Hi @hartpjb,
The logWorth values shown in the effect summary table are -log transformations of each model effect's p-value. This representation can be useful when interpreting the degree of difference in importance between your model effects (i.e. potentially easier to compare than p-values). The Analysis of Variance table is used in evaluating the overall model. More information on these tables can be found in JMP's help documentation: Effect Summary and Analysis of Variance.
Hi Jeff, Thanks for the explanation. logWorth appears unique to JMP. I find no reference to it in books on statistical methods - e.g. Sokal and Rohlf 'Biometry' or Zar 'Biostatistical analysis' or Snedecor 'Statistical methods'. Is logWorth peculiar to certain disciplines? - I am a biologist and perhaps have a limited view of the statistical field.
Data transformations are used in many disciplines; some transformation are functional (i.e. log transform of concentration when evaluating bioassay data) while others are more for aesthetic/visualization purposes. The latter is the case for LogWorth. As mentioned above, this transformation can make it easier to visualize and interpret truncated p-values. Two model effects may have a p-value show as 0.0000, leading you to think they are equally important; when transformed, though, you may find that one model effect is more important than another.
I can't speak to whether LogWorth is specific to JMP - if you're curious and want a more clear answer then you may consider tuning into our virtual JMP Discovery Conference next week. There is a 'Meet the Experts' session where you can chat with our Development Team, the great minds behind JMP
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) 20:244https://doi.org/10.1186/s12874-020-01105-9
"The S-value provides an absolute scale on which to viewthe information provided by a valid P-value, as measuredby calibrating the observed p against a physical mechanismthat produces data with known probabilities. A singlecoin toss produces a binary outcome which can be codedas 1 = heads, 0 = tails, and thus requires only two symbolsor states to record or store; hence the information in asingle toss is called bit, short for binary digit, or a shannon.The information describing a sequence of s tosses requiress bits to record or store; thus, extending thismeasurement to a hypothesis H with P-value p, we say thetest supplied s = −log2(p) bits of information against H.
"We emphasize that, without further restrictions, our calibrationof the P-value against coin-tossing is only measuringinformation against the test hypothesis, not in supportof it. This limitation is for the purely logical reason thatthere is no way to distinguish among the infinitude of backgroundassumptions that lead to a test with the same or largerP-value and hence the same or smaller S-value. There isno way the data can support a test hypothesis except relativeto a fixed set of background assumptions. Rather thantaking the background assumptions for granted, we preferinstead to adopt a refutational view, which emphasizes thatany claim of support will be undermined by assumptionuncertainty, and is thus best avoided. This caution appliesregardless 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 particulartest with particular background assumptions. A differenttest based on different background assumptions willusually 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 thedata”, for it is always a test of the hypothesis conjoinedwith (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 distributedresponses under the null hypothesis), to the P-value froma permutation test (which assumes only randomization).Finally, as explained in the Supplement, the S-valuecan also be expressed using other logarithmic units suchas natural (base-e) logs, −ln(p), which is mathematicallymore convenient but not as easy to represent physically."
