# What is a logworth statistic, and how useful is it?

My teacher mentioned it today, and there is nearly zero good search results for it, other than one mention each in the SAS and JMP documentation.

It says it is -log10(p-value), but there is almost no explanations of this online. Also it seems like this statistic is widely ignored. It isn't mentioned in any tutorials or in any of the data science papers I have read in the past two years.

## Question

So, what is this statistic, and where does it come from? How useful is it in data science?

logworth is a p-value transformation based on Pearson Chi-Squared test.

Pearson Chi-Squared test evaluates the probability of having a split caused by chance. The higher the Pearson Chi-Squared value, the higher the chance that the split is caused by dependence. A p-value is given according to the Chi-Squared score and the degree of freedom.

Because some data can have high dependence relationship, the p-value can be extremely small. Taking a logworth of p-value (-log(p-value)) allows us to mitigate this extremely low value.

If p is the p-value from a valid test of fit, the logworth can be transformed to a measure of the number of bits of information against the model supplied by the test, via the Shannon transform s = -log2(p) = log10(p)/log10(2), also known as the binary surprisal or S-value from the test. For detailed discussions of this measure available online see Greenland, S., 2019. Valid P-values behave exactly as they should: Some misleading criticisms of P-values and their resolution with S-values. Am. Stat. 73, 106–114. https://doi.org/10.1080/00031305.2018.1529625 and Rafi, Z., Greenland, S., 2020. Semantic and Cognitive Tools to Aid Statistical Science: Replace Confidence and Significance by Compatibility and Surprise. BMC Research Methodology, in press. https://arxiv.org/abs/1909.08579