On Significance II

 "Science usually amounts to a lot more than blind trial and error. Good statistics consists of much more than just significance tests; there are more sophisticated tools available for the analysis of results, such as confidence statements, multiple comparisons, and Bayesian analysis, to drop a few names. However, not all scientists are good statisticians, or want to be, and not all people who are called scientists by the media deserve to be so described." (Robert Hooke, "How to Tell the Liars from the Statisticians", 1983)

"The idea of statistical significance is valuable because it often keeps us from announcing results that later turn out to be nonresults. A significant result tells us that enough cases were observed to provide reasonable assurance of a real effect. It does not necessarily mean, though, that the effect is big enough to be important." (Robert Hooke, "How to Tell the Liars from the Statisticians", 1983)

"A tendency to drastically underestimate the frequency of coincidences is a prime characteristic of innumerates, who generally accord great significance to correspondences of all sorts while attributing too little significance to quite conclusive but less flashy statistical evidence." (John A Paulos, "Innumeracy: Mathematical Illiteracy and its Consequences", 1988)

"A little thought reveals a fact widely understood among statisticians: The null hypothesis, taken literally (and that’s the only way you can take it in formal hypothesis testing), is always false in the real world. [...] If it is false, even to a tiny degree, it must be the case that a large enough sample will produce a significant result and lead to its rejection. So if the null hypothesis is always false, what’s the big deal about rejecting it?" (Jacob Cohen, "Things I Have Learned (So Far)", American Psychologist, 1990)

"Statistical significance testing can involve a tautological logic in which tired researchers, having collected data on hundreds of subjects, then conduct a statistical test to evaluate whether there were a lot of subjects, which the researchers already know, because they collected the data and know they are tired. This tautology has created considerable damage as regards the cumulation of knowledge." (Bruce Thompson, "Two and One-Half Decades of Leadership in Measurement and Evaluation", Journal of Counseling & Development 70 (3), 1992)

"[…] an honest exploratory study should indicate how many comparisons were made […] most experts agree that large numbers of comparisons will produce apparently statistically significant findings that are actually due to chance. The data torturer will act as if every positive result confirmed a major hypothesis. The honest investigator will limit the study to focused questions, all of which make biologic sense. The cautious reader should look at the number of ‘significant’ results in the context of how many comparisons were made." (James L Mills, "Data torturing", New England Journal of Medicine, 1993)

"When significance tests are used and a null hypothesis is not rejected, a major problem often arises - namely, the result may be interpreted, without a logical basis, as providing evidence for the null hypothesis." (David F Parkhurst, "Statistical Significance Tests: Equivalence and Reverse Tests Should Reduce Misinterpretation", BioScience Vol. 51 (12), 2001)

"If you flip a coin three times and it lands on heads each time, it's probably chance. If you flip it a hundred times and it lands on heads each time, you can be pretty sure the coin has heads on both sides. That's the concept behind statistical significance - it's the odds that the correlation (or other finding) is real, that it isn't just random chance." (T Colin Campbell, "The China Study", 2004)

"A type of error used in hypothesis testing that arises when incorrectly rejecting the null hypothesis, although it is actually true. Thus, based on the test statistic, the final conclusion rejects the Null hypothesis, but in truth it should be accepted. Type I error equates to the alpha (α) or significance level, whereby the generally accepted default is 5%." (Lynne Hambleton, "Treasure Chest of Six Sigma Growth Methods, Tools, and Best Practices", 2007)

"For the study of the topology of the interactions of a complex system it is of central importance to have proper random null models of networks, i.e., models of how a graph arises from a random process. Such models are needed for comparison with real world data. When analyzing the structure of real world networks, the null hypothesis shall always be that the link structure is due to chance alone. This null hypothesis may only be rejected if the link structure found differs significantly from an expectation value obtained from a random model. Any deviation from the random null model must be explained by non-random processes." (Jörg Reichardt, "Structure in Complex Networks", 2009)