In various articles on the Chi-squared statistical test is referenced a threshold value of 0.05 for the probability density to reject the null hypothesis. This value is usually given as a "convention".
What is the source of this threshold? Is there any reference article justifying it that I could cite?
This article might help you.
http://www.p-value.info/2013/01/whats-significance-of-005-significance_6.html
Basically, the p-value is nothing but the probability in favor of null hypothesis. So if it is significantly less ; hence we tend to reject the null hypothesis.
Dear Luís,
The 0.05-convention is a general one for expressing significance levels in statistics and there is no need to cite a paper for it. Nevertheless, it's good to keep in mind that it is just a number without any "real" basis. In my opinion, a p-value of 0.06 is equally worth considering than p=0.05.
Best regards,
thomas
The p-value is technically the probability of getting data as extreme as the data you have, when the null hypothesis is actually true. That is, of finding an effect when there really isn't one. That is, a false positive.
The 0.05 cut-off isn't used in all fields, and isn't used in all occasions. But, as you say, most of the time we use it by "convention". It's basically for historical reasons. As I understand, in the first half of the twentieth century, as statisiticians were developing the "null hypothesis significance test" framework that is so common today, Fisher proposed that making a false positive error about 1 out of 20 times was reasonable.
Of course this might be grossly unreasonable depending on what you are doing. If you are involved in medical research, you may need to be much more certain than that. On the other hand, if you are screening a whole bunch of treatments in an experiment with low statistical power, you might want to retain treatments meeting a 0.10, 0.15, or 0.20 threshold for further testing.
Like everything in statistics, it only means what it means, and it's up to the researcher to decide if the result has any practical or scientific meaning.
Dear Luís,
Gerald Dallal devotes a chapter in "The Little Handbook of Statistical Practice" on "Why P=0.05". He states that the practice goes back to R.A. Fisher. He has published an (older) online version of his book's chapter:
http://www.jerrydallal.com/LHSP/p05.htm
It is really nicely written book and the chapter explains in detail with multiple quotes and references the influence that Fisher has had on the subject.
Best wishes,
Immo
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