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Abstract:
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Many data stories told us that testing point null hypotheses have produced increasingly active and stronger opposition, including draconian suggestions that significance testing should be banned. Within the current paradigm of hypothesis testing, the Jeffreys-Lindley paradox is the most cited disagreement between the frequentist and Bayesian statisticians. This paradox divides frequentists and Bayesians in an irreconcilable way when big data are analyzed. It has been actively discussed and many solutions have been proposed, albeit, none entirely reasonable. We recommend that point null hypotheses of a normal mean should be abandoned and replaced by interval null hypotheses accompanied by the practically meaningful alternative hypotheses. This proposal is established on the implications of the Zero probability theorem proved by C.R. Rao and Lovric in 2016. This theorem implicitly leads to the final dissolution of the Lindley paradox. We regard that this new paradigm will not only eradicate most of the objections against frequentist testing and breathe a new life into them, but also considerably reconcile communication in inference between frequentist and Bayesian approaches.
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