Posted on Feb 16th, 2018

**Summary:** When Bayesians speak of probability, they mean plausibility.

The famous Matrix trilogy is set in a dystopic future where most of mankind has been enslaved by a computer network, and the few rebels that remain find themselves on the brink of extinction. Just when the situation seems beyond salvation, a messiah –called Neo– is awakened and proceeds to free humanity from its silicon overlord. Rather than turn the other cheek, Neo’s main purpose seems to be the physical demolition of his digital foes (‘agents’), a task that he engages in with increasing gusto and efficiency. Aside from the jaw-dropping fight scenes, the Matrix movies also contain numerous references to religious themes and philosophical dilemma’s. One particularly prominent theme is the concept of free will and the nature of probability.

Posted on Feb 9th, 2018

In an earlier blog post we discussed a response (co-authored by 88 researchers) to the paper “Redefine Statistical Significance” (RSS; co-authored by 72 researchers). Recall that RSS argued that *p*-values near .05 should be interpreted with caution, and proposed that a threshold of .005 is more in line with the kind of evidence that warrants strong claims such as “reject the null hypothesis”. The response (“bring your own alpha”, BYOA) argued that researchers should pick their own alpha, informed by the context at hand. Recently, the BYOA response was covered in *Science*, and this prompted us to read the revised, final version (hat tip to Brian Nosek, who attended us to the change in content; for another critique of the BYOA paper see this preprint by JP de Ruiter).

Posted on Feb 1st, 2018

*This is a guest post by Scott Glover.*

In a recent blog post, Eric-Jan and Quentin helped themselves to some more barbecued chicken.

The paper in question reported a *p*-value of 0.028 as “clear evidence” for an effect of ego depletion on attention control. Using Bayesian analyses, Eric-Jan and Quentin showed how weak such evidence actually is. In none of the scenarios they examined did the Bayes Factor exceed 3.5:1 in favour of the effect. An analysis of this data using my own preferred method of likelihood ratios (Dixon, 2003; Glover & Dixon, 2004; Goodman & Royall, 1988) gives a similar answer – an AIC-adjusted (Akaike, 1973) value of λadj = 4.1 (calculation provided here) – meaning the data are only about four times as likely given the effect exists than given no effect. This is consistent with the Bayesian conclusion that such data hardly deserve the description “clear evidence.” Rather, these demonstrations serve to highlight the greatest single problem with the *p*-value – *it is simply not a transparent index of the strength of the evidence*.

Beyond this issue, however, is another equally troublesome problem, one inherent to null hypothesis significance testing (NHST): *any-sized effect can be coaxed into being statistically significant by increasing the sample size* (Cohen, 1994; Greenland et al., 2016; Rozeboom, 1960). In the ego depletion case, a tiny effect of 0.7% is found to be significant thanks to a sample size in the hundreds.