Distribution of the product confidence limits for the indirect effect: Program PRODCLIN

This article describes a program, PRODCLIN (distribution of the PRODuct Confidence Limits for INdirect effects), written for SAS, SPSS, and R, that computes confidence limits for the product of two normal random variables. The program is important because it can be used to obtain more accurate confidence limits for the indirect effect, as demonstrated in several recent articles (MacKinnon, Lockwood, & Williams, 2004; Pituch, Whittaker, & Stapleton, 2005). Tests of the significance of and confidence limits for indirect effects based on the distribution of the product method have more accurate Type I error rates and more power than other, more commonly used tests. Values for the two paths involved in the indirect effect and their standard errors are entered in the PRODCLIN program, and distribution of the product confidence limits are computed. Several examples are used to illustrate the PRODCLIN program. The PRODCLIN programs in rich text format may be downloaded from www.psychonomic.org/archive.     

BootES: An R package for bootstrap confidence intervals on effect sizes

Bootstrap Effect Sizes (bootES; Gerlanc & Kirby, 2012) is a free, open-source software package for R (R Development Core Team, 2012), which is a language and environment for statistical computing. BootES computes both unstandardized and standardized effect sizes (such as Cohen’s d, Hedges’s g, and Pearson’s r) and makes easily available for the first time the computation of their bootstrap confidence intervals (CIs). In this article, we illustrate how to use bootES to find effect sizes for contrasts in between-subjects, within-subjects, and mixed factorial designs and to find bootstrap CIs for correlations and differences between correlations. An appendix gives a brief introduction to R that will allow readers to use bootES without having prior knowledge of R.     

Age differences in feeling-of-knowing and confidence judgements as a function of knowledge domain

For two semantic knowledge domains, general and computer-related, feeling-of-knowing (FOK) and confidence level (CL) ratings and their relative accuracy were assessed in young, middle-aged, and older adults, after test difficulty was equated across age groups. Global memory self-efficacy beliefs were also assessed for each domain. As expected, greater age was associated with poorer memory self-efficacy beliefs only in the computer domain. The oldest two groups were found to be more underconfident than young adults when rating their FOK but not their CL, for computer items but not for general items. Statistical control of age differences in memory self-efficacy beliefs in the relevant domain greatly reduced this age effect on computer-related FOK ratings. This finding suggests that absolute FOK judgments are more closely related to memory self-efficacy beliefs than are CL judgments. Gamma correlations between judgments and recognition performance revealed that all age groups were equally accurate in FOK and in CL judgments, in both domains.     

An application of the poisson race model to confidence calibration

In tasks as diverse as stock market predictions and jury deliberations, a person's feelings of confidence in the appropriateness of different choices often impact that person's final choice. The current study examines the mathematical modeling of confidence calibration in a simple dual-choice task. Experiments are motivated by an accumulator model, which proposes that information supporting each alternative accrues on separate counters. The observer responds in favor of whichever alternative's counter first hits a designated threshold. Confidence can then be scaled from the difference between the counters at the time that the observer makes a response. The authors examine the overconfidence result in general and present new findings dealing with the effect of response bias on confidence calibration.     

Remember,know, confidence and the mirror effect: Changes as a function of discriminability conditions

Recognition memory for Spanish-Catalan cognate and noncognate words was tested at retention intervals of 20 minutes, 1 hour, and 24 hours (Experiment 1) using a remember/know response procedure, and requiring a confidence judgement on the yes/no response. Noncognate words were accompanied by more “remember” responses than cognates, and overall A' was significantly different from remember A', except in the cognate condition at the longest retention interval. A strong mirror effect for the cognate-noncognate stimulus class was found for overall responding, and for high but not low confidence, indicating a differential use of recollection and familiarity in recognition. In general, the pattern of results was inconsistent with Donaldson's (1996) signal detection model, indicating that, when available, subjects use two different sources of information for discrimination. The examination of individual hits and false alarms as a function of confidence indicated that “remember” is uniformly associated with high confidence, but “know” shows a bipolar pattern. In Experiment 2, new and old words were repeated at test 2 and 3. Repetition greatly affected the difference between the discrimination indices, indicating that an increase in the familiarity of new words prevented the use of a dual source of information in recognition. Results are discussed in terms of Rajaram's distinctiveness (1996, 1998) and Reder, Nhouyvanisvong, Schunn, Ayers, Angstadt, and Hiraki's (2000) SAC theories.     

Thoughts on the limits of a mutual technique*

Ferenczi’s appreciation of the inherently mutual nature of the analytic encounter led him, and many who followed, to explore the value of mutual openness between patient and analyst. Specifically, Ferenczi saw the analyst’s openness as an antidote to his earlier defensive denial of his failings and ambivalence toward the patient, which had undermined his patient’s trust. My own view is that, while the analyst’s openness with the patient can indeed help reestablish trust and restore a productive analytic process in the short term, it also poses long-term dangers. In certain treatments it may encourage “malignant regression”, where the patient primarily seeks gratification from the analyst, resulting in an unmanageable “unending spiral of demands or needs” (Balint, 1968, p. 146). I suggest that an analyst’s “confessions”, in response to the patient’s demand for accountability, can sometimes reinforce the patient’s fantasy that healing comes from what the analyst gives or from turning the tables on his own sense of helplessness and shame by punishing or dominating the analyst. In such situations, the patient’s fantasy may dovetail with the analyst’s implicit theory that healing includes absorbing the patient’s pain and even accepting his hostility, thus confirming the patient’s fantasies, intensifying his malignant regression and dooming the treatment to failure. When malignant regression threatens, the analyst must set firmer boundaries, including limits on her openness, in order to help the patient shift his focus away from expectations of the analyst and toward greater self-reflection. This requires the analyst to resist the roles of rescuer, failure, or victim—roles rooted in the analyst’s own unconscious fantasies.     

Statistical inference for a linear function of medians: confidence intervals,hypothesis testing,and sample size requirements

When the distribution of the response variable is skewed, the population median may be a more meaningful measure of centrality than the population mean, and when the population distribution of the response variable has heavy tails, the sample median may be a more efficient estimator of centrality than the sample mean. The authors propose a confidence interval for a general linear function of population medians. Linear functions have many important special cases including pairwise comparisons, main effects, interaction effects, simple main effects, curvature, and slope. The confidence interval can be used to test 2-sided directional hypotheses and finite interval hypotheses. Sample size formulas are given for both interval estimation and hypothesis testing problems.     

An antisymmetric psychometric function on a logarithmic scale

This very brief report introduces a psychometric function, very suitable for psychophysical data that displays Weber-like behaviour, because it is antisymmetric on a logarithmic scale.