log10p

Log10P denotes the base-10 logarithm of a probability value P, most commonly a p-value from a statistical test. If P is a probability in the interval (0, 1], then log10P lies in (-∞, 0], with log10(1) = 0 and log10(0.01) = -2. The transformation is used to compress very small probabilities into a more manageable range and to facilitate comparisons across tests.

A related and widely used quantity is -log10(P), which is nonnegative and increases as P decreases. For example, P = 0.001 yields -log10(P) = 3, and P = 1e-6 yields 6. In practice, -log10 P is commonly used in data visualization and reporting, such as in volcano plots or in tables ranking statistical significance. While log10P is simply a transform of a p-value, many readers prefer the -log10(p) form because larger values correspond to stronger evidence against the null hypothesis.

Limitations include that P cannot be exactly zero; extremely small values may underflow to zero in finite precision arithmetic, making log10P undefined. When this occurs, software often reports a minimum nonzero p-value, resulting in a large but finite log10P. Log10P relates to other logarithmic scales through the identity log10P = ln(P) / ln(10). In summary, log10P is a mathematical transformation used to express p-values on a logarithmic scale, with -log10(P) frequently favored for interpretation and visualization.