Perception of correlation reexamined

Almost all studies of adult notions of correlation between dichotomous variables show that people do not incorporate two conditional probabilities as they should according to normative definitions. However, these studies disagree considerably about what correlational notions people do have. This paper identifies three factors that contribute to the variability in research results. The first two factors were mentioned in the literature, and the evidence concerning them is summarized: (1) the way data are presented and (2) the instructions subjects receive. A third factor is suggested and studied; the type of variables between which correlation is judged may affect subjects’ notion of correlation, Specifically, asymmetric, present/absent variables (e.g., symptom: present, absent) may strengthen the incorrect notion of correlation as the tendency of two events to coexist (e.g., presence of symptom and presence of disease) disregarding the complementary events. In three experiments, subjects were asked to choose among five interpretations of the sentence “A strong [or no] relationship exists between [two variables],” The above prediction was confirmed.     

Grelling’s Paradox

Grelling’s Paradox is the paradox which results from considering whether heterologicality, the word-property which a designator has when and only when the designator does not bear the word-property it designates, is had by ‘ ȁ8heterologicality’. Although there has been some philosophical debate over its solution, Grelling’s Paradox is nearly uniformly treated as a variant of either the Liar Paradox or Russell’s Paradox, a paradox which does not present any philosophical challenges not already presented by the two better known paradoxes. The aims of this paper are, first, to offer a precise formulation of Grelling’s Paradox which is clearly distinguished from both the Liar Paradox and Russell’s Paradox; second, to offer a solution to Grelling’s Paradox which both resolves the paradoxical reasoning and accounts for unproblematic predications of heterologicality; and, third, to argue that there are two lessons to be drawn from Grelling’s Paradox which have not yet been drawn from the Liar or Russell’s Paradox. The first lesson is that it is possible for the semantic content of a predicate to be sensitive to the semantic context; i.e., it is possible for a predicate to be an indexical expression. The second lesson is that the semantic content of an indexical predicate, though unproblematic for many cases, can nevertheless be problematic in some cases.     

Computing Power of Tests of the Variance of Treatment Effects in Designs With Two Levels of Nesting

Experiments that involve nested structures may assign treatment conditions either to entire groups (such as classrooms or schools) or individuals within groups (such as students). Although typically the interest in field experiments is in determining the significance of the overall treatment effect, it is equally important to examine the inconsistency of the treatment effect in different groups. This study provides methods for computing power of tests for the variability of treatment effects across level-2 and level-3 units in three-level designs, where, for example, students are nested within classrooms and classrooms are nested within schools and random assignment takes place at the first or the second level. The power computations take into account nesting effects at the second (e.g., classroom) and at the third (e.g., school) level as well as sample size effects (e.g., number of level-1 and level-2 units). The methods can also be applied to quasi-experimental studies that examine the significance of the variation of group differences in an outcome or associations between predictors and outcomes across level-2 and level-3 units.     

Perceptual simulation in property verification

If people represent concepts with perceptual simulations, two predictions follow in the property verification task (e.g., Isface a property of GORILLA?). First, perceptual variables such as property size should predict the performance of neutral subjects, because these variables determine the ease of processing properties in perceptual simulations (i.e., perceptual effort). Second, uninstructed neutral subjects should spontaneously construct simulations to verify properties and therefore perform similarly to imagery subjects asked explicitly to use images (i.e., instructional equivalence). As predicted, neutral subjects exhibited both perceptual effort and instructional equivalence, consistent with the assumption that they construct perceptual simulations spontaneously to verify properties. Notably, however, this pattern occurred only when highly associated false properties prevented the use of a word association strategy. In other conditions that used unassociated false properties, the associative strength between concept and property words became a diagnostic cue for true versus false responses, so that associative strength became a better predictor of verification than simulation. This pattern indicates that conceptual tasks engender mixtures of simulation and word association, and that researchers must deter word association strategies when the goal is to assess conceptual knowledge.     

Relations between visceral and behavioral function in men at bedrest

Multiple physiological measurements as well as a self-assessment of arousal was made in eight men on the first, third, and fifth days of bedrest. On the third day, additional measurements of performance on memory and dexterity tasks were made. Univariate analysis did not reveal any physiological variable to either predict subsequent performance well or to co-vary acutely with it; however, self-rating scores did prove to be useful predictors of subsequent performance. Principal components analysis suggested an“alertness” factor comprised of physiological measures as well as selfratings which helped in predicting better performance. Although the individual patterns of correlations between variables on each of the three test days was variable, even more variability between subjects was found on the performance testing day. We believe this effect of behavioral activation may be due to the injection of common, slow temporal trends into many of the different data sets.     

The generation effect: A meta-analytic review

The generation effect refers to the finding that subjects who generate information (e.g., produce synonyms) remember the information better than they do material that they simply read. Meta-analytic techniques were used to summarize 445 effect sizes over 86 studies, thereby assessing the magnitude and 11 potential moderators of the generation effect. The size of the generation effect across the 86 studies was .40--a benefit of almost half a standard deviation of generation over reading. The variability of the effect size due to moderator type was substantial, and we attempted to use this information to clarify several theories that have been proposed to explain the generation effect.     

Intraindividual Variability of Neuromotor Function Predicts Falls Risk in Older Adults and those with Type 2 Diabetes

This study was designed to examine the effect of increasing age and type 2 diabetes on the average responses and inter- and intraindividual variability of falls risk, reaction time, strength, and walking speed for healthy older adults and older persons with type 2 diabetes (T2DM). Seventy-five older individuals (controls) and 75 persons with T2DM aged between 50 and 79 years participated in the study. Assessments of falls risk, reaction time (RT), knee extension strength, and walking speed were conducted. The results revealed that advancing age for both control and T2DM groups was reflected by a progressive increase in falls risk, decreased leg strength and a decline (i.e., slowing) of reactions and gait speed. Conversely, the level of intraindividual variability for the RT, strength and gait measures increased with increasing age for both groups, with T2DM persons tending to be more variable compared to the healthy controls of similar age. In contrast to the intraindividual changes, measures of interindividual variability revealed few differences between the healthy elderly and T2DM individuals. Taken together, the findings support the proposition that intraindividual variability of neuromotor measures may be useful as a biomarker for the early detection of decline in physiological function due to age or disease.     

Variability and detection of invariant structure

Two experiments investigated learning of nonadjacent dependencies by adults and 18–month–olds. Each learner was exposed to three–element strings (e.g., pel–kicey–jic) produced by one of two artificial languages. Both languages contained the same adjacent dependencies, so learners could distinguish the languages only by acquiring dependencies between the first and third elements (the nonadjacent dependencies). The size of the pool from which the middle elements were drawn was systematically varied to investigate whether increasing variability (in the form of decreasing predictability between adjacent elements) would lead to better detection of nonadjacent dependencies. Infants and adults acquired nonadjacent dependencies only when adjacent dependencies were least predictable. The results point to conditions that might lead learners to focus on nonadjacent versus adjacent dependencies and are important for suggesting how learning might be dynamically guided by statistical structure.     

Self-concept and psychosocial adjustment in adolescence

This study analyses the relationship between a multidimensional measure of self-concept, Self-concept Form-5 Questionnaire (AF5), and a broad set of adolescents' psychosocial adjustment indicators. From the responses of 1,281 participants (53.7% females) aged 12 to 17 years ( M = 14.98 years, SD = 1.74 years), results indicated that higher self-concept scores corresponded to better psychological adjustment, good personal skills and fewer behavioral problems. Although a positive relationship between social self-concept and drug use was found, this significant relationship disappeared once the adolescent's age and sex was controlled for. These results support the idea that the self-concept is a basic theoretical construct closely related to the psychosocial adjustment in adolescence. Also this study helps explain some contradictory results reported in the literature (i.e., a positive relationship between social self-concept and drug use), by showing how the statistical control of a third variable effect (i.e., age) avoids reaching conclusions based on spurious relationships.     

Visual variability affects early verb learning

Research demonstrates that within‐category visual variability facilitates noun learning; however, the effect of visual variability on verb learning is unknown. We habituated 24‐month‐old children to a novel verb paired with an animated star‐shaped actor. Across multiple trials, children saw either a single action from an action category (identical actions condition, for example, travelling while repeatedly changing into a circle shape) or multiple actions from that action category (variable actions condition, for example, travelling while changing into a circle shape, then a square shape, then a triangle shape). Four test trials followed habituation. One paired the habituated verb with a new action from the habituated category (e.g., ‘dacking’ + pentagon shape) and one with a completely novel action (e.g., ‘dacking’ + leg movement). The others paired a new verb with a new same‐category action (e.g., ‘keefing’ + pentagon shape), or a completely novel category action (e.g., ‘keefing’ + leg movement). Although all children discriminated novel verb/action pairs, children in the identical actions condition discriminated trials that included the completely novel verb, while children in the variable actions condition discriminated the out‐of‐category action. These data suggest that – as in noun learning – visual variability affects verb learning and children's ability to form action categories.     

Aging and intraindividual variability in performance: analyses of response time distributions

It has been suggested that older adults are more variable in their performance because they are more prone to lapses of either attention or intention. In the present experiment, 9 young and 9 older adults each performed nearly 2000 trials of a same-different judgment task. As expected, older adults were slower and more variable than young adults. When the age-related difference in speed was taken into account, however, the older adults were, if anything, less variable than the young adults. When younger and older adults' RT distributions were analyzed using quantile-quantile plots and by fitting ex-Gaussian and Weibull functions, there was no consistent evidence that older adults' distributions were more skewed than young adults', as would be predicted by age-related increases in lapses of attention or intention. Importantly, there was a positive, linear relation between RT and intraindividual variability, and the same relation was observed both within subjects (practice increased speed and reduced variability) as well as between subjects (regardless of age, slower individuals were more variable). Thus, the present results suggest that there may be a general law governing the relation between average RT and variability, and that the greater performance variability of older adults primarily reflects their greater average RTs.     

Prediction and judgment as indicators of sensitivity to covariation of continuous variables

The present study used both judgments of strength of relationship and measures of the ability to predict one variable from another to assess subjects’ sensitivity to the covariation of two continuous variables. In addition, one group of subjects judged strength of relationship after merely observing the presentation of 60 pairs of two-digit numbers, and a second group made strength judgments after being actively engaged in predicting one member of a pair when given the other. The prediction and judgment data provide different pictures of subjects’ sensitivity to covariation. The subjects were quite poor at estimating strength of relationship but, by some measures, good at predicting one variable from another. Judgments were not strongly influenced by whether subjects had previously engaged in overt prediction. The implications of these results for the literature on covariation estimation are discussed.     

A global factor in the Hermann grid illusion or an artifact?

In the first of the present experiments, subjects were required to estimate the strength of the Hermann grid illusion in grids containing various numbers of intersectionseven though those grids were not actually presented. The positive relationship found by Wolfe (1984) for real grids was, nevertheless, replicated. It is argued that this suggests that a response bias might have been the source of his effect (although other possibilities are also noted). In addition, in a second experiment, subjects who were not aware of the fact that grid size was being manipulated (i.e., between subjects) showed no consistent effect of that factor, thus supporting the same suggestion.     

Searching for reliable relationships with statistics packages: an empirical example of the potential problems

Many social scientists appear to possess an overconfidence in the reliability of research results from a single, small-sample, inferential study. In this article, the authors speculate that "user-friendly" statistics packages have the potential to exacerbate statistical misinterpretation by providing researchers with a tool to explore data easily and identify what is interpreted as "reliable" relationships. This article contains an empirical demonstration of the potential problems that arise when a large number of statistical tests are interpreted. Results show that statistically significant results may be unreliable. Also, a zero relationship can erroneously appear as a medium to large effect size relationship when a small sample is used (e.g., n = 30). The authors suggest the need for multiple replications as the criterion of a reliable finding.     

Understanding the effects of sample size on the variability of the mean

In the first three experiments, we attempted to learn more about subjects' understanding of the importance of sample size by systematically changing aspects of the problems we gave to subjects. In a fourth study, understanding of the effects of sample size was tested as subjects went through a computerassisted training procedure that dealt with random sampling and the sampling distribution of the mean. Subjects used sample size information more appropriately for problems that were stated in terms of the accuracy of the sample average or the center of the sampling distribution than for problems stated in terms of the tails of the sampling distribution. Apparently, people understand that the means of larger samples are more likely to resemble the population mean but not the implications of this fact for the variability of the mean. The fourth experiment showed that although instruction about the sampling distribution of the mean led to better understanding of the effects of sample size, subjects were still unable to make correct inferences about the variability of the mean. The appreciation that people have for some aspects of the law of large numbers does not seem to result from an in-depth understanding of the relation between sample size and variability.     

Priming and binding in and across perception and action: a correlational analysis of the internal structure of event files

Individual performance was compared across three different tasks that tap into the binding of stimulus features in perception, the binding of action features in action planning, and the emergence of stimulus-response bindings (“event files”). Within a task correlations between the size of binding effects were found within visual perception (e.g., the strength of shape-location binding correlated positively with the strength of shape-colour binding) but not between perception and action planning, suggesting different, domain-specific binding mechanisms. To some degree, binding strength was predicted by priming effects of the respective features, especially if these features varied on a dimension that matched the current attentional set.     

Priming and binding in and across perception and action: A correlational analysis of the internal structure of event files

Individual performance was compared across three different tasks that tap into the binding of stimulus features in perception, the binding of action features in action planning, and the emergence of stimulus–response bindings (“event files”). Within a task correlations between the size of binding effects were found within visual perception (e.g., the strength of shape–location binding correlated positively with the strength of shape–colour binding) but not between perception and action planning, suggesting different, domain-specific binding mechanisms. To some degree, binding strength was predicted by priming effects of the respective features, especially if these features varied on a dimension that matched the current attentional set.     

SENSORY AND PREPARATORY FACTORS IN RESPONSE LATENCY: The visual intensity function

Simple reaction times under irregular order of stimulus presentation are studied as a function of three luminous intensities viewed foveally and covering five log I units at the upper half of the brightness scale. Response latency varies inversely and rectilineariy with log I within this range. Respondents tend to converge in average latency but differ more in variability as stimulus strength is reduced, the more variable subjects even at high intensity suffering relatively greater loss in speed. Both positive and negative practice effects are observed, which seem partly dependent on stimulus intensity.     

Immediate reproduction of temporal information under four cognitive strategies

The main purpose was to determine the retention characteristics of temporal information when subjects experienced time under a retention interval of immediate reproduction and various cognitive strategies for time estimation. Four levels of cognitive strategy were used, viz., conscious, mental counting, counting aloud without auditory cues, and counting aloud with auditory cues. The latter three cognitive strategies were experimenter-defined, time-aiding techniques. Subjects were instructed to refrain from employing time-aiding techniques under a conscious cognitive strategy for time estimation. Visual durations of 1, 2, and 4 sec. were estimated by 12 subjects under the method of reproduction. Two measures of performance were computed, viz., variable and constant errors. The general conclusions were: (a) the effectiveness of mental counting, counting aloud without auditory cues, and counting aloud with auditory cues as cognitive strategies over conscious cognitive strategy in terms of variability depends on the duration used, and (b) in terms of accuracy and variability an increase in the number of cues under time-aiding techniques does not necessarily produce better performance.     

Effects of UCS intensity and postpeak acquisition trials on classical conditioning of the SCR

The present study examined the effects of UCS intensity and number of postpeak acquisition trials on classical conditioning and extinction of the SCR. A 2 × 3 design was employed in which subjects received either a 1, 2, or 4 mA shock UCS and either two or 16 acquisition trials beyond the peak CR. While conditioning was demonstrated during acquisition, there was no relationship between strength of conditioning and intensity of UCS. The phenomenon of stronger resistance to extinction following fewer acquisition trials (e.g., two past the peak CR) than with many (e.g., 16 past the peak CR) was demonstrated only for the groups that were conditioned with the 4 mA UCS. Resistance to extinction varied positively with UCS intensity, but only for the subjects who received two postpeak acquisition trials. Sixteen trials beyond the peak CR resulted in the UCS intensity having little or no effect on resistance to extinction.