Statistical Significance Does Not Equal Geological Significance: Reply to Comments on “Lies, Damned Lies, and Statistics (in Geology)”

In my Eos Forum of 24 November 2009 (90(47), 443), I used the chi‐square test to reject the null hypothesis that earthquakes occur independent of the weekday to make the point that statistical significance should not be confused with geological significance. Of the five comments on my article, only the one by Sornette and Pisarenko [2011] disputes this conclusion, while the remaining comments take issue with certain aspects of the geophysical case study. In this reply I will address all of these points, after providing some necessary further background about statistical tests. Two types of error can result from a hypothesis test. A Type I error occurs when a true null hypothesis is erroneously rejected by chance. A Type II error occurs when a false null hypothesis is erroneously accepted by chance. By definition, thep value is the probability, under the null hypothesis, of obtaining a test statistic at least as extreme as the one observed. In other words, the smaller thep value, the lower the probability that a Type I error has been made. In light of the exceedingly small p value of the earthquake data set,Tseng and Chen's [2011] assertion that a Type I error has been committed is clearly wrong. How about Type II errors?