‘Atmosphere’, matching,and logic in syllogistic reasoning

The frequency of error in syllogism solving suggests that not all subjects are using logic. The atmosphere and matching hypotheses suggest what they might be doing instead but predict some of the same (correct and incorrect) responses. Reexamination of the data supporting the atmosphere hypothesis (Sells, 1936) shows that the procedure employed was unsatisfactory and that the results obtained support the matching hypothesis as well as they support the atmosphere hypothesis. It is argued on theoretical grounds that the matching hypothesis should be preferred. An experiment is reported in which subjects (N=71) were required to draw conclusions from syllogistic premises and to construct premises from which given conclusions followed. It is shown that subjects may be divided into three groups: (n=16) consisting of subjects who used logic and made few errors; (n=25) of subjects whose correct and incorrect responses were in accordance with the matching hypothesis; and (n=30) of subjects who were not matching but trying to do logic and not doing it well.     

Optimal behavior and concurrent variable interval schedules

Behavior maintained with 2-component concurrent variable interval schedules of reinforcement (CONC VIVI) is described well by the matching law. Deviations from matching behavior have been handled by adding free parameters to the matching law equation. With CONC VIVI schedules there are infinitely many solutions to the matching law equation at each value of the procedural parameters. However, at each value of the procedural parameters, only one combination of durations of intervals spent in each VI component (dwell times) yields the combined maximum reinforcement rate. The equations that yield the optimal dwell times solution for CONC VIVI schedules are mathematically incompatible with the matching law. Optimal performance and matching coincide only when the parameter values of the two VI components are equal. It seems reasonable to use optimal behavior to assess performance in these schedules. Researchers have not compared optimal and empirical performances in CONC VIVI possibly because the equations for optimal dwell times (ODT) can be solved only numerically. We present a table of ODT for a wide range of VIs and changeover delays. We also derive a function m that can be used to compare matching data and the matching behavior predictions of optimization. We prove that 0.5<m<1.003502, and we describe some of the more nteresting properties of the function.     

Managerial career patterns: A review of the empirical evidence

Despite the ubiquitous presence of the term “career patterns” in the discourse about careers, the existing empirical evidence on (managerial) career patterns is rather limited. From this literature review of 33 published empirical studies of managerial and similar professional career patterns found in electronic bibliographic databases, it is clear that upward mobility is still the norm, even when contrasting traditional to “new” careers. We argue that the nature and number of unique career patterns identified is strongly influenced by where and when the data were collected (i.e. empirical access), and how career patterns are measured. Our review further shows organizations clearly still act as containing social structures for the patterning of managerial careers, and that contemporary managerial careers, despite some evidence of increasing inter-organizational mobility, have new boundaries which induce linearity. We provide insights for further conceptualization of managerial career patterns and for advancing methodological approaches, including the use of optimal matching analysis and narratives. By expanding the scope of career pattern dimensions beyond time and direction, this review provides ground for further research on managerial career patterns.     

A partial matching theory of the mirror effect in immediate probed recognition

A set of experiments on immediate probed recognition of digit triples is reported in which the variables were list length (five, six, seven, or eight triples), the probability that a probe was old (.33, .5, or .67), and whether the digit triples were presented with an auditory component or articulatory suppression. Previous work had suggested that the false alarm (FA) rate in this paradigm was lower when auditory information was available than when it was not; this observation had led to the development of thepartial matching theory of immediate probed recognition, according to which FAs could arise not only as a result of unlucky guesses but also when new probes shared a first digit in common with a partially retained target triple. It was argued that partial memory representations were less likely following auditory presentation than following articulatory suppression. Partial matching theory is contrasted with therational response theory, according to which all FAs are unlucky guesses; partial matching theory gave a better account of the present experimental data than did rational response theory. However, a logical relationship between the two theories was suggested, a consequence of which was that rational response theory could be modified to include partial matching in such a way as to account for mirror effects, not only in unusually difficult immediate probed recognition tasks, but also in the more commonly studied mixed test list paradigm involving words of high or low frequency.     

Reinforcement of least-frequent sequences of choices

When a pigeon's choices between two keys are probabilistically reinforced, as in discrete trial probability learning procedures and in concurrent variable-interval schedules, the bird tends to maximize, or to choose the alternative with the higher probability of reinforcement. In concurrent variable-interval schedules, steady-state matching, which is an approximate equality between the relative frequency of a response and the relative frequency of reinforcement of that response, has previously been obtained only as a consequence of maximizing. In the present experiment, maximizing was impossible. A choice of one of two keys was reinforced only if it formed, together with the three preceding choices, the sequence of four successive choices that had occurred least often. This sequence was determined by a Bernoulli-trials process with parameter p. Each of three pigeons matched when p was ½ or ¼. Therefore, steady-state matching by individual birds is not always a consequence of maximizing. Choice probability varied between successive reinforcements, and sequential statistics revealed dependencies which were adequately described by a Bernoulli-trials process with p depending on the time since the preceding reinforcement.     

An analytic comparison of Herrnstein's equations and a multivariate rate equation

Herrnstein's equations are approximations of the multivariate rate equation at ordinary rates of reinforcement and responding. The rate equation is the result of a linear system analysis of variable-interval performance. Rate equation matching is more comprehensive than ordinary matching because it predicts and specifies the nature of concurrent bias, and predicts a tendency toward undermatching, which is sometimes observed in concurrent situations. The rate equation contradicts one feature of Herrnstein's hyperbola, viz., the theoretically required constancy of k. According to the rate equation, Herrnstein's k should vary directly with parameters of reinforcement such as amount or immediacy. Because of this prediction, the rate equation asserts that the conceptual framework of matching does not apply to single alternative responding. The issue of the constancy of k provides empirical grounds for distinguishing between Herrnstein's account and a linear system analysis of single alternative variable-interval responding.     

Probability matching in choice under uncertainty: Intuition versus deliberation

Gaissmaier and Schooler (2008) [Gaissmaier, W., & Schooler, L. J. (2008). The smart potential behind probability matching. Cognition, 109, 416-422] argue that probability matching, which has traditionally been viewed as a decision making error, may instead reflect an adaptive response to environments in which outcomes potentially follow predictable patterns. In choices involving monetary stakes, we find that probability matching persists even when it is not possible to identify or exploit outcome patterns and that many “probability matchers” rate an alternative strategy (maximizing) as superior when it is described to them. Probability matching appears to reflect a mistaken intuition that can be, but often is not, overridden by deliberate consideration of alternative choice strategies.     

Addressing confounding errors when using non-experimental, observational data to make causal claims

In their recent book, Is Inequality Bad for Our Health?, Daniels, Kennedy, and Kawachi claim that to “act justly in health policy, we must have knowledge about the causal pathways through which socioeconomic (and other) inequalities work to produce differential health outcomes.” One of the central problems with this approach is its dependency on “knowledge about the causal pathways.” A widely held belief is that the randomized clinical trial (RCT) is, and ought to be the “gold standard” of evaluating the causal efficacy of interventions. However, often the only data available are non-experimental, observational data. For such data, the necessary randomization is missing. Because the randomization is missing, it seems to follow that it is not possible to make epistemically warranted claims about the causal pathways. Although we are not sanguine about the difficulty in using observational data to make warranted causal claims, we are not as pessimistic as those who believe that the only warranted causal claims are claims based on data from (idealized) RCTs. We argue that careful, thoughtful study design, informed by expert knowledge, that incorporates propensity score matching methods in conjunction with instrumental variable analyses, provides the possibility of warranted causal claims using observational data.     

On two types of deviation from the matching law: bias and undermatching

Data on choice generally conform closely to an equation of the form: log(B₁/B₂)=a log(r₁/r₂+log k, where B₁ and B₂ are the frequencies of responding at Alternatives 1 and 2, r₁ and r₂ are the obtained reinforcement from Alternatives 1 and 2, and a and k are empirical constants. When a and k equal one, this equation is equivalent to the matching relation: B₁/B₂=r₁/r₂. Two types of deviation from matching can occur with this formulation: a and k not equal to one. In some experiments, a systematically falls short of one. This deviation is undermatching. The reasons for undermatching are obscure at present. Some evidence suggests, however, that factors favoring discrimination also favor matching. Matching (a=1) may represent the norm in choice when discrimination is maximal. When k differs from one, its magnitude indicates the degree of bias in choice. The generalized matching law predicts that bias should take this form (adding a constant proportion of responding to the favored alternative). Data from a variety of experiments indicate that it generally does.     

Matching versus optimal data selection in the Wason selection task

It has been reported as a robust effect that people are likely to select a matching case in the Wason selection task. For example, they usually select the 5 case, in the Wason selection task with the conditional “if an E, then a not-5”. This was explained by the matching bias account that people are likely to regard a matching case as relevant to the truth of the conditional (Evans, 1998). However, because a positive concept usually constructs a smaller set than its negative one does (a rarity assumption), it is more effective to get information on the truth of the conditional in a positive set than in a negative set. Thus the optimal data selection account can also explain the effect. The set size of Q and matching by introducing negation were manipulated independently in four experiments. From the results it was inferred that the so-called matching bias was an amalgam of two different cognitive components—relevance judgement by matching and optimal data selection.     

Concurrent random-interval schedules and the matching law

In Experiment I, a group of eight pigeons performed on concurrent random-interval schedules constructed by holding probability equal and varying cycle time to produce ratios of reinforcer densities of 1:1, 3:1, and 5:1 for key pecking. Schedules for a second group of seven were constructed with equal cycle times and unequal probabilities. Both groups deviated from simple matching, but the two forms of the schedules appeared to produce no consistent patterns of deviation. The data were found to be consistent with those obtained in concurrent variable-interval situations. The parameters of the matching equation in the form of Y=k X^a were estimated; the value of k was unity and a was 0.84. In Experiment II, six pigeons were exposed to two conc RI RI schedules in which one component increasingly approximated an FI schedule. The value of k was not 1.0. Concurrent RI RI schedules were shown to represent a continuum from conc FI VI to conc VI VI schedules. The use of the exponential equation in testing “matching laws” suggests that a<1 will continue to be observed, and this will set limits on the form of new laws and the assumed or rational values of the component variables in these laws.     

Predictions from a model of global psychophysics about differences between perceptual and physical matches

A well-known phenomenon is that ??matched?? successive signals do not result in physical identity. This phenomenon has mostly been studied in terms of how much the second of two signals varies from the first, which is called the time-order error (TOE). Here, theoretical predictions led us to study the more general question of how much the matching signal differs from the standard signal, independent of the position of the matching signal as the first or second in a presentation. This we call non-equal matches (NEM). Using Luce??s (Psychological Review, 109, 520?C532, 2002, Psychological Review, 111, 446?C454, 2004, Psychological Review, 115, 601, 2008, Psychological Review, 119, 373?C387, 2012) global psychophysical theory, we predicted NEM when an intensity z is perceived to be ??1 times a standard signal x.?? The theory predicts two different types of individual behaviors for the NEM, and these predictions were evaluated and confirmed in an experiment. We showed that the traditional definition of TOE precludes the observation, and thus the study, of the NEM phenomenon, and that the NEM effect is substantial enough to alter conclusions based on data that it affects. Furthermore, we demonstrated that the custom of averaging data over individuals clearly leads to quite misleading results. An important parameter in this modeling is a reference point that plays a central role in creating variability in the data, so that the key to obtaining regular data from respondents is to stabilize the reference point.     

Learning models for a continuum of sensory states reexamined

Dorfman and Biderman evaluated an additive-operator learning model and some special cases of this model on data from a signal-detection experiment. They found that Kac's pure error-correction model gave the poorest fit of the special models when the predictions were generated from the maximum likelihood estimates and the initial cutoffs were set at an a priori value rather than estimated. First, this paper presents tests of an asymptotic theorem by Norman, which provide strong support for Kac's model. On the final 100 trials, every subject but one gave probability matching, and the response propcrtions appropriately normed were approximately normally distributed with variance π(1 ? π). Further analyses of the Dorfman-Biderman data based upon maximum likelihood and likelihood-ratio tests suggest that Kac's model gives a relatively good, but imperfect fit to the data. Some possible explanations for the apparent contradiction between the results of these new analyses and the original findings of Dorfman and Biderman were explored. The investigations led to the proposal that there may be nonsystematic, random drifts in the decision criterion after correct responses as well as after errors. The hypothesis gives a minor modification of the conclusions from Norman's theorem for Kac's model. It gives asymptotic probability matching for every subject, but a larger asymptotic variance than π(1 ? π), which agrees with the data. The paper also presents good Monte Carlo justification for the use of maximum likelihood and likelihood-ratio tests with these additive learning models. Results from Thomas' nonparametric test of error correction are presented, which are inconclusive. Computation of Thomas' p statistic on the Monte Carlo simulations showed that it is quite variable and insensitive to small deviations from error correction.     

Further confirmation ofsame vs.different processing differences

Two four-digit numbers were matched in a “same-different” reaction time paradigm. In the “all-same” condition, the subject respondedsame if all digits matched anddifferent otherwise. In the “all-different” condition, the subject responded same if at least one digit matched anddifferent if all digits differed. In either condition, the number of matching digits ranged from zero to four. The all-same results supported previous work: the fewer the number of mismatches, the slower the response, except that zero mismatches resulted in a response faster than one mismatch. These findings have been taken as supporting a two-process model: an identity detector mechanism and a self-terminating feature-matching process. An alternative one-process model could explain the results by assuming that the “same” response is primed during the match process. However, the all-different results showed reaction time to be a monotonie function of the number of matching digits. Such a finding contradicted the priming model and supported a two-process model.     

Choice in quail neonates: the origins of generalized matching

Although newborns have surprised scientists with their learning skills, proficiency on concurrent schedules of reinforcement requires (in effect) the ability to integrate and compare behavior–consequence relations over time. Can very young animals obey the quantitative relation that applies to such repeated choices, the generalized matching law? The provenance of the skill is not well understood, and this study provides the first investigation of matching in neonates. Northern bobwhite (Colinus virginianus) hatchlings pecked left and right targets on a touchscreen for heat delivery on a concurrent variable-interval reinforcement schedule. Within 5 days after hatching, the chicks showed sensitivity levels significantly greater than zero, but short of typical adult levels. However, stable sequential patterns emerged almost immediately, including a consistent choose-rich tendency after unreinforced responses, one that entails some degree of temporal integration. These exploratory data suggest that the basic ability to match develops quickly in this precocial species, but that more extensive experience may be required to achieve the higher sensitivities typically seen in adults.     

Undermatching: a reappraisal of performance on concurrent variable-interval schedules of reinforcement

The extant data for pigeons' performance on concurrent variable-interval schedules were examined in detail. Least-squares lines relating relative pecks and time to the corresponding relative reinforcements were obtained for four studies. The between-study group slopes for time and pecks and five of seven within-study group slopes from individual studies were less than 1.00. This suggested the generality that pigeons respond less to the richer reinforcement schedule than predicted by matching. For pecks, a nonparametric test for distribution of points also supported this concept of undermatching (to the richer reinforcement schedule). In addition, using mean squared error as the criterion, a cubic curve fit the peck proportion data better than any line or other polynomial. This indicates that the relation between peck and reinforcement proportions may be nonlinear.     

A preferential matching problem

A matching method proposed by Dr. C. E. Stuart is presented in some detail and the essentials for a test of significance are derived. This method differs from the older matching methods in that partial credit is allowed for a near miss. A slight variation of the method permits the matching of one item withM sets ofn traits.     

Short-term memory in the pigeon with presentation time precisely controlled

Delayed matching-to-sample was studied in the pigeon using a procedure which precisely controlled the presentation time of the sample stimulus. Experiments 1 and 2 revealed that (a) accuracy of matching increased as a negatively accelerated function of presentation time, (b) accuracy declined when an interstimulus interval was introduced between successive presentations of the sample stimulus, and (c) the rate at which accurate matching was restored after an interstimulus interval was greatest when the initial presentation of the sample was short and the interval was long. It was concluded that a theory of STM based on the growth and decay of trace strength could account adequately for all of these findings. Experiment 3 studied trace interaction by presenting two sample stimuli first in succession and then simultaneously for choice. Predictions from trace competition theory about the specific lengths of presentation of these stimuli at which choice of the second stimulus should be 50% or deviate systematically below 50% were not supported. It appears that a recency mechanism in addition to competition is necessary to explain trace interaction effects.     

Perceptual processes in matching and recognition of complex pictures

The role of perceptual feature sampling in speeded matching and recognition was explored in 4 experiments. Experiments 1-3 involved a perceptual matching task with pictures of various objects and scenes. In Experiments 2 and 3, same-different judgments were given under time pressure. The main objective of the matching task was to obtain measures of the perceptual processing rates of different object features. Experiment 4 was an old-new recognition experiment, in which the same stimuli as those in the matching task were used. Response signals were used to limit processing time in the recognition task. The results demonstrated that it is possible to predict speeded recognition performance from performance in perceptual matching. A simple stochastic feature-sampling model provides a unified account of the data from the 4 experiments.     

Testing the hypothesized effect of dysgenic fertility on intelligence with existing reaction time data: A comment on Woodley,te Nijenhuis,and Murphy (2013)

Dysgenic fertility has supposedly resulted in a decline in general intelligence (g) over time. In light of evidence that simple visual reaction time (RT) is inversely related to IQ, Woodley et al. (2013) tested the hypothesized dysgenic effect by subjecting to a meta-regression simple visual RT data collected over 100 years in 15 studies. This analysis found that RT had significantly increased according to a linear function over this time period. Woodley et al. then used this result to estimate the rate at which g had declined over the same period. The present comment points out that there are large gaps in the distribution of RTs analyzed by Woodley et al. with respect to year tested, and that RT in males did not vary as a function of year in the 13 studies published from 1941 on. It is concluded that although existing data are consistent with the idea that g has been adversely affected by dysgenic fertility, it cannot be determined at what rate g has fallen over time.