(Goal here is to point out that these things are still being incorrectly defined despite the multiple decades of papers pointing out that people use these incorrect definitions, not to make fun of folks who were probably forced to write outside of their area of subject expertise)
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"The p-value is the probability that the observed data are consistent with the null hypothesis." - A Dictionary of Social Research Methods (2016)
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"...p-values are usually compared to a predetermined value called the level of significance and if they exceed that, the null hypothesis is accepted and if not, it is rejected". - A Dictionary of Social Research Methods (2016)
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"[In sequence analysis a p value is] a statistical measure of the significance of a match obtained by searching a database with a query sequence." Oxford Dictionary of Biochemistry and Molecular Biology (2nd ed, 2008)
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"The closer the p‐value to 0, the more significant the match." Oxford Dictionary of Biochemistry and Molecular Biology (2nd ed, 2008)
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"... part of the output of a statistical test, such as regression or ANOVA, that can take a value between 0.0 and 1.0. This is the probability that the observed difference or association among variables has arisen by chance." A Dictionary of Business Research Methods (2016)
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"In statistics, the estimated probability of rejecting the null hypothesis (H0) when H0 is true, expressed as a number between 0 and 1." A Dictionary of Ecology (5 ed., 2016)
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"the probability that sample data will be as or more extreme [as] that would be observed if the null hypothesis were true. Extreme being defined in terms of a significance level that is determined in advance, commonly 5%, or p=0.05, meaning one chance in 20 of being incorrect"...
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[continued from above] "... If p < 0.05 the result is considered statistically significant, and usually denoted by an asterisk; if p < 0.01 the result is statistically highly significant (**)." - A Dictionary of Environment and Conservation (3 ed., 2016)
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"For example, a p-value of 0.01 (p = 0.01) means there is a 1 in 100 chance the result occurred by chance. " A Dictionary of Dentistry (2010)
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A definition I think is more or less correct despite its slightly weird use of tenses:"The probability that a given test statistic would take the observed value, or one which was less likely, if the null hypothesis had been true." Concise Oxford Dictionary of Mathematics (2014)
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Addendum - a definition I like to use is: "A P value gives the probability of obtaining data as or more extreme as was observed, under the statistical null hypothesis.
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When teaching I then say something like "What we're effectively doing is positing a hypothetical world where the null is strictly true (including any statistical assumptions) and saying, in that world how often would we get data as (or more) extreme as that which we observe here"
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..."It doesn't tell us anything about whether our theory is correct, or what we should believe" - then talk about the disagreement between Fisher/Neyman & Pearson and how p-vals are used in each framework. I then repeat the definition every week until some of the students get it
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I think making the hypothetical world stuff explicit helps because students intuitively understand that you cannot directly use the probability of the data in *that* world to assess the probability of your hypothesis being correct in *this* world.
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And I think teaching about the disagreement b/w Fisher and N&P helps make the material more exciting, and make them realise that if even the progenitors of the methods couldn't agree, maybe they can also critically engage with the ideas that underlie these procedures
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