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.” - D. A. S. Fraser, 2019



For R:

Install the Package From CRAN


Install the Developer Version


Check out the Examples.

For Stata:

Check out the Article on Using Stata for concurve.


  • ggplot2
  • metafor
  • parallel
  • dplyr
  • tibble
  • survival
  • survminer
  • scales

"Statistical software enables and promotes cargo-cult statistics. Marketing and adoption of statistical software are driven by ease of use and the range of statistical routines the software implements. Offering complex and “modern” methods provides a competitive advantage. And some disciplines have in effect standardised on particular statistical software, often proprietary software.

Statistical software does not help you know what to compute, nor how to interpret the result. It does not offer to explain the assumptions behind methods, nor does it flag delicate or dubious assumptions. It does not warn you about multiplicity or p-hacking. It does not check whether you picked the hypothesis or analysis after looking at the data, nor track the number of analyses you tried before arriving at the one you sought to publish – another form of multiplicity. The more “powerful” and “user-friendly” the software is, the more it invites cargo-cult statistics." - Stark & Saltelli, 2018


  1. Stark PB, Saltelli A. Cargo-cult statistics and scientific crisis. Significance. 2018;15(4):40-43.
  2. Poole C. Beyond the confidence interval. Am J Public Health. 1987;77(2):195-199.
  3. Sullivan KM, Foster DA. Use of the confidence interval function. Epidemiology. 1990;1(1):39-42.
  4. Rothman KJ, Greenland S, Lash TL. Modern epidemiology. 2012.
  5. Singh K, Xie M, Strawderman WE. Confidence distribution (CD) – distribution estimator of a parameter. arXiv [mathST]. 2007.
  6. Schweder T, Hjort NL. Confidence and Likelihood*. Scand J Stat. 2002;29(2):309-332.
  7. Amrhein V, Trafimow D, Greenland S. Inferential Statistics as Descriptive Statistics: There is No Replication Crisis if We Don’t Expect Replication. Am Stat. 2019
  8. Greenland S. Valid P-values Behave Exactly As They Should. Some misleading criticisms of P-values and their resolution with S-values. Am Stat. 2019;18(136).
  9. Fraser DAS. The p-value Function and Statistical Inference. Am Stat. 2019