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When to reject a null hypothesis

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  • #51792

    bigbavarian
    Participant

    When performing hypothesis testing, when should you reject a null hypothesis? <.05?
    I have a been a little confused in some of the readings online. 
    Thanks
     

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    #180589

    Ken Feldman
    Participant

    You can reject your Null Hypothesis when the p value is less than your selected alpha level. It may be .05 or .01 or .10 or any other value of risk that you are willing to take regarding the type 1 error.

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    #180590

    bigbavarian
    Participant

    Thank you for confirming.  I was starting to pull my hair out.

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    #180592

    e
    Participant

    Where do you stand when the p-value equals your alpha risk exactly…at least to the decimal places displayed in Minitab?
    Curiosity of this cat.

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    #180595

    Robert Butler
    Participant

    If the reject was P < .05 and you have a situation where, to the best of your knowledge, P = .05 then this means P is not less than .05 so it does not meet your criteria and you do not reject the null.

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    #180598

    Ken Feldman
    Participant

    Use common sense is the rule I use. The selection is arbitrary so if it is .05 vs .04 or .06, make a reasonable decision and don’t worry much about decimal places.

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    #180602

    BTDT
    Participant

    Darth:
    R.A. Fisher (1890-1962)“…either there is something in the treatment, or a coincidence has occurred such as does not occur in 1 in 20 trials”(Journal of the Ministry of Agriculture of Great Britain, 1926)This always seemed like pretty good common sense to me.Cheers, Alastair

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    #180668

    R. Eric Reidenbach
    Participant

    When setting a p level keep in mind what “rejecting the null hypothesis” really means.  It means that you do not have sufficient information to accept the hypothesis.  This is not quite as strong as “rejecting” a null hypothesis.  Unfortunately, too many statistics users do not understand this and the “rejection” becomes a lot stronger than it really is.  Accordingly, the lower the p level (p of 5% or P of 1%) the more stringent the statement you can make about the hypothesis and more sure you can be about your conslusions.

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    #180675

    Swaggerty
    Participant

    Hi Eric:When I discuss rejecting the null hypothesis in class, I literally state that alpha (type 1 risk – sending an innocent person to jail) is a basic guideline. When the p-value is significantly larger or significantly smaller than .05, it is really straight forward.
    P-value high: do not reject Ho – at a 95% Confidence level, we do not have enough evidence beyond a reasonable doubt to convict!
    P-value low: reject Ho (p

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    #180686

    Vallee
    Participant

    Robert,I understand in controlled situations .05 is a good measurement, especially in my old psychology research world; however, in the common/frequent six sigma applications of today do you think more is getting rejected or accepted than should be or not enough? After all, the controls are not the same and their is usually more noise present in everyday life. There was a big push in the academic world before I left it to accept more studies in peer reviewed magazines to share lessons learned that would not have been accepted before because of a higher p value. HF Chris Vallee

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    #180692

    Taguchi
    Member

    When nothing happens,then it is H0
    When you plan to achieve a target then it is H1
     

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    #180693

    Robert Butler
    Participant

      HF,
       I don’t have a sense that any more or less is being accepted/rejected. For me, and for those who review what I’ve done, the issue isn’t so much the choice of the cut point as it is one of “honoring the contract ” and describing the significance of your results (or lack thereof) in terms of the originally stated goals. 
      There have been instances in peer reviewed articles where we found things in the “close but no cigar” category which, even with the statistically insignificant  observed numeric differences, would have been of value either physically or clinically.  In cases such as this we’ll provide the usual summary table, note our failure to meet our pre-specified goal, comment on how close we came and suggest that even though we did not reach our statistical goal there would be merit in additional investigations. 
      In a discussion last year I posted a summary of some ways one can go about reporting near misses of this type.
    https://www.isixsigma.com/forum/showmessage.asp?messageID=145121
       

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    #180721

    Vallee
    Participant

    Robert,Thanks for the input and validity of sharing “near misses”in some cases. HF Chris Vallee

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    #180729

    Rajeev seth
    Participant

    If you have taken Alpha Risk as 5% then you will reject Null Hypothesis if p value is less than 0.05. If it is more than 0.05 you are fail to reject Null Hypothesis
    Rajeev

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    #180736

    Chris Seider
    Participant

    If I take your last bit of logic further, if the risk to the business is so high how would you know which side of the null hypothesis to take?
    Not sure it makes sense from a practical point of view….but understand your connection.
    Also, if the risk of the business was paramount, then why set an alpha or beta risk–just do the safest thing and potentially never drive the business to new breakthroughs?  I digress with my musings…  So I’m clear, I’m NOT advocating use of business risk for a statistical test which is to be void of emotion.
     

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    #180738

    Szentannai
    Member

    Hi,
    a point that I find important is that the p value gives the risk of a false alarm (alpha risk) with the assumption that everything else in the measurement was done perfectly – MSA is fully OK, there is no bias in the sampling etc. etc.
    The actual risk of making a type 1 error is in reality far bigger – p only measures this one component of it. Of course in a cleanly done DMAIC you are supposed to check for all these factors before getting to a p – so the question is really: were those steps done correctly enough?
    Regards
    Sandor 
     

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    #180751

    Swaggerty
    Participant

    Certainly, if there is a business risk associated with the decision we reach, we would want to reduce either alpha and/or beta risks – e.g. investment examples, call centres for medical questions, etc.The ramification of this reduction in risk (i.e. reducing alpha and beta, thus we are not as ready to reject the null) is that these two risks are key components in sample size calculations for continuous data. The lower the risk we are willing to take, the higher the sample size should be.

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    #180752

    Chris Seider
    Participant

    More samples is always good if possible…..
    However, I’m just stating that the business impact is not lessened if we take a 5% or 1% risk because the impact will be felt if we make the wrong conclusion based on our alpha/beta risks.  Only the CHANCE of the negative business impact is reduced with more samples giving more confidence.
    I had originally reacted because of someone’s earlier post that if one had an original 5% alpha risk, the selection of the null hypothesis rejection would be influenced by the business risk.  The assessment of business risk should give you alpha/beta risk BEFORE you start doing your statistical comparison.
     

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    #180754

    Swaggerty
    Participant

    You hit the nail right on the head. Too many practitioners back into the setting of the risks after the fact. That’s why we refer to setting of risks “a proiri”.

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    #180755

    Swaggerty
    Participant

    That should be “a priori”.

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    #180756

    Chris Seider
    Participant

    I figured we were drilling in on the same point.

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    #182526

    Abu Jazi
    Participant

    Hi Eric ,
    I just want to ask , why is rejecting a null hypothesis is stronger than failed to reject it ( accept it ) ? and if anyone knows the answer please tell me , and please give some links or books that prove it .

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    #182538

    Abu Jazi
    Participant

    Hi Eric ,
    I just want to ask , why is rejecting a null hypothesis is stronger than failed to reject it ( accept it ) ? and if anyone knows the answer please tell me , and please give some links or books that prove it .

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    #182539

    R. Eric Reidenbach
    Participant

    Remeber, that to reject a null hypothesis says that we do not have enough information (proof) to accept it.  You have to keep in mind that this is a probablistic statement.  Too often, significance tests are treated as if they were incontrovertible truth when in fact they are not.  You may accept a null hypothesis when you shouldn’t and you may reject it when you shouldn’t.
    As far as links to books, I prefer Nunnally, Psychometric Theory.
    I hope this helps.

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    #182540

    Mikel
    Member

    Wrong

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    #182548

    Mikel
    Member

    Rejecting the null means we have very strong evidence that the null is
    not correct.

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    #182554

    Ken Feldman
    Participant

    Not sure I am comfortable with the word “strong”. That might be a function of the selected alpha error which we are using as our decision point. We might have “significant” evidence.

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    #182557

    Mikel
    Member

    We can argue semantics, at least I’ve got the data going in the correct
    direction.

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    #182558

    Bower Chiel
    Participant

    Hi EveryoneYou might find it interesting to look at the paper entitled “Sifting the evidence—what’s wrong with significance tests?” by Jonathan A C Sterne and George Davey Smith available free at http://www.ptjournal.org/cgi/content/full/81/8/1464.I particularly like the “spectrum” diagram for suggested interpretation of P values from published medical research.Best Wishes
    Bower Chiel

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    #182562

    Natanyahoo
    Participant

    Wrong!

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    #182603

    Craig
    Participant

    When p is low, reject Ho
    That’s all you’ll ever need to know
    How poetic!
    Oh by the way, if you set alpha at .05 and the p value was exactly .05…and you fail to reject the null…and you stopped investigating this X variable…..YOU’RE FIRED

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