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Calculating z scores

Six Sigma – iSixSigma Forums Old Forums General Calculating z scores

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  • #48572

    Janet
    Participant

    I have a process that is running with a mean of 3 inches and a standard deviation of 1 inch.  If the specification limit is 7 inches, what is the z value?

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    #164280

    Cone
    Participant

    I guess u are asking for the sigma level(z), right? By applying the equation(boundary vlaue = mean + z*standard deviation), the z value = 4
     

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    #164283

    Dr. Scott
    Participant

    Janet,
    What is the sample size that led you to the sample mean of 3 and standard deviation of 1? If you have around 30 observations, then your Z would be around 20. But I assume you don’t have a measure of the entire population, so the T statistic would be more appropriate to use. In either case, the result would be around Z or T = 20. But you need the mean, standard deviation, and sample size to know for sure.
    My guess you running around 3-4 sigma depending on your answers to the questions above.
    Regards,
    Dr. Scott
     
     
     

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    #164293

    New ATI
    Participant

    You  have  to  calculate it  using  the  formula,it  is  simple ,or  you  may  ask  Stevo

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    #164295

    Juran Fan
    Participant

    Dr. Scott,I am looking to replicate the famous experiment from the Juran on
    Quality tapes. He talked of trying different liquors mixed with water to
    find what was making him drunk.What should the sample size be for this?

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    #164303

    Dr. Scott
    Participant

    Hello Juran Fan,
    First you would have to determine whether you are interested in measuring the legal definition of drunk (i.e., .08 BAC), or whether you are interested in measuring the point of impairment using another test (such as field sobriety test). Then there are factors such as amount of alcohol, amount of water, time of consumption, male or female, amount and contents of food, medical conditions such as diabetes, liver size, Blah, blah, blah.
    Bottom line is it takes a 180 lb male to consume around 5.75 ounces of 40% alcohol (on average) within an hour to make that person legally drunk (.08 BAC +/- .01). But the variables I mentioned above do have, or have been suggested to have, an effect on this conclusion. For example, the same amount of alcohol for a 120 female would nearly double the BAC (and still would depend on the other factors involved).
    Using the factors Alcohol (0 or 6 oz), Sex (male or female), and Water (0 or 6 oz), then the sample size would be a total of 16 assuming a std. dev. of .01 in BAC.
    I hope this answer is as useless as your question. In other words, don’t forget something else Juran said: “My job of contributing to the welfare of my fellow man is the great unfinished business.”
    Contribute please,
    Dr. Scott

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    #164305

    Juran Fan
    Participant

    Should I use randomization when setting this up?

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    #164317

    Blessed thy be
    Participant

    “My job of contributing to the welfare of my fellow man is the great unfinished business.” Blessed are the one’s who are totally delusioned about their earthshattering contributions on the isixsigma discussion forum. Dr. Scott, you’re so blessed!

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    #164318

    Ken Feldman
    Participant

    Hey Blessed,
    So, if my goal is to spread a little knowledge, learn a little now and then, have some fun, exchange some thoughts with really smart people, do some offline networking with some really talented professionals and cause some trouble when so inclined, does that make me unblessed?  Might be revealing if some of the more frequent posters shared their thoughts as to why they post on this site.

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    #164322

    Dr. Scott
    Participant

    Juran Fan,
    It is always better to randomize to restrict the possibility of an unidentified (outside) factor unknowingly influencing the results.
    In some cases randomization is not practical (e.g., setup costs, time contracts, new technology installations, etc.).
    Otherwise, yes you should randomize.
    Regards,
    Dr. Scott

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    #164323

    Dr. Scott
    Participant

    Blessed thy be,
    Dr. Juran said it, I only quoted him. So bless him. And, by the way, I do feel blessed. I have received opportunities that 30 years ago I would not have even imagined receiving. But, by the grace of God, I am able to accomplish more than I ever thought I could.
    I truly hope God blesses you in such a way as well.
    Also, please check your grammar and spelling before posting again.
    Dr. Scott

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    #164326

    Dr. Scott
    Participant

    B,
    It is easier to get you to reveal your faults than I originally thought. :-)
    Best of Luck to You,
    Dr. Scott

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    #164327

    Dr. Scott
    Participant

    Darth,
    All I can say is “Right On”! Seems our purpose is the same afterall.
    Cordially,
    Dr. Scott

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    #164328

    Great Scott
    Participant

    “running around 3-4 sigma “
    What sort of rubbish is this ?  Go back to school !!!!

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    #164331

    Dr. Scott
    Participant

    I am your school :-).
    I am starting to enjoy ostensibly knowledgeable people like you. You have nothing to contribute, nothing to discuss, and nothing to deliberate. You only offer insults. That is a very bad flaw. Some would call that psychopath: a mentally ill or unstable person; especially: a person affected with antisocial personality disorder.
     
    I only wish the antisocial part applied to you, so you would stop bringing social issues to this professional forum which would mean you would no longer be here.
     
    Why don’t you tell me what the Z is without historical data? Are you even able to do so, or would you rather continue to be a non-contributor?
    Dr. Scott

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    #164332

    Dr. Scott
    Participant

    Sorry for the delay, if that is what you meant. Seems for some odd reason people normally pay me for my time, so I give more to them. As I see it, you are a waste of my time. And, unfortunately for everyone here or anywhere else, you are waste of their time and money (if you actually earn any) too.
    And, stop changing your name. Be a real person and at least stick to one alias.
    Dr. Scott

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    #164333

    Blessed
    Participant

    z score, t-score … that is such baby stuff that I even wonder why you bother. Every introductory textbook including Wilkipedia has the answer. Do you really think that your rule of thumb of 30 is a great contribution? BTW, I only respond to your silly tirades when you get totally out of control, like in your Juran quote (Juran was the only non-statistician who had to rub into everybody’s face he was one … you’re awfully similar to him). Other than that, I couldn’t care less about your opinions and your “famous” contributions. … and “fruitcake”, “idiot”, and your absolutely out of control ranting about “Jack Daniels” that’s worthy a professional aka “Dr.” aka “consultant” … any other titles you can randomly throw around to make you feel better about yourself? As for my contributions, YOU don’t worry have to worry about them. I find it embarrasing to sign them with “Dr. XYZ” in an environment that is dedicated to professionals who for the most part are still working on their academic education. Have a good night. You really need one to clear your mind :-))))).
    P.S. A “Z” is the last letter of the alphabet in capital letter. If you want to know what the formula for a z-value is (population/sample) and how to use it in its various practical applications, please use the google search function. I’m not your statistics mentor.

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    #164334

    First Impressions
    Participant

    This is my first visit to this sight, and Im dissapointed with what I have read. Is this site proffessional or a chat forum for bagging each other?

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    #164336

    Dr. Scott
    Participant

    Ok Blessed, I will indulge your fantasy to be me one last time. Read my BOLD below in response to your post.
    z score, t-score … that is such baby stuff that I even wonder why you bother.
    Because Z represents a population and T represents a sample. If it so text book, why didn’t you know it? Is it because you can’t read? I can help you with that as well. Sorry for my error in not capitalizing Z and T in the post you referenced.
    Every introductory textbook including Wilkipedia has the answer. Do you really think that your rule of thumb of 30 is a great contribution?
    The rule of 30 isn’t my contribution. I wish I could say it was, but that belongs to others such as Deming, Shewhart, and Juran. But it works. If you had any real experience at all, then you would know that.
    BTW, I only respond to your silly tirades when you get totally out of control, like in your Juran quote (Juran was the only non-statistician who had to rub into everybody’s face he was one … you’re awfully similar to him).
    I will take your comparison to Dr. Juran as a compliment. And yes he was an expert in statistics (learned from Dr. Deming as I did). Would you like to discredit Dr. Deming as well? Juran also recognized the importance of corporate culture or personality in the whole mix of things. Something I don’t think should be dismissed. Deming wasn’t as good at that, especially in public settings.
    Other than that, I couldn’t care less about your opinions
    Please then, if you could care less about my opinions, then stop responding to them.  
    and your “famous” contributions. …
    I have never claimed to be famous, nor have I claimed any of my contributions to be famous. I only know that I am good, and that my techniques are effective.
    and “fruitcake”, “idiot”, and your absolutely out of control ranting about “Jack Daniels”
    Did you do a control chart on my control regarding ranting about JD? If so, can I see your data that shows it “out of control”? Indeed, I suspect such discussions are more in control in this forum. Though inappropriate, I might agree. And if you read the threads regarding my Jack Daniel’s discussions, I have apologized for that, and I have also apologized for name calling. And I have slipped once in each case since (once with you). But, if do not appreciate being called names (e.g., idiot or fruitcake), then post your own name and stick to it, and stop acting like either (ooops I might have slipped again).
    that’s worthy a professional aka “Dr.” aka “consultant” … any other titles you can randomly throw around to make you feel better about yourself?
    And as far as my academic education goes, I received my PhD in business with focus on statistics and psychology over a decade ago. I also have a degree in pre-medicine. I also learned personally from Dr. Edwards Deming. I also was a student with (not of) Dr. Don Wheeler. So, just to make you more secure, I am only studying now from experience and the knowledge of others (BTW, I suggest you do the same). Oh, I do not use any aka names as you do. I am always Dr. Scott. Who the heck are you?
    As for my contributions, YOU don’t worry have to worry about them. I find it embarrasing
    (you again should be ashamed again that you cannot spell embarrassing correctly. I am not saying English is the superior language as you suggested in your previous post. I am only saying if you are going to use it, then use it correctly)
    to sign them with “Dr. XYZ” in an environment that is dedicated to professionals who for the most part are still working on their academic education.
    You should be embarrassed not to stick to one name, fake or not (which in your case is always fake, never the same).  You should also be embarrassed when you are wrong, but be proud you have learned from your mistake.
    Have a good night. You really need one to clear your mind :-))))).
    My mind is never clear. I am always studying or working on problems. A clear mind is comatose. Maybe that is what you aspire to be.
    P.S. A “Z” is the last letter of the alphabet in capital letter. If you want to know what the formula for a z-value is (population/sample) and how to use it in its various practical applications, please use the google search function. I’m not your statistics mentor.
    The z letter is also the last letter of the alphabet in lower case. And no, the formula for Z is Different than what you say. It is (Y1 – Y2)/Sigma (that is the Big sigma using N in the denominator rather than the little one with n-1). And so no, you are not my statistics mentor. Apparently I am yours. God knows you need one.
    Regards,
     
    Dr. Scott
     

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    #164337

    Dr. Scott
    Participant

    Unfortunately, many have used it for only “bagging” each other. But that is not the purpose of this site. The purpose is to help each other, share knowledge, or solve process improvement issues.
    Sorry if I have disappointed you with my defenses. Do not hold it against the site.
    Regards,
    Dr. Scott
     
     

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    #164338

    Dr. Scott
    Participant

    Not so Great,
    It is called statistics. Have your ever heard of them or the skills used to identify them?
    If not, then you are welcome to take my classes and have me as you Sensei.
    Dr. Scott

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    #164342

    Ape
    Participant

    z-score tells you how far a sampled value from the mean – expressed in standard deviations, thus:
    z = (x – mean) / StDev 

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    #164343

    Brandon
    Participant

    First – there is a heck of a lot of good stuff here. Serious queries are posted and a number of helpful responses are given. In that regard it serves frequently as a surogate mentor for those who don’t have access to one.
    However, to your point, it is also a reflection of human nature. So, yes, there are egos and attitudes…just a sample set of the population.
    Have faith and return if you need help with an issue – you will likely get it.

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    #164344

    Brandon
    Participant

    Dr. S, your comment about a clear mind reminded me of a statement made by Leslie Nielsen the comedic actor. When asked why he works so hard he said, “I hate doing nothing…you never know when you’re done!”

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    #164347

    Brandon
    Participant

    Well there you go Janet…20+ posts to your query and Ape finally gives you a straightforward, comprehendable answer. Not saying others didn’t contribute as well – but the simplicity of the answer impressed me. Thanks Ape.

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    #164348

    Blessed
    Participant

    You’re blessed, really blessed … Still four questions open:
    1. What was Likert’s publication from 1929 that you bragged about the other day?
    2. Why do you suggest a test re-test reliability on a survey?
    3. And the capitalized Z in one case is a population, in the other the T is a sample? What are you on?
    4. You forgot “graduated from one of the top 25 Universities in the US”, Hm, second place is still a loser, and that places you right and square in the middle of the field with now not much expectation for permanent tenure. Maybe, that’s why you’re such a bitter, old, part-time consultant who has to share his limited and now outdated knowledge and his imagined CV so profusely on this site. z and t values, give us a break!
    Whatever way you turn it. You’re a very sad case. There simply isn’t very much to you other than your self-delusion.
    As for the first-timer: Don’t bother, this site is a recycling bin of various introductory topics in statistics, with “Dr.” Scott assumming he’s the Dean of the Sesame Street Statistics Faculity on a public forum.

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    #164349

    Ward
    Participant

    Darth,Yesterday was my final day with the mother ship. I do not know what I will be doing, but after 7 years, I knew I could no longer continue with the mother ship.Pete aka “He who attempts to stow colleagues in the trunk”

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    #164354

    Ape
    Participant

    Thanks Brandon – your welcome.
    IMHO this forum adds only value when a question is answered or a discussion is held based on facts- anything else is waste.
    But who am I to judge othes…….?

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    #164355

    Ape
    Participant

    Reading the question again – I agree with Gary that, given your data, your asking for the sigma -score: the number of standards deviations between the process mean and the nearest spec. limit. In your case, your process is operating at level of sigma = 4

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    #164357

    Blessed
    Participant

    The simple questions, like the z question get answered with a zeal that is borderline commendable. But follow up questions on false claims and false statements by “Dr. Scott” get systematically dropped. “Dr.” Scott is notorious for answering the easy questions, and for playing the “ad hominem card” when his false claims and false statements are questioned. Let’s see if he can somehow give us a full citation of that assumed paper by Likert from 1929. And what his explanation for a test-retest reliability on a survey is. Answering these questions is what differentiates a “Dr.” from a trained practicioner. But my hopes are very low at this point. Also, a PhD in both business administration and psychology is simply nonsense. This combination (i.e. business administration and general psychology) is simply not offered at any of the top 25 Universities in this country.

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    #164358

    Ken Feldman
    Participant

    Sent a response to wifey’s email but you can contact me at [email protected]
     

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    #164363

    Brandon
    Participant

    Eeemmmm…. waste or entertainment sometimes. I enjoy that too.

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    #164393

    Vinny, PhD, MBB
    Member

    Darthmeister,
     
    Since you were kind enough to ask and since it roughly coincided with one of my visits to the isixsigma.com homeland, I initially began posting on this site as an outlet from the pedantic and continued for a time because it was a meeting and debating place for highly creative nonlinear thinkers in the business process improvement field.   
     
    Then the site had a shift to the more pedantic with fewer riots incited, no great debates planned and more small-minded picking at each other.    Anytime pettiness counts more than mathematics and wit, you’re tracking in the wrong direction (in my gentle and humble opinion) – plus I began to appreciate Stan4’s input so I figured I was in the throes of some severe psyche warping myself.   
     
    But it is good to see you back on screen. I hope all’s well and give a buzz next time you’re in Chicago.
     
    Vinny, PhD (from a really good school), MBB (from a really successful deployment in advanced medical devices)

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    #164400

    Dwight
    Participant

    You’ll be missed Pete.  Give my best to Springsteen next time you’re at the Club together.  Keep in touch.

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    #164403

    Mikel
    Member

    you do love to toot your own horn, probably because no one else will give you a blessing. 

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    #164414

    Stevo
    Member

    I know I was not asked my opinion, but with all of the other worthless responses to your question, what is one more.
     
    In my experience, people who have a problem to solve and are looking at the Z score are either:

    Stalling,  waiting for inspiration
    Looking to baffle his/her client with statistics
    Lack the skills to explain the situation is layman terms
    Answering a test question
     
    So, forget your slide ruler and take the easy path using a statistical package (i.e. Minitab).
     
    If you can explain what you are going to use the Z score for and there is not a better path, I will apologize profusely.
     
    Dr Stevo

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    #164416

    Brandon
    Participant

    Dr. Stevo – I have this pain in my side….could you look at it?

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    #164418

    BC
    Participant

    First,
    There are a couple things going on with this site that you need to keep in context.  One is what you observed–some electronic boxing matches, if you will.  Best thing is, read these at lunchtime or at the end of the day and enjoy the entertainment.  The price is right.  The second thing is, there are several posts that could be described as “lazy” or “redundant”, the same basic questions being asked over and over and over.  Granted, a newbie to this site might think this is a good place to ask such questions, but the regulars get irritated by them, expecially when many of the questions can be answered using Google or the blue bar on iSixSigma.
    My advice to you is, don’t give up on this site or this forum.  Read it for a few days to get a feel for the personalities; whose opinions are consistently worth reading for information (Quality Colorado, R Butler and others), whose opinions are worth reading for entertainment (Stan, Darth, New ATI or any of his/her pseudonyms).  The rest you’ll just have to pick through.  And if you want to ask a question, try to look it up first yourself and you won’t get screamed at.

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    #164435

    Mikel
    Member

    Darth,That wasn’t me. Someone is suffering from Stan envy – must have a
    pretty hollow life.

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    #164440

    Dr. Scott
    Participant

    Blessed AH,
    Likert received his PhD in 1932 from Columbia Univeristy (Likert, Rensis (1932): A technique for the measurement of attitudes. Archives of Psychology No. 140.). Dr. R. Likert developed his scale (the Likert Scale) in 1929 and tested it within his dissertation. It has also been used and “somewhat” confirmed by Thurstone (Thurstone, L. L. and E.J. Chave (1929): The measurement of attitudes. Chicago: University of Chicago Press.)
    Also see the isixsigma post: https://www.isixsigma.com/forum/showmessage.asp?messageID=127101
    My PhD is in Business Administration. Supporting areas of a PhD are chosen by the candidate and approved by the dissertation committee chairperson and the dissertation committee (sort of like a minor chosen by an undergrad, except that s/he is free to choose). I chose mine in Psychology, and it was unanimously approved.
    You would know such things if you had any sort of credentials or degree(s). But obviously you do not.
    Now please get over it.

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    #164441

    Dr. Scott
    Participant

    Blessed AH,
    You’re blessed, really blessed … Still four questions open:
    I am not the one that calls me “blessed” (though I feel I have been). Why you call yourself “Blessed” is a mystery to me and others I am sure. I have yet to see you offer or receive ANY value in this forum.
    1. What was Likert’s publication from 1929 that you bragged about the other day?
    Please quote by “brag” of the work I only quoted which was developed by a truly talented man. (Still trying to figure out what your claim the name blessed is).
    Likert received his PhD in 1932 from Columbia Univeristy (Likert, Rensis (1932): A technique for the measurement of attitudes. Archives of Psychology No. 140.). Dr. R. Likert developed his scale (the Likert Scale) in 1929 and tested it within his dissertation. It has also been used and “somewhat” confirmed by Thurstone (Thurstone, L. L. and E.J. Chave (1929): The measurement of attitudes. Chicago: University of Chicago Press.)
    Also refer to the isixsigma post: https://www.isixsigma.com/forum/showmessage.asp?messageID=127101
    2. Why do you suggest a test re-test reliability on a survey?
    It depends on the nature and form of the survey. But in short, it is not a test re-test that I recommended, but rather a method of replication. Are you familiar with that term? Or are you merely as mere as you appear?
    3. And the capitalized Z in one case is a population, in the other the T is a sample? What are you on?
    Z or z and T or t represents a population versus samples. What I am on is the correct use of stats to improve processes? What are you on? 
    4. You forgot “graduated from one of the top 25 Universities in the US”, Hm, second place is still a loser, and that places you right and square in the middle of the field with now not much expectation for permanent tenure. Maybe, that’s why you’re such a bitter, old, part-time consultant who has to share his limited and now outdated knowledge and his imagined CV so profusely on this site. z and t values, give us a break!
    Being a PhD graduate from a top 25 university places my degree in the top .32% of all universities. Oh, and in case you are wondering, I was top 3% in my class. Furthermore, at least I graduated. I bet you wish you had. And I suspect you wish it was from a top 25 school.
    Whatever way you turn it. You’re a very sad case. There simply isn’t very much to you other than your self-delusion.
    My statements are of fact or opinion! I have previously given you the definition of delusion or delusional, but your memory seems impaired. So here it is again for you; “a: something that is falsely or delusively believed or propagated b: a persistent false psychotic belief regarding the self or persons or objects outside the self that is maintained despite indisputable evidence to the contrary; also : the abnormal state marked by such beliefs.
    YOU seem to fit that definition so very well.
    As for the first-timer: Don’t bother, this site is a recycling bin of various introductory topics in statistics, with “Dr.” Scott assumming he’s the Dean of the Sesame Street Statistics Faculity on a public forum.
    Then why don’t you add to the recycle bin and answer a question yourself now and then, rather than becoming a part of the bin that makes it smell so bad? And please learn how to spell.
    And if you feel up to it, challenge me with something not so “simple” (if you can beg a question from someone that knows more than you).
    And for one last time; you seem to keep questioning my degree. My PhD is in Business Administration with a supporting area in Psychology. Supporting areas of a PhD are chosen by the candidate and approved by the dissertation committee chairperson and the dissertation committee (sort of like a minor chosen by an undergraduate, except that s/he is free to choose their minor). I chose mine in Psychology, and it was unanimously approved by the committee.
    You would know such things if you had any sort of credentials or degree(s). But obviously you do not.
    Now please get over it. I have wasted enough time on you.
    Though you are not my friend, and I have absolutely no respect for your behavior, I do sincerely wish that you are able to find help to improve yourself and your attitude toward others.
     Take care,
    Dr. Scott

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    #164448

    Ken Feldman
    Participant

    Unfortunately, it appears that my screen name has been co-opted as well.  I haven’t been able to post for a few days yet my name appears.  Once again, the Forum has drifted into bullsxxt and is the reason I pulled out a few months ago.  Probably time to do it again since there seems to be little contribution going on and just the usual mudslinging.  Be advised that any Darth posting beyond this one is not mine.  I will monitor the site for a while and if the tone changes a bit, I will return. 

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    #164450

    Ward
    Participant

    I am ashamed to admit that I read through all of this. Does isixsigma ever moderate these forums?

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