike Carnell
    Participant

    Matt,
    Good point. I hope people are paying attention to your comment because that is really what the SS methodology is. No new tools. Just understanding you need to understand if you have equal variances before you select the formula you will use for the t test. Understanding you need to know about normality before you select the Bartletts or Levines test.
    It is about understanding the flow from one tool to another.
    Thanks.

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    #75838

    Carl
    Participant

    Two sample T could be used to determine if any two operators have “different” mean call lengths.  This test does require relatively normal data from each operator.
    ANOVA could be used to determine if any two or more out of 3+ operators have “different” mean call lengths.  Again, this test requires normal data from each operator and similar variance between groups.
    If you are just starting data collection, consider doing some graphical comparisons first, before jumping right into Hypothesis testing.  Comparing dotplots or histograms by Operator may show you obvious differences in means and/or variation in call lengths.  It will also show you how normal/bell shaped the histograms are.
    If it turns out that your data by operator are not all normal, but have “similar” variation, consider running non parametric medians tests for Hypothesis testing.  Times data with zero at lower bound are often not normal. 
     
     
     
     

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    #75839

    Tom Pyzdek
    Participant

    I just finished reading this thread and I find it disturbing. The original message posed a very simple, straightforward statistical question. Two people in the thread (Ex-MBB and Robert Butler) presented the correct answer to this question. A few others raised important technical issues regarding testing of underlying assumptions of the two tests.) Others emphasized the importance of understanding the process and making sure that the correct question was being asked.
    So far, so good. My issue is that the remaining people in the thread don’t understand the basic statistical theory that underlie these two commonly used, basic techniques. In the paper “Six Sigma Black Belts: What Do They Need to Know?” (JQT, October 2001, 391), Roger Hoerl talks about the fact that Six Sigma BB training de-emphasises theory and focuses on “practical applications.” This discussion illustrates the problem with that approach. Ex-MBB and Robert Butler seem to be the only two that understood the theory, but subsequent posts ignored what they said. I suspect it’s because, as Deming so often said, without theory there can be no learning. People simply ignore what they don’t understand.
    I don’t mean to start trouble or to insult anyone, but I suggest that if you’re a Black Belt with a theoretical question like this one, seek the help of a qualified MBB or statistician. Posting your question on a forum or asking peers whose only training is an off-the-rack BB course is asking the blind to lead the blind.
    Tom

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    #75841

    Mike Carnell
    Participant

    Tom,
    I’m not sure what you found particularly disturbing. I think your first assumption that it is a straight forward statistical question is part of your issue. If you will look at the last 1 or 2 sentences in the original post you will see that it may have opened up some areas in some peoples minds – mine in particular. If in fact as the original post suggests that there is a comparison being made in this call center type operation then there should be more to the analysis than means.
    If you have followed some of the other threads where we have discussed to risks associated with commenting on advice without having intimate knowledge of the problem. It is always a risk and the majority seem to have felt that the onus for sorting it out belonged to person doing the post.

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    #75842

    Monte Bainter
    Participant

    Recognizing that I’m not perfect, I re-read the original question and my response.  It provides an on-the-nose/dead-on correct answer to the question posed at the bottom of the original message, and then goes on to provide factors that must be considered (given my best possible interpretation of a simple question confounded by presentation that included time breakouts without explanation) in order for the poster to fully evaluate his application.  How might I have re-phrased my answer so that you could recognize its accuracy?

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    #75861

    Anonymous
    Participant

    [Message removed by administrator for spam violations.]

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    #75864

    Tom Pyzdek
    Participant

    Mike,
      As I said, I have no problem with any of the posts that address the importance of understanding the process and making sure that the correct questions are being asked. This is essential to answering any “statistical question.” The issues raised by your post are right on the money.
    Tom

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    #75865

    Tom Pyzdek
    Participant

    This message was posted by someone using my name. Have any of you had this experience? I rarely post anywhere, so I’m not sure how to deal with it or to prevent it from happening in the future. Any suggestions?
     Tom

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    #75866

    Mike Carnell
    Participant

    Tom,
    I was involved in a conversation with Annonymous one evening when all of a sudden Annonymous logged on and warned me that there were two annonymouses in the string.
    I get into an exchange from time to time with another person called Stanley. There are two distincly different styles depending on the topic. When Greg Brue is mentioned it triggers someone who a couple of us believe we have identified.
    It is a problem and until recently I didn’t really appreciate the need for some to have anonymity.
    Kind of a difficult situation.

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    #75867

    iSixSigma Community
    Participant

    Tom,
    An email message was sent to the email address on file. Please respond to it from that email address and we will remove the spam forum posting ASAP. We apologize for the inconvenience.
    Thank you,
    iSixSigma Community

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    #75874

    Jack Welch
    Participant

    I hope you all know when I reply to threads I’m not the real Jack Welch.  I never want to infer another person’s opinion. 
    Thanks,
    Jack Welch

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    #75880

    Murray
    Participant

    Tom,
    Get real. If the level of knowledge on this site is an indicator of knowledge of the 6 sigma community, we are in trouble. The questions are basic and we have a low level manager from Motorola, Mike Carnell, out here pretending to be the fountain of knowledge and getting away with it.
    Go worry about something that matters, like getting a good certification standard in place. ASQ’s is a joke.

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    #75883

    Cannizzo
    Participant

    Allen,
    If your attitude is any indicator of the quality organization of your organization or that in America, we are all in trouble.
    It’s much easier to tear down than it is to build up. At least Mike Carnell and others are building something by helping others on this site. What have you done lately besides tear down this site, this forum, and other peoples’ thirst for knowledge?
    What are you doing to help get a “good certification standard in place” — and why does that even matter over everything else? Are you a member of ASQ? Do you actively do something besides throw your monthly Quality Progress on the desk pile?
    Think about the repurcussions before you type. Let’s try to be constructive rather than destructive.
    Carol

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    #75888

    Mike Carnell
    Participant

    Really?

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    #75890

    Mike Carnell
    Participant

    Allen,
    Seems like the anger management classes aren’t working.
    I offer up my opinion. There are no obligations on anyones part to take my advice.
    As far as my Motorola background. It had nothing to do with the management position. I was fortunate enough to work with a lot of really talented people at Motorola. Names that have become fairly well known in the SS community. We did some good stuff. If that bothers you it is your problem not mine.
    The comment about the level of knowledge in the SS community was pretty crass. It is a place where a lot of people show up to ask questions and get a wide variety of answers. Since you classified them as “Basic” and that is a little judgemental as a back handed attempt of seld agrandization, I will assume you are probably rat holed in some job that isn’t equal to the level that you intelligence demands. If you are a little frustrated with your lot in life, you probably need to realize that the cause is you.
    As far as Tom’s contribution. Like any other author he has laid himself out publicly for what he believes in his book. That takes a certain amount of commitment and conviction. And the title to your book is….? Actually we will settle for anything positive you have to offer?
    If you want to take this off line my email is @aol.com">SixSigmaAp@aol.com. Just so Stanley doesn’t get all tense it is an offer to discuss things on email not an attempt at intimidation.

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    #75891

    James A
    Participant

    Carol,
    I’ve only just caught up with this thread’s latest developments, and it’s not often I really wish I’d said something already stated by someone else.  But I this time I do.  Thank you.
    James A

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    #75892

    Smithsigma
    Member

    I also have a confession to make…my name isn’t REALLY Smithsigma.

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    #75895

    Leung
    Participant

    Carol — if someone offers you a gift and you do not accept it, to whom does the gift belong?
    Ben

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    #75896

    Cannizzo
    Participant

    Ben,
    Point well taken. I just hate to see others discouraged by someone bearing false gifts. In my family we learned to stick up for others when we thought it was justified. Old habits are hard to break.
    Carol

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    #75898

    Terry
    Member

    OK let’s all take a deep breath and chill out.
    Ever wonder why Six Sigma and Change is so difficult?  Here’s my take on this thread:
    1.   First, we have allowed the process to take the place of the original problem and lose focus on the basics.  Read the origninal problem, then read the responses, especially the last 25% of them – It’s like that “whisper game” we all played in grammar school. 
    2.  This is another good example of a tool looking for a problem. Let’s be honest, are we ready to use a statistical tool when we really do not understand the process i.e., the details (other than time) between these people.  Is time the best measure of performance?  Are we just trying to apply a tool so we can get our manditory Six Sigma project done? 
    3.  75% of the discussions in this thread are totally irrelevant (especially the personal slams) to the original problem.  We have allowed those damn emotions and egos to slip in ! 
    Now what was the real problem and the facts again?.  I forgot after reading all of these responses.  No wonder we can’t get this Six Sigma stuff to stick !
    Terry

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    #75899

    Jack Welch
    Participant

    Well said….there is a lot to be learned in these threads.  The normally intelligent (is that how you spell it?)  people take what value they can from different postings.  Some people don’t ever read mine because most times they are usless. But thats the beauty of having a head on your shoulders; you can make and choose thoughts you believe in and know a reasonable reply from one of mine or one of the other idiots who post here.  Without a little humor and diversion even 6S would be boring as hell! 
    Did i say that?
    Jack Welch..not the real one again!

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    #75904

    Michael Ervick
    Participant

    Frank,
    One more opinion to consider.  As a consultant, I would tend to begin to answer your question by asking  more questions. 
    For example: Why is this information important to you?  What kind of a decision will this information help you make?  How will that decision impact the quality of service to the customer?
    I try to avoid collecting and analyzing data that adds no value, simply because it defeats the underlying purposes of Six Sigma and Process Improvement.
    Michael

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    #75906

    Terry
    Member

    Good points Mike.  You said what I tried to say, only better.  We’re not ready for the analysis yet because we do not fully understand the problem, the process, baseline performance, and causals.  They skipped the DM in DMAIC.  Ahhh . . . The statistical tools are more glamorous than the basics anyway, right? 
    Terry

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    #75909

    Sambuddha
    Member

    I believe we cannot afford to keep our sense of judgement or humor locked up somewhere and participate in discussions as these. Every participant in this forum have background, tastes, priorities, roles that are different. Then why expect consistent output.
    With respect to information sharing, I agree with Tom, we need to be responsible enough to share the information that we know are correct to the best of our knowledge and leave the rest to those who know about stuff we do not know.
    There is no shame in not knowing. I know some, and do not know a lot. Inspite of the fact that the information disseminated here ranges from accurate facts to unverified conjectures, I believe I have learnt many new concepts, and new twists on old concepts. Haven’t we all?
    And when Jack (Welch) says some thing “straight from the gut”, I take it for the value he tries to provide….namely a respite from dry discussions. We have a choice there….to ignore those posts if we want.
    I also do not care where anyone came from….. as long as that person enhances my knowledge base, it can only be my own complex that would prevent me from acknowledging with gratitude the kind act of sharing information with all of us. Regarding fountain of knowledge….does it exists? Do we remember what Einstein had said….”collecting pebbles on the beach”.
    Let us not forget that!
    Best,
    Sambuddha

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    #75919

    JP Rothery
    Participant

    Allen why do you pick on Mike Carnell.
    Whenever I see a response from Mike I read it first and read the rest of the threads and then re-read Mikes. I have learned a lot from Mike and the other good contributors in this forum.
    As I have said before this forum is a great knowledge base.
    If you think the knowledge level is low why bother wasting your time browsing the forum. 
    Regards
    JP Rothery

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    #75926

    Mike Carnell
    Participant

    JP,
    Thanks for the help. I agree with you on the input to the forum.
    My preference has always been to do site support and when you are in a one on one with someone it can really truncate the way you see things. When you read a lot of these threads it gives you a lot of different options that might not have ever come up in a one on one situation.
    In one of the threads a few months ago someone made the remark that it was a safe place to ask stupid questions. That in itsself makes it valuable.
     

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    #75945

    Murray
    Participant

    JP,
    Mike is a real big boy, he can take care of himself. I am intrigued by people who use places like this to reinvent themselves. Mikey is doing just take so I pick on him occassionally. As Mike points out, we all have the right to read or not read, respond or not respond.
    Back to Tom’s comment, what intellectual snobbery! A forum where questions are clearly not well reasoned or thought out and Tom wants us all to be statistically fluent. What is he thinking?

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    #75954

    Mike Carnell
    Participant

    Allen,
    As far as my motivation for being on the site – I am amazed that you know so much about me since I don’t think we have spoken since 98. Talk about arrogance.
    Before you accuse Tom of intellectual snobbery you really need to re-read youpost that started this. Particularly your comment on “the level of Six Sigma knowledge…” That would be …… yes I believe that would come under the catagory of intellectual snobbery as well.
    Interesting change in tone.

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    #75957

    Mike Carnell
    Participant

    Jack & SmithSigma,
    I am really confused now.

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    #75959

    Jack Welch
    Participant

    I been reading this thread,.,,,,,,,….and think of it, some people call me a Disturbed Person…… Lighten up boys and girls!

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    #75964

    Mike Carnell
    Participant

    Jack,
    There is a little more going on in the background than the general audience is perceiving.

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    #75966

    Jack Welch
    Participant

    Sorry Mike,
    I am sure there are old bridges to build back up, or leave burned down..whatever works for you folks!   Actually, I hold a bridge rebuilding philosophy myself.
     

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    #75968

    Mike Carnell
    Participant

    Jack,
    I am sorry it has been chosen to be played out here. That was why I made the original offer to take it off line. It doesn’t have anything to do with the general population of iSixSigma.
    There are some issues where the ethics run so deep the bridge stays burned.
    Thanks for the support.

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    #76130

    Smithsigma
    Member

    I shouldn’t have made a comment previously…I was just trying to lighten the mood a little.
     

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    #76223

    Mike Carnell
    Participant

    Smith,
    I think most of us appreciate your efforts. Particularly after the way some people took this thread. 
    There are some people who have chosen to masquerade as someone they are not by using other peoples names. This is going to cost us valuable input from people like Tom Pyzdek.
    There are others who potshot and seem to believe they have intimate knowledge of what motivate people. They speak for groups like “authors” when they haven’t written anything, etc. That is causing some of the disruptions like you saw in this thread.
    The iSixSigma Community wants the site to be open without people having to register a name. The down side is there are game players that some just won’t deal with. They are caught in the middle.
    Thanks.
     

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    #76230

    SixSigmaGuy
    Participant

    Here here!
    But, why does “The iSixSigma Community wants the site to be open without people having to register a name”?  What’s wrong with registering a name if you are seriously interested in the discussion topic that you are subscribing to.  Masquerading is bad in my opinion and should not be allowed.
    Although I believe everyone should be registered, I do think we need to allow anonymity as many people on this discussion group work for major corporations that have strict confidentially policies.  But we can have both registration (to prevent abuse) and anonymity (as long as there is not abuse) in my opinion.

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    #76232

    Mike Carnell
    Participant

    I can’t speak fot iSixSigma community but as closely as they monitor the site I am sure they will take note of your suggestion.
    I am not sure if you noticed but when you post these days there is an IP Address (Recorded to prevent abuse) that was not there before. I don’t know what it does but I am sure it connects to something.

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    #76233

    iSixSigma Community
    Participant

    Good spot Mike. We implemented the improved forum functionality this weekend (thanks for volunteering to test-drive it) — part of which is recording the IP address of users who make posts to the forum. This allows us to track users who are abusing the terms and conditions of the site (using other’s names, foul language, posting spam, etc.).
    SixSigmaGuy: Thank you for your suggestion. It’s valued and noted. We are in the beginning process of developing a system that would allow those interested in reserving a name to do so (preventing others from posting under a reserved name). The system would still allow others to post without registering, hopefully creating the best of all worlds.
    iSixSigma Community

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