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Presenting confidence intervals around means is a common method of expressing uncertainty in data. Loftus and Masson (1994) describe confidence intervals for means in within-subjects designs. These confidence intervals are based on the ANOVA mean squared error. Cousineau (2005) presents an alternative to the Loftus and Masson method, but his method produces confidence intervals that are smaller than those of Loftus and Masson. I show why this is the case and offer a simple correction that makes the expected size of Cousineau confidence intervals the same as that of Loftus and Masson confidence intervals. Confidence intervals (CIs) are a staple in the presentation of psychological data because they allow researchers to quickly gage the amount of uncertainty in data (Rouder & Morey, 2005). For within-subjects designs, there are several approaches to creating confidence intervals. For a given design it may not be clear which to choose. Consider a simple within-subjects design with two conditions, a pre-test and post-test. For this design, there are multiple methods of generating confidence intervals. I will discuss each in turn. Approaches to confidence intervals The standard way to build confidence intervals is to compute the standard error of the mean for each condition, and multiply it by the appropriate t-distribution quantile. In order to make this concrete, Table 1 lists hypothetical data for N = 10 participants. A paired t t-test reveals a significant

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Bayesian hypothesis testing presents an attractive alternative to p value hypothesis testing. Part I of this series outlined several advantages of Bayesian hypothesis testing, including the ability to quantify evidence and the ability to monitor and update this evidence as data come in, without the need to know the intention with which the data were collected. Despite these and other practical advantages, Bayesian hypothesis tests are still reported relatively rarely. An important impediment to the widespread adoption of Bayesian tests is arguably the lack of user-friendly software for the run-of-the-mill statistical problems that confront psychologists for the analysis of almost every experiment: the t-test, ANOVA, correlation, regression, and contingency tables. In Part II of this series we introduce JASP (http://www.jasp-stats.org), an open-source, cross-platform, user-friendly graphical software package that allows users to carry out Bayesian hypothesis tests for standard statistical problems. JASP is based in part on the Bayesian analyses implemented in Morey and Rouder’s BayesFactor package for R. Armed with JASP, the practical advantages of Bayesian hypothesis testing are only a mouse click away.

Bayesian parameter estimation and Bayesian hypothesis testing present attractive alternatives to classical inference using confidence intervals and p values. In part I of this series we outline ten prominent advantages of the Bayesian approach. Many of these advantages translate to concrete opportunities for pragmatic researchers. For instance, Bayesian hypothesis testing allows researchers to quantify evidence and monitor its progression as data come in, without needing to know the intention with which the data were collected. We end by countering several objections to Bayesian hypothesis testing. Part II of this series discusses JASP, a free and open source software program that makes it easy to conduct Bayesian estimation and testing for a range of popular statistical scenarios (Wagenmakers et al. this issue).

Visual working memory is often modeled as having a fixed number of slots. We test this model by assessing the receiver operating characteristics (ROC) of participants in a visual-working-memory change-detection task. ROC plots yielded straight lines with a slope of 1.0, a tell-tale characteristic of all-or-none mnemonic representations. Formal model assessment yielded evidence highly consistent with a discrete fixed-capacity model of working memory for this task.working memory ͉ capacity ͉ mathematical models of memory ͉ short-term memory T he study of the nature and capacity of visual working memory (WM) is both timely (1) and controversial (2, 3). A popular conceptualization is that visual WM consists of a fixed number of discrete slots in which items or chunks are temporarily held (2, 4, 5). Nonetheless, there are dissenting viewpoints in which the discreteness is taken as, at most, a convenient oversimplification (6, 7). In this article, we provide a rigorous test of the fixed-capacity model for a visual WM task. Herein, we apply this test to items that differ in color, although the test is suitable to examine the generality of capacity limits across various materials.We used a common version (8-15) of the task popularized by Luck and Vogel (4, 16) (see Fig. 1A). At study, participants are presented with an array of colored squares. At test, a single square is presented; this square is either the same color as the corresponding square in the study array (a "same trial") or a novel color (a "change trial"). Participants simply decide whether the test square is the same as or different from the corresponding studied square. In this task, where the color of each square is unique and the colors are well separated, capacity is the number of squares (objects) that may be held in visual WM. This object-based view of capacity is supported by previous research (4), in which performance does not vary with the number of manipulated features per object.Previous demonstrations of fixed capacity have relied on plotting capacity estimates as a function of the number of to-be-remembered items. Fixed capacity is claimed because capacity estimates tend to asymptote at three to four items for array sizes of four to six items. This approach, however, is not the most rigorous for this model. There are three weaknesses in previous demonstrations: (i) The asymptote of the capacity estimated may be mimicked by models without recourse to fixed capacity; (ii) previous demonstrations are made with aggregate data, and an asymptote in the group aggregate does not necessarily imply asymptotes in all or any individuals; and (iii) the stability of these asymptotes has not been formally assessed. These weaknesses motivate a more constrained test, to be presented subsequently.The Fixed-Capacity Almost-Ideal Observer Model. We define the fixed-capacity ideal observer as one who maximizes the probability of a correct response given the constraint that visual WM is discrete and limited in the number of items that may be held. Here, we derive th...

This article was originally submitted for publication to the Editor of Advances in Methods and Practices in Psychological Science (AMPPS) in 2015. When the submitted manuscript was subsequently posted online (Silberzahn et al., 2015), it received some media attention, and two of the authors were invited to write a brief commentary in Nature advocating for greater crowdsourcing of data analysis by scientists. This commentary, arguing that crowdsourced research "can balance discussions, validate findings and better inform policy" (Silberzahn & Uhlmann, 2015, p. 189), included a new figure that displayed the analytic teams' effectsize estimates and cited the submitted manuscript as the source of the findings, with a link to the preprint. However, the authors forgot to add a citation of the Nature commentary to the final published version of the AMPPS article or to note that the main findings had been previously publicized via the commentary, the online preprint, research presentations at conferences and universities, and media reports by other people. The authors regret the oversight.

This paper introduces JASP, a free graphical software package for basic statistical procedures such as t tests, ANOVAs, linear regression models, and analyses of contingency tables. JASP is open-source and differentiates itself from existing open-source solutions in two ways. First, JASP provides several innovations in user interface design; specifically, results are provided immediately as the user makes changes to options, output is attractive, minimalist, and designed around the principle of progressive disclosure, and analyses can be peer reviewed without requiring a "syntax". Second, JASP provides some of the recent developments in Bayesian hypothesis testing and Bayesian parameter estimation. The ease with which these relatively complex Bayesian techniques are available in JASP encourages their broader adoption and furthers a more inclusive statistical reporting practice. The JASP analyses are implemented in R and a series of R packages.