To curb research misreporting, replace significance and confidence by compatibility

It is well known that the statistical analyses in health-science and medical journals are frequently misleading or even wrong. Despite many decades of reform efforts by hundreds of scientists and statisticians, attempts to fix the problem by avoiding obvious error and encouraging good practice have not altered this basic situation. Statistical teaching and reporting remain mired in damaging yet editorially enforced jargon of "significance", "confidence", and imbalanced focus on null (no-effect or "nil") hypotheses, leading to flawed attempts to simplify descriptions of results in ordinary terms. A positive development amidst all this has been the introduction of interval estimates alongside or in place of significance tests and P-values, but intervals have been beset by similar misinterpretations. Attempts to remedy this situation by calling for replacement of traditional statistics with competitors (such as pure-likelihood or Bayesian methods) have had little impact. Thus, rather than ban or replace P-values or confidence intervals, we propose to replace traditional jargon with more accurate and modest ordinary-language labels that describe these statistics as measures of compatibility between data and hypotheses or models, which have long been in use in the statistical modeling literature. Such descriptions emphasize the full range of possibilities compatible with observations. Additionally, a simple transform of the P-value called the surprisal or S-value provides a sense of how much or how little information the data supply against those possibilities. We illustrate these reforms using some examples from a highly charged topic: trials of ivermectin treatment for Covid-19.