Commentary: The P-value, devalued. 

By Goodman S. 

Date: 01/2003
Journal: Int J Epidemio

Summary :

  • Berkson critiqued the p value but did not offer a real alternative.​
  • Fisher pointed out that it may be difficult to limit what we call ‘null’ and ‘alternative’ hypothesis.​
  • Goodman presented an alternative to the P-value: ​

The likelihood ratio: The LR is defined as the ratio of the data’s probability under two hypotheses:

  • The P-value is not comparative, so  it is not an evidential measure and does not behave like one.​
  •  It is often a monotonic function of the maximum LR, the LR of the hypothesis with maximum likelihood (i.e. the MLE) versus the null. ​
  • how do we pre-specify alternative hypotheses? The easiest way is to choose a single non-null parameter value, e.g. the ‘minimum important difference’. ​
  • weighted likelihood ratio: averaging the likelihood function over all values of the treatment difference included in the alternative hypothesis.​
  • Using the relationship between the fixed sample size P-value and the maximum LR will provide better results.​