21  The Issues of \(p\)-value and Statistical Significance

Our brain has this annoying habit to think that […], if under some hypothesis, results are unlikely, then the hypothesis is unlikely. This is false. – Christophe Michel (1974 - )

There are three types of lies: lies, damn lies, and statistics. – Benjamin Disraeli (1804 - 1881)

We have been using the classical or frequentist approach to do a variety of statistical inferences. But Dr. Yu once said he never uses p-value in his own research, and there are many issues with what is taught in Intro Stats (MATH 1700/4720/4740). In fact, the null hypothesis significance testing (NHST) paradigm and the p-value usage have been much criticized and shown to be problematic, misused, and resulting in reproducibility and replication crisis in scientific research.

Some references are

• Wikipedia: Misuse of p-values

• A. Reinhart (2015), “Statistics Done Wrong”, No Starch Press, San Francisco.

• R. L. Wasserstein and Nicole A. Lazar (2016), “The ASA Statement on p-Values: Context, Process, and Purpose”, The American Statistician, 70:2, 129-133.

• V. Amrhein, S. Greenland and B. McShane (2019), “Retire statistical significance”, Nature, 567, 305-307.

• B. McShane, D. Gal, A. Gelman, C. Robert and Jennifer L. Tackett (2019), “Abandon Statistical Significance”, The American Statistician, 73:sup1, 235-245.

• A. Gelamn and E. Loken (2014), “The Statistical Crisis in Science”, American Scientist, 102, 460-465.

• R. L. Wasserstein, A. L. Schirm and N. A. Lazar (2019), “Moving to a World Beyond p < 0.05”, The American Statistician, 73:sup1, 1-19.

• Statistically Discernible by Editorial of Journal of Statistics Education