Data as evidence

In an earlier article, Gordon Drummond summarized ongoing changes in how statistics are being used in experimental physiology. He described the near-ubiquitous use of the P value, cautioning against declaring an analysis 'statistically significant'. He mentioned alternative approaches, including Bayesian and likelihood approaches. This article focuses on the latter approach, although I initially take another look at the P value. Then the likelihood approach is introduced with a very artificial example to enable the concept to be grasped easily. Next, a more realistic example is described, with associated calculations. A further example using real categorical data is explained, showing how it relates to and is superior to the oft-used χ² test. A final discussion reveals that the likelihood approach, although mathematically and statistically accurate, is poorly supported by literature and training.