"What the use of a p-value implies, therefore, is that a hypothesis that may be true may be rejected because it has not predicted observable results that have not occurred." (Harold Jeffreys, "Theory of Probability", 1939)
"A quotation of a p-value is part of the ritual of science, a sprinkling of the holy waters in an effort to sanctify the data analysis and turn consumers of the results into true believers." (William Cleveland, "Visualizing Data", 1993)
"A common misconception is that an effect exists only if it is statistically significant and that it does not exist if it is not [statistically significant]." (Jonas Ranstam, "A common misconception about p-value and its consequences", Acta Orthopaedica Scandinavica 67, 1996)
"It’s a commonplace among statisticians that a chi-squared test (and, really, any p-value) can be viewed as a crude measure of sample size: When sample size is small, it’s very difficult to get a rejection (that is, a p-value below 0.05), whereas when sample size is huge, just about anything will bag you a rejection. With large n, a smaller signal can be found amid the noise. In general: small n, unlikely to get small p-values. Large n, likely to find something. Huge n, almost certain to find lots of small p-values." (Andrew Gelman, "The sample size is huge, so a p-value of 0.007 is not that impressive", 2009)
"The p-value is a concept so misaligned with intuition that no civilian can hold it firmly in mind. Nor can many statisticians." (Matt Briggs, "Why do statisticians answer silly questions that no one ever asks?", Significance Vol. 9(1), 2012)
"Statistical significance refers to the probability that something is true. It’s a measure of how probable it is that the effect we’re seeing is real (rather than due to chance occurrence), which is why it’s typically measured with a p-value. P, in this case, stands for probability. If you accept p-values as a measure of statistical significance, then the lower your p-value is, the less likely it is that the results you’re seeing are due to chance alone." (John H Johnson & Mike Gluck, "Everydata: The misinformation hidden in the little data you consume every day", 2016)
"When statistical inferences, such as p-values, follow extensive looks at the data, they no longer have their usual interpretation. Ignoring this reality is dishonest: it is like painting a bull’s eye around the landing spot of your arrow. This is known in some circles as p-hacking, and much has been written about its perils and pitfalls." (Robert E Kass et all, "Ten Simple Rules for Effective Statistical Practice", PLoS Comput Biol 12(6), 2016)
"Remember that a p-value merely indicates the probability of a particular set of data being generated by the null model–it has little to say about the size of a deviation from that model (especially in the tails of the distribution, where large changes in effect size cause only small changes in p-values)." (Clay Helberg)
