Priyantha Wijayatunga’s Contribution to the Discussion of ‘Testing by Betting: A Strategy for Statistical and Scientific Communication’ by Glenn Shafer
本文通过一个大规模伯努利试验的例子，质疑当估计值与假设值几乎相等且标准误极小时进行假设检验的必要性，认为统计结果的使用常是主观或情境依赖的。
Second, consider a test (see Sprenger, 2013); out of 104,490,000 Bernoulli trials, 52,263,471 are successes and 52,226,529 are failures, therefore observed probability of success is 0.5001768. For testing if the true value of it is 0.5, we get a p-value that is lower than 0.01. Therefore, it is rejected at 0.01. The standard error of the estimate of the probability of success is 0.00004891394 that is almost equal to its value under null hypothesis. For the purpose of deciding if the true probability of success is 0.5, do we need to do a hypothesis test, since the empirical estimate is almost the same as the test value, and the standard error of the estimate is practically zero? What is the purpose of doing a test under these circumstances? If we take that the standard error to be zero, then we should accept that the value of the estimate is 0.5. We do not need hypothesis tests to communicate the statistical result in this case. The hypothesis tests are only mathematically objective procedures that have no subjective opinions embedded in them. However, use of any statistical result is often subjective or contextual!