Logworth is -log base 10 of the p-value. Taking the log (to any base) of the p-value puts the finding on a more meaningfully interpreted scale than the 0-to-1 scale of a p-value.
Rafi and Greenland (2020) propose using an s-value instead of a p-value; s-value is -log base 2 of the p-value (and so it is proportional to logworth), and can be interpreted by analogy to coin-flipping.
Semantic and cognitive tools to aid statistical science: replace confidence and significance by compatibility and surprise
Rafi and Greenland BMC Medical Research Methodology (2020) 20:244
https://doi.org/10.1186/s12874-020-01105-9
"The S-value provides an absolute scale on which to view
the information provided by a valid P-value, as measured
by calibrating the observed p against a physical mechanism
that produces data with known probabilities. A single
coin toss produces a binary outcome which can be coded
as 1 = heads, 0 = tails, and thus requires only two symbols
or states to record or store; hence the information in a
single toss is called bit, short for binary digit, or a shannon.
The information describing a sequence of s tosses requires
s bits to record or store; thus, extending this
measurement to a hypothesis H with P-value p, we say the
test supplied s = −log2(p) bits of information against H.
"We emphasize that, without further restrictions, our calibration
of the P-value against coin-tossing is only measuring
information against the test hypothesis, not in support
of it. This limitation is for the purely logical reason that
there is no way to distinguish among the infinitude of background
assumptions that lead to a test with the same or larger
P-value and hence the same or smaller S-value. There is
no way the data can support a test hypothesis except relative
to a fixed set of background assumptions. Rather than
taking the background assumptions for granted, we prefer
instead to adopt a refutational view, which emphasizes that
any claim of support will be undermined by assumption
uncertainty, and is thus best avoided. This caution applies
regardless of the test statistic used, whether P-value, Svalue,
Bayes factor, or posterior probability.
"As with the P-value, the S-value refers only to a particular
test with particular background assumptions. A different
test based on different background assumptions will
usually produce a different P-value and thus a different Svalue;
thus it would be a mistake to simply call the S-value
“the information against the hypothesis supplied by the
data”, for it is always a test of the hypothesis conjoined
with (or conditioned on) the assumptions. As a basic example,
we may contrast the P-value for the strict null hypothesis
(of no effect on any experimental unit)
comparing two experimental groups using a t-test (which,
along with randomization, assumes normally distributed
responses under the null hypothesis), to the P-value from
a permutation test (which assumes only randomization).
Finally, as explained in the Supplement, the S-value
can also be expressed using other logarithmic units such
as natural (base-e) logs, −ln(p), which is mathematically
more convenient but not as easy to represent physically."
