E-values

E-values, in the context of statistical hypothesis testing, represent the probability of observing a test statistic as extreme as, or more extreme than, the one actually observed if the null hypothesis is true. Unlike p-values, which are probabilities directly calculated under the null hypothesis, E-values often involve adjustments or transformations to account for multiple hypothesis testing or the size of the search space.

The precise interpretation of an E-value depends on the specific application. In bioinformatics, particularly in sequence alignment and database searching (e.g., BLAST), E-values represent the expected number of hits one could see by chance when searching a database of a particular size. A lower E-value implies a more significant result, suggesting that the alignment is less likely due to random chance. Specifically, an E-value of 0.01 means that one expects 0.01 alignments with a similar score simply by chance in the database being searched. Therefore, the alignment is considered significant.

E-values can also be used as a measure of evidence in other statistical contexts beyond sequence comparison. In such contexts, they are often derived from p-values through a mathematical transformation designed to control the family-wise error rate (FWER) or the false discovery rate (FDR) across multiple tests. This is necessary when performing many tests simultaneously, as the probability of observing a statistically significant result by chance increases with the number of tests performed.

It is important to note that E-values are not measures of effect size or the probability that the alternative hypothesis is true. They only provide an indication of the statistical significance of a result within the framework of the null hypothesis. While a low E-value suggests that the result is unlikely to have occurred by chance, it does not guarantee the biological or practical relevance of the finding.