When can we trust theF-approximation of the box-test?

Consider a multivariate context withp variates andk independent samples, each of sizen. To test equality of thek population covariance matrices, the likelihood ratio test is commonly employed. Box'sF-approximation to the null distribution of the test statistic can be used to computep-values, if sample sizes are not too small. It is suggested to regard theF-approximation as accurate if the sample sizesn are greater than or equal to 1+0.0613p ²+2.7265p-1.4182p ^0.5+0.235p ^1.4* In (k), for 5p30,k20.This research was supported by the Deutsche Forschungsgemeinschaft through Ste 405/2-1.     

Early Feeding,Child Behaviour and Parenting as Correlates of Problem Eating

Mealtimes are a common source of stress for families. Examining factors related to problem eating may provide markers by which to identify families requiring assistance and salient targets for treatment. The current study investigated parenting practices and cognitions, generalisation of child behavioural issues, and early feeding history as they relate to problem eating in typically developing young children. We compared a community sample of 105 parents of 1.5–6-year-old children via survey and observation with 96 parents seeking treatment for their child’s problem eating. History of problems with breastfeeding, χ²(1)?=?3.88, p?=?.049, and the transition to solids, χ²(1)?=?7.27, p?=?.007, were more common among problem eaters than comparisons. Problem eaters had a greater number of problem behaviours outside of mealtimes, F(1181)?=?10.88, p?=?.001, though not more frequently than comparisons and not to clinical levels, F(1181)?=?1.81, p?=?.181. Parents of problem eaters reported more unhelpful mealtime parenting strategies, F(1155)?=?22.59, p?<?.001, yet general parenting style was similar by group, F(1187)?=?0.42, p?=?.527. Parents’ cognitions about mealtimes, F(1155)?=?119.81, p?<?.001, including mealtime-specific self-efficacy, F(1155)?=?171.30, p?<?.001, were poorer amongst problem eaters, and were the only factors to predict problem eating in the total sample. General parenting self-efficacy was poorer in parents of problem eaters (Behaviour: F(1187)?=?42.36, p?<?.001; Setting: F(1187)?=?10.64, p?=?.001). Evidence of feeding issues in infancy may support early detection of and intervention for later problem eating. The significance of broader child behaviour is less clear. Parent factors, particularly those specific to mealtimes, and cognitive in nature (including mealtime parenting self-efficacy) clearly differentiated the groups, and represent important targets for intervention.     

Cannabinoid and cholinergic systems interact during performance of a short-term memory task in the rat

It is now well established that cannabinoid agonists such as Δ⁹–tetrahydrocannabinol (THC), anandamide, and WIN 55,212-2 (WIN-2) produce potent and specific deficits in working memory (WM)/short-term memory (STM) tasks in rodents. Although mediated through activation of CB1 receptors located in memory-related brain regions such as the hippocampus and prefrontal cortex, these may, in part, be due to a reduction in acetylcholine release (i.e., cholinergic hypofunction). To determine the interaction between cannabinoid and cholinergic systems, we exposed rats treated with WIN-2 or cholinergic drugs to a hippocampal-dependent delayed nonmatch to sample (DNMS) task to study STM, and recorded hippocampal single-unit activity in vivo. WIN-2 induced significant deficits in DNMS performance and reduced the average firing and bursting rates of hippocampal principal cells through a CB1 receptor-mediated mechanism. Rivastigmine, an acetylcholinesterase inhibitor, reversed these STM deficits and normalized hippocampal discharge rates. Effects were specific to 1 mg/kg WIN-2 as rivastigmine failed to reverse the behavioral and physiological deficits that were observed in the presence of MK-801, an NMDA receptor antagonist. This supports the notion that cannabinoid-modulated cholinergic activity is a mechanism underlying the performance deficits in DNMS. Whether deficits are due to reduced nicotinic or muscarinic receptor activation, or both, awaits further analysis.Administration of both synthetic and phytocannabinoids, including Δ⁹–tetrahydrocannabinol (Δ⁹–THC), WIN 55,212-2 (WIN-2), and CP 55,940, impair working memory (WM) and short-term memory (STM) through a CB1 receptor-mediated mechanism in rats (Lichtman et al. 1995; Lichtman and Martin 1996; Hampson and Deadwyler 1998, 1999, 2000; Braida and Sala 2000; Egashira et al. 2002). This suggestive evidence for endocannabinoid involvement in memory formation was confirmed by Terranova and coworkers (1996), who demonstrated that the CB1 receptor antagonist rimonabant facilitated short-term olfactory memory, and this was partially reversed by the muscarinic receptor antagonist scopolamine. This suggests an interaction between cannabinoid and cholinergic systems such that endocannabinoid tone suppresses cholinergic transmission. Consequently, rats pretreated with eptastigmine, a second-generation cholinesterase inhibitor remained unaffected by the full CB1 receptor agonist CP 55,940 when tested in an eight arm radial maze (Braida and Sala 2000). And more recent evidence from Mishima and coworkers (2002) suggests that a block of cholinesterase with physostigmine and tetrahydroaminoacridine protects against WM impairments induced by Δ⁹–THC. These findings further support a potential role of the cholinergic system in cannabinoid-induced memory impairments.The exact mechanisms for this interaction still remain elusive, although cholinergic projection neurons from medial septum to hippocampus are likely to play an important role (Harkany et al. 2003, 2005; Fitz et al. 2008). However, the neuromodulatory action of pharmacologically active cannabinoids on septo-hippocampal cholinergic activity in vivo remains unexplored. Within the hippocampus, cannabinoids presynaptically inhibit the release of acetylcholine, possibly through the activation of CB1 receptors located on cholinergic nerve terminals given that these effects were blocked by rimonabant (Gifford and Ashby Jr. 1996; Gifford et al. 1997a, 2000; Kathmann et al. 2001a). Direct in vivo microdialysis studies in awake rats also showed cannabinoid-induced decreases in acetylcholine release in the hippocampus through a CB1 receptor-mediated mechanism (Gessa et al. 1997; Carta et al. 1998). High doses of rimonabant alone increase the amount of acetylcholine release in the hippocampus (Gessa et al. 1997, 1998) either by blocking the tonic inhibitory influence of endocannabinoids and/or through its inverse agonism at CB1 receptors. Such actions are in agreement with a 100% greater increase in electrically evoked hippocampal acetylcholine release in CB1^−/− mice (Kathmann et al. 2001b).In contrast, low doses of Δ⁹–THC (0.01–0.15 mg/kg), WIN-2 (0.01–0.5 mg/kg), and HU-210 (0.001–0.004 mg/kg) have been shown to enhance acetylcholine release (Acquas et al. 2000, 2001), indicating that cannabinoid modulation of acetylcholine release in the hippocampus is “biphasic.” This has been further supported by the work carried out by Tzavara and coworkers (2003), who demonstrated that low (0.5 mg/kg, intraperitoneally [i.p.]) and high (5 mg/kg, i.p.) doses of WIN-2 induce transient stimulation and prolonged inhibition of hippocampal acetylcholine efflux, respectively. This demonstrates that the dose of cannabinoids plays a key role in determining how much acetylcholine is released in the hippocampus.Such an interaction is likely to play an important role during the performance of a delayed nonmatch to sample (DNMS) task but has not been explored. Hence, a comprehensive pharmacological assessment was carried out here to (1) reveal the existence of such an interaction in terms of DNMS performance and (2) assess a possible cannabinoid-acetylcholine cross-talk on burst characteristics of hippocampal principal cells in CA3 and CA1.     

Some exact conditional tests of independence forR ×C cross-classification tables

Exact conditional tests of independence in cross-classification tables are formulated based on the ² statistic and statistics with stronger operational interpretations, such as some nominal and ordinal measures of association. Guidelines for the table dimensions and sample sizes for which the tests are economically implemented on a computer are given. Some selected sample sizes and marginal distributions are used in a numerical comparison between the significance levels of the approximate and exact conditional tests based on the ² statistic.The authors are grateful for the suggestions of the referees and for computer funding provided by the Northeast Regional Data Center at the University of Florida.     

A Comparison of Sexual Relationships Among Hispanic Men by Sexual Orientation: Implications for HIV/STI Prevention

Hispanic men experience high rates of HIV infection and other sexually transmitted infections (STIs) when compared to non-Hispanic whites. Many factors contribute to HIV/STI risk among Hispanic men. Some researchers have suggested that primary relationships may be a source of HIV/STIs because some men engage in sexual relationships outside of the primary relationship. However, little is known about this among Hispanic men, and less is known about how sexual relationships differ by sexual orientation. The purpose of this study was twofold: (1) to determine if Hispanic men engage in sexual relationships outside of primary relationships; and (2) to compare sex outside of primary relationships by sexual orientation. Data for this study were obtained from a larger study that investigated health risks of Hispanic men residing in the U.S.–Mexico border community. Participants were recruited from agencies that provided services to Hispanic men. Participants completed a structured interview that included questions about primary relationships and sex outside of primary relationships. The sample consisted of 103 Hispanic men (50 heterosexual, 43 gay, and 10 bisexual Hispanic men), but two participants refused to answer relationship questions, resulting in a sample of 101 Hispanic men. About one-third of the participants (n = 29) reported sex outside of the primary relationship, but no differences were found between the gay/bisexual and heterosexual men, X ² (2, N = 101) = 9.91, p = .128. More gay/bisexual men reported sex with the primary partner and another person at the same time than heterosexual men, X ² (2, N = 101) = 13.32, p = .010. More gay/bisexual men reported open relationships when compared to heterosexual men, X ² (2, N = 101) = 17.23, p = .008, and more gay/bisexual men reported sex outside the primary relationship without the primary partner’s knowledge, X ² (2, N = 101) = 15.09. p = .020. However, more heterosexual men reported that condoms were not used for sex outside the primary relationship when compared to gay/bisexual men, X ² (2, N = 101) = 14.01, p = .029. Sex outside of primary relationships presents some implications for HIV/STI prevention among Hispanic men. Because gay/bisexual men experience higher rates of HIV/STI, more attention needs to be focused on all forms of relationships to prevent acquisition of HIV/STIs. Among heterosexual Hispanic men more attention needs to be given to reinforcement of safer sex practices both outside the primary relationship, and within the primary relationship if high risk sex is occurring outside the primary relationship. More research is needed on the reasons for sex outside the primary relationship among Hispanic men, as well as research to promote safer sex practices when sex occurs outside of the primary relationship.     

A Comparison of the Construct Validity of Two Alternative Approaches to the Assessment of Psychopathy in the Community

This study compared the validity of 2 different self-report approaches to the assessment of psychopathy in nonforensic samples: the Psychopathy Resemblance Index (PRI), derived from a measure of normal personality functioning, and the Self-Report Psychopathy Scale (SRP), developed specifically to assess the maladaptive traits associated with psychopathy. In 2 adult samples (n ₁ = 260, n₂ = 250), the PRI and the SRP were positively correlated with each other and with measures of maladaptive personality traits related to Machiavellianism and narcissism. However, unlike the SRP, the PRI was independent of trait empathy and general psychopathology and was positively associated with trait emotional intelligence. These results suggest that the PRI captures a more adaptive variant of psychopathy than does the SRP.     

Behavioral deficits and subregion-specific suppression of LTP in mice expressing a population of mutant NMDA receptors throughout the hippocampus

The NMDA receptor (NMDAR) subunit GluN1 is an obligatory component of NMDARs without a known functional homolog and is expressed in almost every neuronal cell type. The NMDAR system is a coincidence detector with critical roles in spatial learning and synaptic plasticity. Its coincidence detection property is crucial for the induction of hippocampal long-term potentiation (LTP). We have generated a mutant mouse model expressing a hypomorph of the Grin1^N598R allele, which leads to a minority (about 10%) of coincidence detection-impaired NMDARs. Surprisingly, these animals revealed specific functional changes in the dentate gyrus (DG) of the hippocampal formation. Early LTP was expressed normally in area CA1 in vivo, but was completely suppressed at perforant path-granule cell synapses in the DG. In addition, there was a pronounced reduction in the amplitude of the evoked population spike in the DG. These specific changes were accompanied by behavioral impairments in spatial recognition, spatial learning, reversal learning, and retention. Our data show that minor changes in GluN1-dependent NMDAR physiology can cause dramatic consequences in synaptic signaling in a subregion-specific fashion despite the nonredundant nature of the GluN1 gene and its global expression.According to Hebb''s postulate, neurons require a molecular mechanism to detect synchronous activity in order to change the strength of synaptic connectivity (Hebb 1949). NMDA receptors (NMDARs) are molecular coincidence detectors, and selective NMDAR antagonists block the induction of long-term potentiation (LTP) in both the dentate gyrus (DG) and CA1 regions of the hippocampus (Bliss and Collingridge 1993; Martin et al. 2000). NMDARs have been long known for their role in spatial learning, but more recently have been implicated in other forms of cognitive function and dysfunction (Gruart et al. 2006; Whitlock et al. 2006; Castner and Williams 2007; Kristiansen et al. 2007; Wilson and Linster 2008).Neuronal NMDARs are hetero-tetrameric ligand-gated ion channels typically comprised of two types of subunits. Two copies of the mandatory GluN1 subunit (or NR1 subunit [Collingridge et al. 2009] encoded by Grin1) are associated with two copies from the GluN2 family, GluN2A–D (or NR2A–D). The GluN1 subunit is expressed ubiquitously both spatially and temporally throughout the developing and adult brain. Global knockout mice models of the GluN1 subunit are postnatally lethal within hours after birth (Forrest et al. 1994; Li et al. 1994), and cell-specific GluN1 mice knockouts (Tsien et al. 1996; Nakazawa et al. 2002; McHugh et al. 2007; Niewoehner et al. 2007) have provided insights on how specific synapses and regional neuronal networks are dependent on NMDAR function.The early postnatal lethality of the global GluN1 knockout is in contrast to the null mutants of the four AMPA receptor genes and other major synaptic proteins, such as αCaMKII (Silva et al. 1992a,b; Jia et al. 1996; Zamanillo et al. 1999; Meng et al. 2003). This can be at least partially explained by the absence of any close GluN1 homologs, which could functionally compensate for the absence of the GluN1 subunit. Recombinant expression studies defined the GluN1 subunit as a mandatory component of NMDARs. This constellation provides a specific opportunity to test whether different local neuronal subnetworks are affected differentially by mutant Grin1 alleles associated with subtle alterations of the functional properties of NMDARs.GluN1 subunits with the N598R point mutation (GluN1^R) yield functional NMDARs that are Mg²⁺ insensitive and Ca²⁺ impermeable (Burnashev et al. 1992; Mori et al. 1992). The Grin1^N598R allele that codes for GluN1^R subunits is a gain-of-function mutation that is dominant lethal, even in heterozygous and hemizygous lines (Single et al. 2000; Rudhard et al. 2003). NMDARs with GluN1^R subunits do not act as coincidence detectors and, interestingly, mice expressing exclusively the GluN1^R allele lack whisker-related pattern formation in the neonate brainstem (Rudhard et al. 2003).To investigate the functional importance of GluN1 subunits with the N598R point mutation, we took advantage of the generation of a variant mutant line of mice (GluN1^Rneo/+) expressing a minority (around 10%) of these mutant NMDARs. Even though the majority of the NMDARs are normal, all neurons expressing NMDARs will contain a subset of receptors carrying this mutation.Therefore, this mouse model is an ideal candidate to study the impact of subtle alterations of NMDAR function on different neuronal networks, such as those comprising the hippocampal formation.Studies examining region-specific targeted disruption of GluN1 expression in subregions of the hippocampus have revealed subtle yet important contributions of this NMDAR subunit in synaptic plasticity and spatial learning and memory. CA1-restricted knockout of GluN1 expression in the hippocampus caused impaired spatial learning and memory as well as reduced CA1-LTP (Tsien et al. 1996). In the case of the disruption of GluN1 expression in the DG region of the hippocampus, more subtle behavioral impairments were apparent, including the inability to discriminate between two similar contexts (pattern separation) and deficits in spatial working memory despite normal LTP in the CA1 region (McHugh et al. 2007; Niewoehner et al. 2007).Our GluN1^Rneo/+ mice differ from the region-specific GluN1 mutant mice in that they express the mutant hypomorph at the same level in different subregions of the hippocampus. Interestingly, we found that this allele leads to substantial differences in short- and long-term plasticity between area CA1 and the DG of the hippocampus. The specific impairment in the DG was accompanied by impaired spatial recognition, spatial learning, reversal learning, and retention. Our data establish the possibility of a circuit-specific phenotype caused by a mutant variant of a globally expressed major nonredundant synaptic protein.     

Variable criteria sequential stopping rule: Validity and power with repeated measures ANOVA,multiple correlation,MANOVA and relation to Chi-square distribution

The variable criteria sequential stopping rule (vcSSR) is an efficient way to add sample size to planned ANOVA tests while holding the observed rate of Type I errors, α_o, constant. The only difference from regular null hypothesis testing is that criteria for stopping the experiment are obtained from a table based on the desired power, rate of Type I errors, and beginning sample size. The vcSSR was developed using between-subjects ANOVAs, but it should work with p values from any type of F test. In the present study, the α_o remained constant at the nominal level when using the previously published table of criteria with repeated measures designs with various numbers of treatments per subject, Type I error rates, values of ρ, and four different sample size models. New power curves allow researchers to select the optimal sample size model for a repeated measures experiment. The criteria held α_o constant either when used with a multiple correlation that varied the sample size model and the number of predictor variables, or when used with MANOVA with multiple groups and two levels of a within-subject variable at various levels of ρ. Although not recommended for use with χ² tests such as the Friedman rank ANOVA test, the vcSSR produces predictable results based on the relation between F and χ². Together, the data confirm the view that the vcSSR can be used to control Type I errors during sequential sampling with any t- or F-statistic rather than being restricted to certain ANOVA designs.     

Long-term stability of the French WISC-IV: Standard and CHC index scores

Introduction

The assumption of the stability of intelligence is the source of the predictive value of the Intelligence Quotient (e.g., Full Scale IQ). However, few studies have investigated the long-term stability of one of the most frequently used tests in the field of cognitive assessment: the Wechsler Intelligence Scale for Children – 4th edition (WISC-IV).

Finite structural axiomatization of every finite-valued propositional calculus

In [2] A. Wroski proved that there is a strongly finite consequence C which is not finitely based i.e. for every consequence C ⁺ determined by a finite set of standard rules C C ⁺. In this paper it will be proved that for every strongly finite consequence C there is a consequence C ⁺ determined by a finite set of structural rules such that C(Ø)=C ⁺(Ø) and = (where , are consequences obtained by adding to the rules of C, C ⁺ respectively the rule of substitution). Moreover it will be shown that under certain assumptions C=C ⁺.     

Individual differences in spatial pattern separation performance associated with healthy aging in humans

Rodent studies have suggested that “pattern separation,” the ability to distinguish among similar experiences, is diminished in a subset of aged rats. We extended these findings to the human using a task designed to assess spatial pattern separation behavior (determining at time of test whether pairs of pictures shown during the study were in the same spatial locations). Using a standardized test of word recall to divide healthy aged adults into impaired and unimpaired groups relative to young performance, we demonstrate that aged impaired adults are biased away from pattern separation and toward pattern completion, consistent with the rodent studies.Memory impairment is a common complaint among aging individuals, yet the variability within the aging population is great in both rats (Gallagher et al. 2006; Robitsek et al. 2008) and humans (Hilborn et al. 2009). A rodent model of aging (Gallagher et al. 2006; Wilson et al. 2006) has demonstrated that ∼50% of healthy rats qualify as cognitively “impaired” by scoring outside the range of the young performance in a standard protocol (Gallagher et al. 1993). The other half, the “unimpaired” rats, perform on par with young adults, demonstrating a natural degree of variability in cognitive aging. In this study, we sought to capitalize on the variability observed in the aging of both rats and humans in a study of spatial pattern separation.One source of variability in memory performance is hypothesized to be tied to changes in the input to the dentate gyrus (DG), which has been shown in the rat to be affected by the aging process. Smith et al. (2000) reported a selective impairment in layer II entorhinal input into the DG and CA3 regions of the hippocampus in rats with cognitive impairment. Similarly, the number of synapses in the outer receiving layer of DG was reduced in autopsied aged brains and correlated with earlier performance on a delayed recall task (Scheff et al. 2006). Finally, in a human imaging study, Small et al. (2002) observed that 60% of their aging sample demonstrated diminished MRI signal in the hippocampal region (including the DG) and also had a greater decline in memory performance. These findings support the notion that changes in the DG associated with aging may affect memory performance.The DG may be particularly important for the computations that underlie pattern separation (Treves and Rolls 1994; McClelland et al. 1995; Norman and O''Reilly 2003). “Pattern separation” refers to the process by which similar inputs are stored as distinct, nonoverlapping representations. In contrast, “pattern completion” refers to the process by which an existing representation can be reinstated by the presentation of a partial or degraded cue. Numerous studies in the rodent have identified the importance of the DG for pattern separation using electrophysiological methods (Leutgeb et al. 2004, 2005, 2007; Leutgeb and Leutgeb 2007), immediate early gene expression (Vazdarjanova and Guzowski 2004), lesions (Lee et al. 2005; Gilbert and Kesner 2006; Goodrich-Hunsaker et al. 2008), and even genetic manipulations (Cravens et al. 2006; Kubik et al. 2007; McHugh et al. 2008). Human neuroimaging has also recently identified activity in the DG (and CA3 regions of the hippocampus) in an object pattern separation task (Kirwan and Stark 2007; Bakker et al. 2008).Given the importance of the DG in pattern separation and its vulnerability to changes that occur with aging, studies have begun to examine pattern separation in older adults. Our laboratory has designed a task to examine object-based pattern separation performance in humans (Kirwan and Stark 2007). In this task, pictures of objects were presented either once or repeatedly throughout the task. Critically, some of the items presented were lures that were similar but not identical to previously shown items. The overlapping features of the lures more heavily engaged pattern separation processes. In young adults, functional magnetic resonance imaging (fMRI) activity in the DG was sensitive to the lures, indicating a role in pattern separation processes in both an explicit (Kirwan and Stark 2007) and implicit (Bakker et al. 2008) version of this task. Toner et al. (2009) used the explicit version of this task to demonstrate that older adults showed a greater tendency to identify lures as “old” (repeated) relative to young adults. These findings were also recently replicated in our laboratory (Yassa et al., in press), with the additional demonstration that older adults exhibit greater fMRI CA3/DG activity for the lures during both encoding and retrieval.Since object-based pattern separation appears to be modulated by the DG in humans, we wondered if these findings could be extended to spatial pattern separation. Rodent studies have demonstrated that the DG has a particular role in spatial pattern separation (Gilbert et al. 2001; Kesner et al. 2004). Specifically, Hunsaker et al. (2008) placed rats with localized DG lesions in an environment with two objects spaced 60 cm apart. When the animals were later placed in the same environment with the same objects now placed 40 cm apart, DG-lesioned animals (unlike control animals) did not re-explore the objects or environment. These data suggest that the DG-lesioned rats were not able to discriminate between the training and test environments. That is, they were impaired in spatial pattern separation. Since converging evidence suggests that one feature of the aging process can be characterized as a DG knockdown, we modified this task design for humans to test spatial pattern separation performance in older adults. While the Hunsaker et al. (2008) task emphasized the distance between the two objects as the source of interference creating a greater need for pattern separation, the paradigm presented here moves an object in any direction, changing both the distance and the angle (i.e., changing more of the spatial relations). We posit that this amount of movement (close, medium, or far) may place similar demands on spatial pattern separation processes as in the rodent task.The present study included 20 young adults (mean age 19.9 yr, range 18–27 yr) and 30 aged adults (mean age 70.4 yr, range 59–80 yr). Aged adults completed a battery of standardized neuropsychological tests, including the Mini-Mental State Exam (Folstein et al. 1975), Rey Auditory–Verbal Learning Task (RAVLT) (Rey 1941), Digit Span, Vocabulary, and Matrices subtests from the Wechsler Adult Intelligence Scale III (Wechsler 1997). The Vocabulary and Matrices scores were entered into a weighted formula along with age, gender, and education to derive estimated IQ scores (Schoenberg et al. 2003). All aged participants scored within the normal age-adjusted ranges on these measures and were cognitively intact. Younger adults also completed the RAVLT and scored within the normal age-adjusted range. These data are presented in Table 

Comments on “the measurement of factorial indeterminacy”

Guttman's index of indeterminacy (2² – 1) measures the potential amount of uncertainty in picking the right alternative interpretation for a factor. When alternative solutions for a factor are equally likely to be correct, then the squared multiple correlation ² for predicting the factor from the observed variables is the average correlation _AB between independently selected alternative solutionsA andB, while var ( _AB )=(1 – ²)²/s, wheres is the dimensionality of the space in which unpredicted components of alternative solutions are to be found. When alternative solutions for the factor are not equally likely to be chosen, ² is the lower bound for E( _AB ); however, E( _AB ) need not be a modal value in the distribution of _AB . Guttman's index and E( _AB ) measure different aspects of the same indeterminacy problem.     

A Comparison of Survey Data Collected by Regular Mail and Electronic Mail Questionnaires

A survey was conducted by the National Council on Measurement in Education (NCME) to examine the telecommunications needs of the organization's membership. A component of this study permitted an examination of two response modalities (regular mail and e-mail) across a number of variables. Separate samples of 585 were drawn to take the survey. The first sample consisted of all those organization members who had registered their e-mail address with the organization while the second sample was randomly selected from those members who did not list an e-mail address. The first group was sent a nine question instrument via e-mail while the second group was asked to fill out a ten question instrument via regular mail. Overall response rates were low and significantly different [30% for the e-mail group and 36% for the regular mail group, ² (1) = 10.42, p < .01], though not uncommon for institutional surveys. Individual item response rates, however, were statistically significantly higher for the e-mail group across a number of dimensions. The results suggest that for some organizations, e-mail questionnaires may be a viable mechanism for conducting surveys. Suggestions are made on how to improve overall response rates.     

Topological representations of Post algebras of order ω+ and open theories based on ω+-valued Post logic

Post algebras of order ⁺ as a semantic foundation for ⁺-valued predicate calculi were examined in [5]. In this paper Post spaces of order ⁺ being a modification of Post spaces of order n2 (cf. Traczyk [8], Dwinger [1], Rasiowa [6]) are introduced and Post fields of order ⁺ are defined. A representation theorem for Post algebras of order ⁺ as Post fields of sets is proved. Moreover necessary and sufficient conditions for the existence of representations preserving a given set of infinite joins and infinite meets are established and applied to Lindenbaum-Tarski algebras of elementary theories based on ⁺-valued predicate calculi in order to obtain a topological characterization of open theories.     

Contextual-Hierarchical Reconstructions of the Strengthened Liar Problem

In this paper we shall introduce two types of contextual-hierarchical (from now on abbreviated by ‘ch’) approaches to the strengthened liar problem. These approaches, which we call the ‘standard’ and the ‘alternative’ ch-reconstructions of the strengthened liar problem, differ in their philosophical view regarding the nature of truth and the relation between the truth predicates T r ⁿ and T r ⁿ⁺¹ of different hierarchy-levels. The basic idea of the standard ch-reconstruction is that the T r ⁿ⁺¹-schema should hold for all sentences of \(\mathcal {L}^{n}\). In contrast, the alternative ch-reconstruction, for which we shall argue in section four, is motivated by the idea that T r ⁿ and T r ⁿ⁺¹ are coherent in the sense that the same sentences of \(\mathcal {L}^{n}\) should be true according to T r ⁿ and T r ⁿ⁺¹. We show that instances of the standard ch-reconstruction can be obtained by iterating Kripke’s strong Kleene jump operator. Furthermore, we will demonstrate how instances of the alternative ch-reconstruction can be obtained by a slight modification of the iterated axiom system KF and of the iterated strong Kleene jump operator.