Stop saying confidence intervals are "better" than p values

One of the common tropes one hears from advocates of confidence intervals is that they are superior, or should be preferred, to p values. In our paper "The Fallacy of Placing Confidence in Confidence Intervals", we outlined a number of interpretation problems in confidence interval theory. We did this from a mostly Bayesian perspective, but in the second section was an example that showed why, from a frequentist perspective, confidence intervals can fail. However, many people missed this because they assumed that the paper was all Bayesian advocacy. The purpose of this blog post is to expand on the frequentist example that many people missed; one doesn't have to be a Bayesian to see that confidence intervals can be less interpretable than the p values they are supposed to replace. Andrew Gelman briefly made this point previously, but I want to expand on it so that people (hopefully) more clearly understand the point.

Asymmetric funnel plots without publication bias

In my last post about standardized effect sizes, I showed how averaging across trials before computing standardized effect sizes such as partial \(\eta^2\) and Cohen's d can produce arbitrary estimates of those quantities. This has drastic implications for meta-analysis, but also for the interpretations of these effect sizes.  In this post, I use the same facts to show how one can obtain asymmetric funnel plots — commonly taken to indicate publication bias — without any publication bias at all. You should read the previous post if you haven't already.

Averaging can produce misleading standardized effect sizes

Recently, there have been many calls for a focus on effect sizes in psychological research. In this post, I discuss how naively using standardized effect sizes with averaged data can be misleading. This is particularly problematic for meta-analysis, where differences in number of trials across studies could lead to very misleading results.

The fallacy of placing confidence in confidence intervals (version 2)

I, with my coathors, have submitted a new draft of our paper "The fallacy of placing confidence in confidence intervals". This paper is substantially modified from its previous incarnation. Here is the main argument:

"[C]onfidence intervals may not be used as suggested by modern proponents because this usage is not justified by confidence interval theory. If used in the way CI proponents suggest, some CIs will provide severely misleading inferences for the given data; other CIs will not. Because such considerations are outside of CI theory, developers of CIs do not test them, and it is therefore often not known whether a given CI yields a reasonable inference or not. For this reason, we believe that appeal to CI theory is redundant in the best cases, when inferences can be justified outside CI theory, and unwise in the worst cases, when they cannot."

The document, source code, and all supplementary material is available here on github.

Multiple Comparisons with BayesFactor, Part 2 - order restrictions

In my previous post, I described how to do multiple comparisons using the BayesFactor package. Part 1 concentrated on testing equality constraints among effects: for instance, that the the effects of two factor levels are equal, while leaving the third free to be different. In this second part, I will describe how to test order restrictions on factor level effects. This post will be a little more involved than the previous one, because BayesFactor does not currently do order restrictions automatically.

Again, I will note that these methods are only meant to be used for pre-planned comparisons. They should not be used for post hoc comparisons.

Multiple Comparisons with BayesFactor, Part 1

One of the most frequently-asked questions about the BayesFactor package is how to do multiple comparisons; that is, given that some effect exists across factor levels or means, how can we test whether two specific effects are unequal. In the next two posts, I'll explain how this can be done in two cases: in Part 1, I'll cover tests for equality, and in Part 2 I'll cover tests for specific order-restrictions.

Before we start, I will note that these methods are only meant to be used for pre-planned comparisons. They should not be used for post hoc comparisons.