Quanta prints two answers for every test you run. The p-value, and next to it, the Bayes factor. Most software makes you pick one, or makes you leave for a second program to get the other. Here is why we put them on the same line.
A p-value can tell you when to doubt the null hypothesis. It can never tell you when to believe it. That is not a flaw in the math, it is what the math was built to do. So every study that comes back non-significant ends in a shrug, and the shrug gets written up as a conclusion anyway. A Bayes factor closes that exact gap. It can say the data support the null, and it can say how strongly. Report only one of these numbers and you have thrown away half of what your data were willing to tell you.
The classroom
A district runs a reading intervention for a year. Sixty-four students get it, sixty-four do not. At the end, the two groups are tested and the difference between them comes back non-significant, p = .21.
The report says the program had no effect. The district cuts it.
Nothing in that test earned the word "no." A non-significant result means the difference was not large enough, given the noise and the sample size, to rule out chance. Maybe the program does nothing. Maybe it helps a little and 128 students were too few to see it. Maybe the reading measure was blunt. The p-value cannot separate those, and it never claimed it could.
Run the same data through the Bayesian side and you get a number that speaks to the actual question. In this case the data turn out to be roughly 2.4 times more likely under "no effect" than under "some effect." That is weak. It tilts toward no effect and it does not arrive. The honest sentence is that the study was inconclusive, and now the researcher has a number that says so, rather than a p-value they have to interpret against its own grain.
Change the result and the point stays. If the data had come back 12 times more likely under no effect, the district would have had real evidence that a year of this program changed nothing measurable in these classrooms. That is a finding. It is publishable, it is actionable, and no p-value of any size could have delivered it.
Two approaches, two questions
The frequentist test asks what would happen across many studies. Set a threshold, run the test, and the p-value tells you how often data this extreme would show up if the null were true. It holds your false-positive rate where you set it. Reviewers expect it, journals require it, and the error control is real.
The Bayesian test asks about the study in front of you. The Bayes factor compares how well each hypothesis predicted the data you actually collected, and returns the ratio. Because it is a ratio, it runs both directions. Evidence for an effect, or evidence for its absence, on the same scale.
There is a cost, and it should be stated plainly. A Bayes factor is computed against an assumption about how big an effect could plausibly be. Change that assumption and the number changes. The field has settled on sensible defaults, but a default is a convention, not a fact about reading interventions. A Bayes factor reported without its assumption is a number nobody can check.
Neither approach is the right one. One controls error over the long run. The other grades evidence in this study. Most applied research needs both answers, which is why Quanta stops making you choose.
How Quanta handles it
Run a one-way ANOVA and the omnibus panel says the frequentist part first, that ReliCheck did not find evidence the group means differ. Directly beneath it sits the other half of the story: Bayes factor BF10 = 0.23. Moderate evidence for no group differences. Then, in the same breath, the assumption that produced it, a JZS fixed-effects prior at r scale 0.5, and the note that this is a balanced-design approximation. The number, its meaning in plain English, and the thing you would need to defend it, all in one place.
That pattern holds across the tests. For t-tests, one-sample, paired, and two-sample, Quanta computes the JZS Bayes factor, the standard from Rouder and colleagues. Correlation gets a Bayes factor against the hypothesis of no association, so a weak correlation can be reported as weak evidence for nothing rather than left to imply it. Regression compares your model against the intercept-only model, which turns "does this predictor earn its place" into a question with an answer. One-way ANOVA uses Rouder's method.
Structural equation modeling gets a Bayes factor too, and here Quanta says something most software would rather not. The SEM Bayes factor is BIC-approximate, and Quanta labels it with that word. It is built from the difference in BIC between models, which rests on a different assumption than the t-test does. It approximates the quantity you want. It is not the same object, and a careful reviewer will know. Report it as a BIC-approximate Bayes factor, because that is the label Quanta already put on it.
All of it is validated against R's BayesFactor package, the implementation the field already trusts. Same inputs, same numbers. Quanta was built to match a known standard rather than invent a private one, which is the same reason its frequentist results are checked against R, SPSS, and NIST.
One last thing about reading the number. A Bayes factor close to 1 means the data barely moved anything, and anything under 3 is not worth a sentence in your abstract. That is why 2.4 in the classroom above was called weak instead of dressed up as proof. Evidence has a size. The work is to report it, not to imply it.
Because the question was never whether the program worked. It was whether the study could tell you.
Quanta runs natively on your Mac, offline. Your data never leaves the machine. relicheck.com