Bayesian t tests for accepting and rejecting the null hypothesis.

Progress in science often comes from discovering invariances in relationships among variables; these invariances often correspond to null hypotheses. As is commonly known, it is not possible to state evidence for the null hypothesis in conventional significance testing. Here we highlight a Bayes factor alternative to the conventional t test that will allow researchers to express preference for either the null hypothesis or the alternative. The Bayes factor has a natural and straightforward interpretation, is based on reasonable assumptions, and has better properties than other methods of inference that have been advocated in the psychological literature. To facilitate use of the Bayes factor, we provide an easy-to-use, Web-based program that performs the necessary calculations.

A hierarchical process-dissociation model.

In fitting the process-dissociation model (L. L. Jacoby, 1991) to observed data, researchers aggregate outcomes across participant, items, or both. T. Curran and D. L. Hintzman (1995) demonstrated how biases from aggregation may lead to artifactual support for the model. The authors develop a hierarchical process-dissociation model that does not require aggregation for analysis. Most importantly, the Curran and Hintzman critique does not hold for this model. Model analysis provides for support of process dissociation--selective influence holds, and there is a dissociation in correlation patterns among participants and items. Items that are better recollected also elicit higher automatic activation. There is no correlation, however, across participants; that is, participants with higher recollection have no increased tendency toward automatic activation. The critique of aggregation is not limited to process dissociation. Aggregation distorts analysis in many nonlinear models, including signal detection, multinomial processing tree models, and strength models. Hierarchical modeling serves as a general solution for accurately fitting these psychological-processing models to data.

Detecting chance: a solution to the null sensitivity problem in subliminal priming.

In many paradigms, the persuasiveness of subliminal priming relies on establishing that stimuli are undetectable. The standard significance test approach is ill-suited as null results may reflect either truly undetectable stimuli or a lack of power to resolve weakly detectable stimuli. We present a novel statistical model as an alternative. The model provides for estimates of the probability that each individual is truly at chance. Researchers may select individuals for whom there are sufficiently high probabilities of true undetectability. The model is hierarchical, and estimation is done within the Bayesian framework.

In vivo and in vitro evidence suggest that HB-EGF regulates endometrial expression of human decay-accelerating factor.

Human endometrium expresses the critical complement component C3 in a cyclic fashion, with the highest expression in the secretory phase. As activated complement can kill cells, self or foreign, the secretory endometrial epithelium protects itself by concomitant expression of complement-protective proteins. The objectives of our present study were to describe the spatial and temporal regulation of the complement-protective protein decay-accelerating factor (DAF) in human endometrium and to identify local regulators of its expression. To describe the cyclic regulation of DAF, immunohistochemistry was performed using the IH4 monoclonal antibody on secretory phase endometrial biopsies taken from normal fertile volunteers in LH-timed cycles (n = 114). DAF expression in human endometrium was predominantly localized to the apical membrane of glandular and luminal epithelium. DAF expression, as assessed by histological scoring analysis, was minimal in the proliferative and early secretory phases and increased markedly on approximately day LH +7 (lumen) and LH +8 (glands). Maximal expression was seen in both glands and lumen by LH +8, and this persisted into menses. Using the RL95-2 endometrial epithelial cancer cell line as a model system, we next examined the cellular regulation of DAF. Treatment with E2 and progesterone, alone or in combination, had little effect on DAF expression. Heparin-binding epidermal growth factor-like growth factor (HB-EGF) treatment increased cell surface and total DAF protein, increasing the signal by 260% on flow cytometry and by 200% on Western blot analysis. Stimulation of DAF protein expression was dose dependent, with maximal expression seen at 1 ng/ml. The stimulatory effects of HB-EGF were also observed at the mRNA level. EGF had effects similar to those of HB-EGF on DAF mRNA and protein expression, suggesting that the HB-EGF effect was mediated at least in part by the Her1 EGF receptor subunit. These studies suggest that DAF expression in the midsecretory phase is stimulated by HB-EGF or other members of the EGF family and may function to protect the epithelial integrity of human endometrium in the face of increased complement expression.

An evaluation of the Vincentizing method of forming group-level response time distributions.

Vincentizing (quantile averaging) is a popular means of pooling response time distributions across individuals to produce a group average. The benefit of Vincentizing is that the resulting histogram "looks like" an average of the individuals. In this article, we competitively test Vincentizing against the more mundane approach of averaging parameter estimates from fits to individuals. We simulate data from three distributions: the ex-Gaussian, the Weibull, and the shifted-Wald. For the ex-Gaussian and the shifted-Wald, parameter averaging outperforms Vincentizing. There is only an advantage of Vincentizing for the Weibull and only when there are few observations per participant. Overall, we recommend that researchers use Vincentizing only in select circumstances and with the knowledge that Vincentized estimates are often inconsistent estimators of averaged parameters.

A comment on Heathcote, Brown, and Mewhort's QMLE method for response time distributions.

Heathcote, Brown, and Mewhort (2002) have introduced a new, robust method of estimating response time distributions. Their method may have practical advantages over conventional maximum likelihood estimation. The basic idea is that the likelihood of parameters is maximized given a few quantiles from the data. We show that Heathcote et al.'s likelihood function is not correct and provide the appropriate correction. However, although our correction stands on firmer theoretical ground than Heathcote et al.'s, it appears to yield worse parameter estimates. This result further indicates that, at least for some distributions and situations, quantile maximum likelihood estimation may have better nonasymptotic properties than a more theoretically justified approach.

Gradual growth versus shape invariance in perceptual decision making.

A dominant theme in modeling human perceptual judgments is that sensory neural activity is summed or integrated until a critical bound is reached. Such models predict that, in general, the shape of response time distributions change across conditions, although in practice, this shape change may be subtle. An alternative view is that response time distributions are shape invariant across conditions or groups. Shape invariance is predicted by some race models in which the first of several parallel fibers to communicate the signal determines the response. We competitively assess a specific gradual growth model, the one-bound diffusion model, against a natural shape-invariant competitor: shape invariance in an inverse Gaussian distribution. Assessment of subtle shape change versus shape invariance of response time distributions is aided by a Bayesian approach that allows the pooling of information across multiple participants. We find, conditional on reasonable distributional assumptions, subtle shape changes in response time that are highly concordant with a simple diffusion gradual growth model and discordant with shape invariance.

Hierarchical models for the probabilities of conception.

In the last thirty years, there has been considerable interest in finding better models to fit data for probabilities of conception. An important early model was proposed by Barrett and Marshall (1969) and extended by Schwartz, MacDonald and Heuchel (1980). Recently, researchers have further extended these models by adding covariates. However, the increasingly complicated models are challenging to analyze with frequentist methods such as the EM algorithm. Bayesian models are more feasible, and the computation can be done via Markov chain Monte Carlo (MCMC). We consider a Bayesian model with an effect for protected intercourse to analyze data from the California Women's Reproductive Health Study and assess the effects of water contaminants and hormones. There are two main contributions in the paper. (1) For protected intercourse, we propose modeling the ratios of daily conception probabilities with protected intercourse to corresponding daily conception probabilities with unprotected intercourse. Due to the small sample size of our data set, we assume the ratios are the same for each day but unknown. (2) We consider Bayesian analysis under a unimodality assumption where the probabilities of conception increase before ovulation and decrease after ovulation. Gibbs sampling is used for finding the Bayesian estimates. There is some evidence that the two covariates affect fecundability.

Multivariate regression trees for analysis of abundance data.

Multivariate regression tree methodology is developed and illustrated in a study predicting the abundance of several cooccurring plant species in Missouri Ozark forests. The technique is a variation of the approach of Segal (1992) for longitudinal data. It has the potential to be applied to many different types of problems in which analysts want to predict the simultaneous cooccurrence of several dependent variables. Multivariate regression trees can also be used as an alternative to cluster analysis in situations where clusters are defined by a set of independent variables and the researcher wants clusters as homogeneous as possible with respect to a group of dependent variables.