The corroboration paradox

Evidentiary propositions E ₁ and E ₂, each p-positively relevant to some hypothesis H, are mutually corroborating if p(H|E ₁ ∩ E ₂) > p(H|E _i ), i = 1, 2. Failures of such mutual corroboration are instances of what may be called the corroboration paradox. This paper assesses two rather different analyses of the corroboration paradox due, respectively, to John Pollock and Jonathan Cohen. Pollock invokes a particular embodiment of the principle of insufficient reason to argue that instances of the corroboration paradox are of negligible probability, and that it is therefore defeasibly reasonable to assume that items of evidence positively relevant to some hypothesis are mutually corroborating. Taking a different approach, Cohen seeks to identify supplementary conditions that are sufficient to ensure that such items of evidence will be mutually corroborating, and claims to have identified conditions which account for most cases of mutual corroboration. Combining a proposed common framework for the general study of paradoxes of positive relevance with a simulation experiment, we conclude that neither Pollock’s nor Cohen’s claims stand up to detailed scrutiny. I am quite prepared to be told…”oh, that is an extreme case: it could never really happen!” Now I have observed that this answer is always given instantly, with perfect confidence, and without any examination of the proposed case. It must therefore rest on some general principle: the mental process being something like this—“I have formed a theory. This case contradicts my theory. Therefore, this is an extreme case, and would never occur in practice.” Rev. Charles L. Dodgson      

SPSS macros to compare any two fitted values from a regression model

In regression models with first-order terms only, the coefficient for a given variable is typically interpreted as the change in the fitted value of Y for a one-unit increase in that variable, with all other variables held constant. Therefore, each regression coefficient represents the difference between two fitted values of Y. But the coefficients represent only a fraction of the possible fitted value comparisons that might be of interest to researchers. For many fitted value comparisons that are not captured by any of the regression coefficients, common statistical software packages do not provide the standard errors needed to compute confidence intervals or carry out statistical tests—particularly in more complex models that include interactions, polynomial terms, or regression splines. We describe two SPSS macros that implement a matrix algebra method for comparing any two fitted values from a regression model. The !OLScomp and !MLEcomp macros are for use with models fitted via ordinary least squares and maximum likelihood estimation, respectively. The output from the macros includes the standard error of the difference between the two fitted values, a 95% confidence interval for the difference, and a corresponding statistical test with its p-value.     

Finite axiomatization for some intermediate logics

LetN. be the set of all natural numbers (except zero), and letD _n ^* = {k ∈N ∶k|n} ∪ {0} wherek¦n if and only ifn=k.x f or somex∈N. Then, an ordered setD _n ^* = 〈D _n ^* , ? _n , wherex? _ny iffx¦y for anyx, y∈D _n ^* , can easily be seen to be a pseudo-boolean algebra. In [5], V.A. Jankov has proved that the class of algebras {D _n ^* ∶n∈B}, whereB =,{k ∈N∶ ? \(\mathop \exists \limits_{n \in N} \) (n > 1 ≧n ² k)is finitely axiomatizable. The present paper aims at showing that the class of all algebras {D _n ^* ∶n∈B} is also finitely axiomatizable. First, we prove that an intermediate logic defined as follows: $$LD = Cn(INT \cup \{ p_3 \vee [p_3 \to (p_1 \to p_2 ) \vee (p_2 \to p_1 )]\} )$$ finitely approximatizable. Then, defining, after Kripke, a model as a non-empty ordered setH = 〈K, ?〉, and making use of the set of formulas true in this model, we show that any finite strongly compact pseudo-boolean algebra ? is identical with. the set of formulas true in the Kripke modelH _B = 〈P(?), ?〉 (whereP(?) stands for the family of all prime filters in the algebra ?). Furthermore, the concept of a structure of divisors is defined, and the structure is shown to beH D _n ^* = 〈P (D _n ^* ), ?〉for anyn∈N. Finally, it is proved that for any strongly compact pseudo-boolean algebraU satisfying the axiomp ₃∨ [p ₃→(p₁→p₂)∨(p₂→p₁)] there is a structure of divisorsD _* ⁿ such that it is possible to define a strong homomorphism froomiH D _n ^* ontoH D _U . Exploiting, among others, this property, it turns out to be relatively easy to show that \(LD = \mathop \cap \limits_{n \in N} E(\mathfrak{D}_n^* )\) .     

Some paraconsistent sentential calculi

In [8] Jakowski defined by means of an appropriate interpretation a paraconsistent calculusD ₂ . In [9] J. Kotas showed thatD ₂ is equivalent to the calculusM(S5) whose theses are exactly all formulasa such thatMa is a thesis ofS5. The papers [11], [7], [3], and [4] showed that interesting paraconsistent calculi could be obtained using modal systems other thanS5 and modalities other thanM. This paper generalises the above work. LetA be an arbitrary modality (i.e. string ofM's,L's and negation signs). Then theA-extension of a set of formulasX is {¦A X}}. Various properties ofA-extensions of normal modal systems are examined, including a problem of their axiomatizability     

The role of fundamental frequency in signaling linguistic stress and affect: Evidence for a dissociation

The fundamental frequency (F0) of the voice is used to convey information about both linguistic and affective distinctions. However, no research has directly investigated how these two types of distinctions are simultaneously encoded in speech production. This study provides evidence thatF0 prominences intended to convey linguistic or affective distinctions can be differentiated by their influence on the amount of final-syllableF0 rise used to signal a question. Specifically, a trading relation obtains when theF0 prominence is used to convey emphatic stress. That is, the amount of finalsyllableF0 rise decreases as theF0 prominence increases. When theF0 prominence is used to convey affect, no trading relation is observed.     

Inspection time and response strategies in a choice response task

The effects of varying stimulus duration on two response measures, percentage correct (p_c) and mean reaction time (RT) were investigated in a lights-keys RT task similar to an inspection time (IT) task. One of either N = 2, 4 or 8 lights came on as the stimulus, followed after a range of stimulus exposure durations (D) by all 8, as a backward mask. It was found that p_c was an ogival function of D for all three levels of choice, and that the standard deviations of the best-fitting normal ogives were equal. It is argued that the standard deviation can be taken as a measure of the neural noise, or error-inducing variability introduced by processing the stimulus, and so this result indicated that noise in the choice reaction task is independent of N. The effect of D on RT was as predicted by an optional accumulator model for 7 Ss with RT decreasing as D increased, while another 2 Ss appeared to have adopted a temporal deadline criterion giving RTs independent of D and equal error and correct RTs. The same two response styles were found in a re-analysis of RT data from an IT study. The p_c vs D curves were comparable for both response styles. The accumulator model commonly assumed to underly IT tasks thus does not describe the behaviour of all Ss. Such individual differences in strategic approach to the IT task should be investigated further, since assuming that all Ss use one approach may hide or confound relationships between IT and other measures of individual difference, such as intelligence. Recommendations for better IT measurement techniques are given.     

A practical solution to the pervasive problems of<Emphasis Type="Italic">p</Emphasis> values

In the field of psychology, the practice ofp value null-hypothesis testing is as widespread as ever. Despite this popularity, or perhaps because of it, most psychologists are not aware of the statistical peculiarities of thep value procedure. In particular,p values are based on data that were never observed, and these hypothetical data are themselves influenced by subjective intentions. Moreover,p values do not quantify statistical evidence. This article reviews thesep value problems and illustrates each problem with concrete examples. The three problems are familiar to statisticians but may be new to psychologists. A practical solution to thesep value problems is to adopt a model selection perspective and use the Bayesian information criterion (BIC) for statistical inference (Raftery, 1995). The BIC provides an approximation to a Bayesian hypothesis test, does not require the specification of priors, and can be easily calculated from SPSS output.     

Redundancy and reduction: Speakers manage syntactic information density

A principle of efficient language production based on information theoretic considerations is proposed: Uniform Information Density predicts that language production is affected by a preference to distribute information uniformly across the linguistic signal. This prediction is tested against data from syntactic reduction. A single multilevel logit model analysis of naturally distributed data from a corpus of spontaneous speech is used to assess the effect of information density on complementizer that-mentioning, while simultaneously evaluating the predictions of several influential alternative accounts: availability, ambiguity avoidance, and dependency processing accounts. Information density emerges as an important predictor of speakers’ preferences during production. As information is defined in terms of probabilities, it follows that production is probability-sensitive, in that speakers’ preferences are affected by the contextual probability of syntactic structures. The merits of a corpus-based approach to the study of language production are discussed as well.     

Relationships between coordination,active drag and propelling efficiency in crawl

This study examines the relationships between the index of coordination (IdC) and active drag (D) assuming that at constant average speed, average drag equals average propulsion. The relationship between IdC and propulsive efficiency (e_p) was also investigated at maximal speed. Twenty national swimmers completed two incremental speed tests swimming front crawl with arms only in free condition and using a measurement of active drag system. Each test was composed of eight 25-m bouts from 60% to 100% of maximal intensity whereby each lap was swum at constant speed. Different regression models were tested to analyse IdC–D relationship. Correlation between IdC and e_p was calculated. IdC was linked to D by linear regression (IdC = 0.246 · D − 27.06; R² = 0.88, P < .05); swimmers switched from catch-up to superposition coordination mode at a speed of ∼1.55 m s⁻¹ where average D is ∼110 N. No correlation between IdC and e_p at maximal speed was found. The intra-individual analysis revealed that coordination plays an important role in scaling propulsive forces with higher speed levels such that these are adapted to aquatic resistance. Inter-individual analysis showed that high IdC did not relate to a high e_p suggesting an individual optimization of force and power generation is at play to reach high speeds.     

Indirect representation and the self-representational theory of consciousness

According to Uriah Kriegel’s self-representational theory of consciousness, mental state M is conscious just in case it is a complex with suitably integrated proper parts, M ₁ and M ₂, such that M ₁ is a higher-order representation of lower-order representation M ₂. Kriegel claims that M thereby “indirectly” represents itself, and he attempts to motivate this claim by appealing to what he regards as intuitive cases of indirect perceptual and pictorial representation. For example, Kriegel claims that it’s natural to say that in directly perceiving the front surface of an apple one thereby perceives the apple itself. Cases such as this are supposed to provide intuitive support for the principle that if X represents Y, and Y is highly integrated into complex object Z, then X indirectly represents Z. In this paper I provide counterexamples to Kriegel’s principle of indirect representation, before going on to argue that we can explain what is going on in those cases in which the subject seems to represent a complex whole by representing one its parts without positing indirect representations anyway. I then argue that my alternative approach is superior to Kriegel’s in a number of ways, thereby rendering his theory of consciousness implausible.     

Bayesian hypothesis testing for psychologists: A tutorial on the Savage–Dickey method

In the field of cognitive psychology, the p-value hypothesis test has established a stranglehold on statistical reporting. This is unfortunate, as the p-value provides at best a rough estimate of the evidence that the data provide for the presence of an experimental effect. An alternative and arguably more appropriate measure of evidence is conveyed by a Bayesian hypothesis test, which prefers the model with the highest average likelihood. One of the main problems with this Bayesian hypothesis test, however, is that it often requires relatively sophisticated numerical methods for its computation. Here we draw attention to the Savage–Dickey density ratio method, a method that can be used to compute the result of a Bayesian hypothesis test for nested models and under certain plausible restrictions on the parameter priors. Practical examples demonstrate the method’s validity, generality, and flexibility.     

Difficulty scaling of recognition items

Usual system: take as scale value the normal deviate corresponding to the areap = (p –p ₀)/(1 –p ₀), wherep is the proportion of correct answers andp ₀ is the chance proportion. Ifp p ₀, the item difficulty is unscalable. Proposed system: take as scale value the normal deviate corresponding to the areap =p ^x , withx so chosen thatp = .5 whenp is half-way betweenp ₀ and 1. Table givesD (=500 + 100z) forp = .00(.01)1.00 and for (= number of alternatives) 2,3,4,5,6,7, .     

I act,therefore I am: Athletic identity and the health action process approach predict sport participation among individuals with acquired physical disabilities

ObjectiveThe study had two objectives 1) to test the fit of the Health Action Process Approach (HAPA) model for sport participation among individuals with acquired physical disabilities and 2) to estimate the extent to which athletic identity predicts intentions to engage in sport within the context of HAPA.DesignProspective cohort of 82 women and 19 men with acquired permanent disabilities (M_age = 44.0; M_{years post-injury} = 16.2; %_{in sport} = 61.7%).MethodAll HAPA indicators and athletic identity were assessed at baseline and sport participation was assessed using the Leisure Time Physical Activity Questionnaire for People with Spinal Cord Injury two weeks later. Structural equation modelling was used to test the HAPA model.ResultsThe HAPA constructs explained 15% of the variance in sport participation and 18% of the variance when athletic identity was added to the model. Instrumental (β = .21), affective (β = .15), and negative outcome expectancies (β = ?.20) were significant predictors of intentions to participate in sport, as was athletic identity (β = .25). Intentions to participate in sport significantly predicted planning (β = .54) yet there was no direct relationship between planning and sport participation (β = ?.008; p > .05). When the relationship between planning and maintenance self-efficacy was reversed, planning had a significant indirect effect on sport participation through maintenance self-efficacy (β = .33).ConclusionThe HAPA model is a good predictive model for sport participation among those with acquired physical disabilities; furthermore, athletic identity accounts for additional variance in sport participation. These constructs can be valuable components of sport promotion programs for this population.     

A Muscle Awareness Model for Changes in Rorschach Human Movement Responses

The present series of studies sought to provide evidence that M would increase under any conditions which make an S more aware of his muscles. The studies demonstrated that at least in women, M increased over a variety of conditions involving heightened muscle awareness. Specifically M increased in conditions utilizing muscle activation, deactivation, hypnosis, and focusing thoughts on the body musculature. The muscle awareness model unlike the sensory-tonic model accounts for increases in M following hyperactivity as well as inhibition.     

Comparing the meanings of “if” and “all”

In this study, we compared the everyday meanings of conditionals (“if p then q”) and universally quantified statements (“all p are q”) when applied to sets of elements. The interpretation of conditionals was predicted to be directly related to the conditional probability, such that P(“if p then q”) = P(q|p). Quantified statements were assumed to have two interpretations. According to an instance-focused interpretation, quantified statements are equivalent to conditionals, such that P(“all p are q”) = P(q|p). According to a set-focused interpretation, “all p are q” is true if and only if every instance in set p is an instance of q, so that the statement would be accepted when P(q|p) = 1 and rejected when this probability was below 1. We predicted an instance-focused interpretation of “all” when the relation between p and q expressed a general law for an infinite set of elements. A set-focused interpretation of “all” was predicted when the relation between p and q expressed a coincidence among the elements of a finite set. Participants were given short context stories providing information about the frequency of co-occurrence of cases of p, q, not-p, and not-q in a population. They were then asked to estimate the probability that a statement (conditional or quantified) would be true for a random sample taken from that population. The probability estimates for conditionals were in accordance with an instance-focused interpretation, whereas the estimates for quantified statements showed features of a set-focused interpretation. The type of the relation between p and q had no effect on this outcome.     

Stigma Consciousness and Subjective Well-Being in Lesbians and Gays

The stigma associated with sexual identity can affect an individual’s well-being. The main goal of this study was to analyse the role of a psychosocial variable, stigma consciousness, on the well-being of lesbian and gay (LG) individuals. For this purpose, a sample of 481 participants completed various questionnaires (M _age = 32.36, SD _age = 9.60). Analysis of these results using structural equations showed two different pathways to cope with the stigma. The first pathway consists of collective action, and the second consists of stigma concealment. Specifically, stigma consciousness positively predicts well-being through group identification and collective action. Stigma concealment, however, negatively predicts well-being through the perception of prejudice. In addition, this work has confirmed that concealment has a direct negative relationship with subjective well-being. These results are interpreted from a psychosocial perspective. Finally, based on our data, we propose future interventions that provide LG individuals with strategies to cope with their perceptions of stigma.     

Walking the talk: Value importance,value enactment,and well-being

Prior research on intrinsic versus extrinsic values has focused on the comparative importance subjects assign to the two types of values, showing that relative intrinsic versus extrinsic value orientation (RIEVO) predicts higher or increased well-being. In two studies, we show that rated action taken regarding the two types of values is just as essential to study. Support was found for four hypotheses: (1) there was a significant behavior/importance gap, such that participants “walked” (acted on values) less than they “talked” (endorsed those values); (2) this was especially true for intrinsic values, an interaction suggesting that the intrinsic ideals of personal growth, community, and connection often receive only lip service; (3) the “walk” (behavior ratings) measure of RIEVO subsumed the “talk” (importance ratings) RIEVO measure’s effects on well-being outcomes, suggesting that researchers interested in predicting well-being from values should perhaps focus on rated value enactment, not value importance; and (4) participants with higher meaning in life, lower search for meaning, more self-concordance at work, and greater chronological age evidenced more consistency between their talking and their walking.