“The full p-value function arguably records the full measurement information that a user should be entitled to know! We also note that the p-value function is widely available for any scalar interest parameter and any model-data combination with just moderate regularity, and has available computational procedures. In addition to the overt statistical position, the p-value function also provides easily and accurately many of the familiar types of summary information: a median estimate of the parameter; a one-sided test statistic for a scalar parameter value at any chosen level; the related power function; a lower confidence bound at any level; an upper confidence bound at any level; and confidence intervals with chosen upper and lower confidence limits. The p value reports all the common inference material, but with high accuracy, basic uniqueness, and wide generality. From a scientific perspective, the likelihood function and p-value function provide the basis for scientific judgments by an investigator, and by other investigators who might have interest. It thus replaces a blunt yes or no decision by an opportunity for appropriate informed judgment.
#statstab #301 Likelihood and the p-value Function
Thoughts: Plot idea by Fraser (2019): "the likelihood function and p-value function provide the basis for scientific judgments by an investigator"
#consonancecurve #pvaluefunction #likelihood #plot
doi.org/10.1080/0003...
