When to reject a null hypothesis

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.

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.

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.

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.

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

  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
   

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

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 
 

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.
 

That should be “a priori”.

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 .

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.

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

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

Wrong!