Hello Aleksander Rodnyy

Maybe this is more a matter of taste.

However, I usually prefer to provide the reader with more information and findings.

Therefore, I think it will be more effective to write the results of effect size and Bayesian t-test.

As a reader, I'd find it convenient to have a scatterplot of the data that also indicated the p-value ("p

Dear Jochen Wilhelm

Thank you for such a detailed answer!

For Bayesian analysis I use JASP and it`s default Cauchy distribution for prior distribution. For Bayesian t-test JASP team also recomend these citations:

Morey, R. D., & Rouder, J. N. (2015). BayesFactor (Version 0.9.11-3)[Computer software].

Rouder, J. N., Speckman, P. L., Sun, D., Morey, R. D., & Iverson, G. (2009). Bayesian t tests for accepting and rejecting the null hypothesis. Psychonomic Bulletin & Review, 16, 225-237.

Do you think it would be correct to publish data processed in this way?

In any case, I am very grateful for your valuable comments.

In my opinion, using "defaults" for Bayesian analyses makes not much sense. If you have specific prior knowledge to include, then use the corresponding prior (reflecting what you already know). Otherwise it seems more like bullshitting to me, as I don't see what miraculous extra value one would get from the data in this way, what goes beyond a simple consideration of the (possibly normalized, if you wish) likelihood.

I would slightly disagree with Jochen Wilhelm . Default priors may help to conduct a Bayesian analysis and maybe some people/audience prefer the Bayesian indices (e.g. BayesFactor or probability of direction) over p-values, BUT here I agree, in this case they do not add really different/new information, since all these parameters are correlated with each other (see Makowski et al., 2019).

In my opinion, Bayesian analyses make sense if you have a) prior knowledge, b) you want to use distributional models with quite specific likelihoods (e.g. "robust" t-distribution instead of a Gaussian), and c) you use Bayesian parameter estimation instead of global indices like BF. But this is just my view.

Makowski, D., Ben-Shachar, M. S., Chen, S. A., & Lüdecke, D. (2019). Indices of effect existence and significance in the Bayesian framework. Frontiers in psychology, 10, 2767.

Another thing that is not taken into account is that when I deliver something a bit divergent from other publications, I have to explain very well to make the results comparable with other research, and if not, I publish according to other studies, to speak in the same context when I want to highlight the result, not the method.

as for what you have to show, too much information could lead to serendipity. So I agree in that respect with Jochen's point.

Rainer Duesing, your position sounds a bit like Fisher's position on Bayesian analysis--see the attached image. ;-)

Bruce Weaver yeah, sounds a little bit like this. ;-) In reality, I would prefer the Bayesian approach nonetheless by now, BUT as we all know, if collaborateurs and/or journals are used to the "classical" approaches, it is difficult to change it (I try to sneak it in through the supplementary material).

But I think both approaches have their own right and you don't have to use a sledgehammer to crack a nut, sometimes a simple t-test can be perfectly fine.

Rainer Duesing do you think it would be better to provide a bunch of BFs and its CIs in supplementary or just use t, p-values and effect sizes in results? One more question - could you please recommend any source to read about informative distributions and how to use it in BF calcs?

Thank you for your valuable comments and advice Carlos Jimenez-Gallardo Rainer Duesing Bruce Weaver Jochen Wilhelm

Aleksander Rodnyy as I said above, it depends on several points and as Jochen Wilhelm said, under default prior conditions, BF and credible interval will not add much new information. Hence, you should think about your audience, what they are used to. If you believe that the Bayesian analyses are worth mentioning, but you want/need to stick to the Frequentist analyses, put the former as additional information in the supplement. Too many information in the manusript may be confusing, but I also think that adding the BF to the Frequentist information does not do any harm.

I am not a proponent of the BF as index, but I think you will find tons of articles from the Wagenmakers research group. If you are more interested in parameter estimation with distributional models (what I prefer), you could start with John Kruschke's and Richard McElreath's books, as well as Paul Bürkner's "brms" package for R (and not to forget Solomon Kurz's "translations" of Kruschke's and McElreath's books to "brms"). You can also calculate BF from distributional parameter estimation, if you analyze it with "brms" and post-process it with "bayestestR" package.

P.S.: Here is a statement from the "bayestestR" package homepage, which I would support: "The adoption of the Bayesian framework for applied statistics, especially in the social and psychological sciences, seems to be developing in two distinct directions. One of the key topics marking their separation is their opinion about the Bayes factor. In short, one school of thought (e.g., the Amsterdam school, led by E. J. Wagenmakers) advocate its use, and emphasize its qualities as a statistical index, while another point to its limits and prefer, instead, the precise description of posterior distributions (using CIs, ROPEs, etc.).

The bayestestR package does not take a side in this debate, and offers tools to carry out analysis irrespective of the school you subscribe to. Instead, it strongly supports the notion of an informed choice."

Present the results of the classical t-test alongside the effect size (Cohen's d) to provide information on the magnitude of the difference. Additionally, include the results of the Bayesian t-test to offer a complementary perspective on the evidence for the observed difference, ensuring clarity and convenience for readers.