Pseudodiagnosticity and preference hierarchy in a search-only inference paradigm.

Bayes' Theorem provides a rationality-standard for information search when there are two mutually exclusive hypotheses and one or more statistical cues pertaining to the likelihoods of the hypotheses. Prior research shows that when people already have a cue pertaining to a hypothesis and are asked to seek additional information to help decide which hypothesis is correct, they tend to exhibit a specific form of pseudodiagnosticity: Rather than seek information that would assess the same cue relative to an alternative hypothesis, they tend to seek information about how a second cue would pertain to the first hypothesis. For example, if people are told that 70% of genuine paintings are landscapes, they then seek to know the percentage of genuine paintings that are watercolor rather than the percentage of fake paintings that are landscapes. However, this response pattern has sometimes been violated in a way that may depend on the cues' numerical values (e.g., 70% vs. 30%), thus raising a question as to the nature of the bias: Does the selection bias characterize the search process per se, or does it reflect the manner in which people utilize already-obtained percentage information? To address these issues, we employed a novel, search-only judgment paradigm in which people were asked to search for cues and to select them without ever obtaining the cues' percentage values. The results confirmed a tendency toward same-hypothesis pseudodiagnosticity both in primary (i.e., most-preferred) and secondary preference, and supported a model in which pseudodiagnosticity can proceed with or without numerical cue data.

Variation in scatterplot displays.

Scatterplots are typically constructed for the purpose of showing the association between two variables. We argue that such scatterplots should not vary in ways that are unrelated to the degree of association. Noting that the publication standards for the preparation of scatterplots are minimal, we review empirical literature that shows that a number of arbitrary features of scatterplots influence the inferences drawn by users. We discuss nine such features. We also review the literature that recommends how scatterplots should be prepared, and we examine 221 scatterplots published in recent journals. There was considerable variation among those published scatterplots. This article concludes with a call for further standardization by way of flexible guidelines.

Probabilistically Valid Inference of Covariation From a Single x,y Observation When Univariate Characteristics Are Known.

Participants were asked to draw inferences about correlation from single x,y observations. In Experiment 1 statistically sophisticated participants were given the univariate characteristics of distributions of x and y and asked to infer whether a single x, y observation came from a correlated or an uncorrelated population. In Experiment 2, students with a variety of statistical backgrounds assigned posterior probabilities to five possible populations based on single x, y observations, again given knowledge of the univariate statistics. In Experiment 3, statistically naïve participants were given a problem analogous to that given in Experiment 1, framed verbally. Experiment 4 replicated Experiment 3 but added an "impossible to determine" response option. Models that rely on computing sample correlations make no predictions about these investigations. From a Bayesian perspective, participants' inferences in all four experiments tended to make probabilistically valid inferences as long as the single datum was directional. The results are discussed in light of the Brunswikian notion of vicarious functioning.

Sample size and correlational inference.

In 4 studies, the authors examined the hypothesis that the structure of the informational environment makes small samples more informative than large ones for drawing inferences about population correlations. The specific purpose of the studies was to test predictions arising from the signal detection simulations of R. B. Anderson, M. E. Doherty, N. D. Berg, and J. C. Friedrich (2005). The results of a simulation study in the present article confirmed and extended previous theoretical claims (R. B. Anderson et al., 2005) that in a yes/no correlation detection task, small-sample advantages should occur but should be restricted to particular decision conditions. In 3 behavioral studies, participants viewed larger or smaller samples of data pairs and judged whether each sample had been drawn from a population characterized by a zero correlation or from one characterized by a greater-than-zero correlation. Consistent with traditional statistical theory, accuracy tended to be greater for larger than for smaller samples, though there was a small-sample advantage in 1 experimental condition. The results are discussed in relation to alternative theoretical and behavioral paradigms such as those of Y. Kareev (e.g., 2005) and K. Fiedler and Y. Kareev (2006).

The perception of scatterplots.

Four experiments investigated the perception of correlations from scatterplots. All graphic properties, other than error variance, that have been shown to affect subjective but not objective correlation (r) were held constant. Participants in Experiment 1 ranked 21 scatterplots according to the magnitude of r. In Experiments 2 and 3, participants made yes/no judgments to indicate whether a scatterplot was high (signal) or low (noise). Values of r for signal and noise scatterplots varied across participants. Differences between correlations for signal and for noise scatterplots were constant in r in Experiment 2, and constant in r2 in Experiment 3. Standard deviations of the ranks in Experiment 1 and d' values in Experiments 2 and 3 showed that discriminability increased with the magnitude of r. In Experiment 4, faculty and graduate students in psychology and sociology made point estimates of r for single scatterplots. Estimates were negatively accelerated functions of objective correlation.

Sample size and the detection of means: a signal detection account.

Using statistical theory as a basis, Kareev (e.g., 1995) claimed that people's ability to correctly infer the existence of a population correlation should be greater for small than for large samples. Simulations by R. B. Anderson, Doherty, Berg, and Friedrich (2005) identified conditions favoring small samples but could not determine whether such an advantage was due to sampling skew, variance, or central tendency displacement. In the present study, we investigated theoretical effects of sample size (n) on the detection of population means under circumstances in which sampling variance is unconfounded with skew or central tendency displacement. The results demonstrate an extremely limited, criterion-specific, small-sample advantage that was attributable to n-related sampling variance and that occurred only with highly conservative, suboptimal criterion placement.

Sample size and the detection of correlation--a signal detection account: comment on Kareev (2000) and Juslin and Olsson (2005).

Simulations examined the hypothesis that small samples can provide better grounds for inferring the existence of a population correlation, p, than can large samples. Samples of 5, 7, 10, 15, or 30 data pairs were drawn either from a population with p=0 or from one with p>0. When decision accuracy was assessed independently for each level of the decision criterion, there was a criterion-specific small-sample advantage. For liberal criteria, accuracy was greater for large than for small samples, but for conservative criteria, the opposite result occurred. There was no small-sample advantage when accuracy was measured as the area under a receiver operating characteristic curve or as the posterior probability of a hit. The results show that small-sample advantages can occur, but under limited conditions.