Exceedance probability for parameter estimates
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Many researchers and statisticians are conflicted over the practice of hypothesis testing and statistical significance thresholds. There are several alternatives, and in this paper we propose one that focuses on estimation. In particular, we focus on the probability that a future parameter estimate will exceed a specified amount. After briefly reviewing background on p-values, significance thresholds, and a few alternatives, we describe the exceedance probability for parameter estimates and provide examples of how the exceedance probability, along with corresponding confidence intervals, can provide useful information for the purposes of drawing inference and making decisions. We focus on applications in one-sample tests and linear regression with potential extensions to generalized linear models and Cox regression. We also discuss connections to conditional and predictive power, and analyze the relationship between confidence intervals for the exceedance probability and confidence intervals for parameter estimates. This relationship leads to an alternative interpretation of confidence intervals for parameter estimates that might be useful for pedagogical purposes.
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