Approximate sample size formulas for the two‐sample trimmed mean test with unequal variances

Yuen's two‐sample trimmed mean test statistic is one of the most robust methods to apply when variances are heterogeneous. The present study develops formulas for the sample size required for the test. The formulas are applicable for the cases of unequal variances, non‐normality and unequal sample sizes. Given the specified α and the power (1?β), the minimum sample size needed by the proposed formulas under various conditions is less than is given by the conventional formulas. Moreover, given a specified size of sample calculated by the proposed formulas, simulation results show that Yuen's test can achieve statistical power which is generally superior to that of the approximate t test. A numerical example is provided.     

Should knowledge entail belief?

The appropriateness of S5 as a logic of knowledge has been attacked at some length in the philosophical literature. Here one particular attack based on the interplay between knowledge and belief is considered: Suppose that knowledge satisfies S5, belief satisfies KD45, and both the entailment property (knowledge implies belief) and positive certainty (if the agent believes something, she believes she knows it) hold. Then it can be shown that belief reduces to knowledge: it is impossible to have false beliefs. While the entialment property has typically been viewed as perhaps the least controversial of these assumptions, an argument is presented that it can plausibly be viewed as the culprit. More precisely, it is shown that this attack fails if we weaken the entailment property so that it applies only to objective (nonmodal) formulas, rather than to arbitrary formulas. Since the standard arguments in favor of the entailment property are typically given only for objective formulas, this observation suggests that care must be taken in applying intuitions that seem reasonable in the case of objective formulas to arbitrary formulas.Research sponsored in part by the Air Force office of Scientific Research (AFSC), under Contract F49620-91-C-0080. The United States Government is authorized to reproduce and distribute reprints for governmental purposes.     

Translation of first order formulas into ground formulas via a completion theory

A translation technique is presented which transforms a class of First Order Logic formulas, called Restricted formulas, into ground formulas. For the formulas in this class the range of quantified variables is restricted by Domain formulas.If we have a complete knowledge of the predicates involved in the Domain formulas their extensions can be evaluated with the Relational Algebra and these extensions are used to transform universal (respectively existential) quantifiers into finite conjunctions (respectively disjunctions).It is assumed that the complete knowledge is represented by Completion Axioms and Unique Name Axioms à la Reiter. These axioms involve the equality predicate. However, the translation allows to remove the equality in the ground formulas and for a large class of formulas their consequences are the same as the initial First Order formulas. This result open the door for the design of efficient deduction techniques.     

ECONOMIC CONSIDERATIONS IN ESTIMATING THE UTILITY OF HUMAN RESOURCE PRODUCTIVITY IMPROVEMENT PROGRAMS

Three economic concepts (variable costs, taxes, and discounting) are applied and incorporated into the previous utility formulas proposed by Brogden (1946, 1949), Cronbach and Gleser (1965), and Schmidt, et al. (1979, 1982). The resulting utility model indicates that the previous formulas are deficient and can produce upwardly biased utility estimates. Empirical examples based on published research (e.g., Schmidt, et al., 1982) are presented indicating the substantial magnitude of the bias given realistic levels of variable costs, taxes, and discount rates. The present utility model is used to adjust for such bias and is shown to provide a more complete and precise utility definition. Implications for future research are discussed.     

Simple Procedures to Estimate Chance Agreement and Kappa for the Interrater Reliability of Response Segments Using the Rorschach Comprehensive System

When determining interrater reliability for scoring the Rorschach Comprehensive System (Exner, 1993), researchers often report coding agreement for response segments (i.e., Location, Developmental Quality, Determinants, etc.). Currently, however, it is difficult to calculate kappa coefficients for these segments because it is tedious to generate the chance agreement rates required for kappa computations. This study facilitated kappa calculations for response segments by developing and validating formulas to estimate chance agreement. Formulas were developed for 11 segments using 400 samples, cross-validated on 100 samples, and applied to the data from 5 reliability studies. On cross-validation, the validity of the prediction formulas ranged from .93 to 1.0 (M = .98). In the 5 reliability studies, the average difference between estimated and actual chance agreement rates was .00048 and the average difference between estimated and actual kappa values was .00011 (maximum = .0052). Thus, the regression formulas quite accurately predicted chance agreement rates and kappa coefficients for response segments.     

Effects of meaningfulness and organization on problem solving and computability judgments

When subjects were required to calculate answers for computable problems and answer questions, an interaction was found corresponding to that obtained by Kieras and Greeno (1975) from judgments of computability. With nonsense formulas, much longer times were required to identify noncomputable problems than to compute answers, with a much smaller difference when formulas consisted of meaningful concepts. The better performance on noncomputable problems and questions with meaningful formulas corroborates an interpretation that those items test the connection of algorithms with general conceptual knowledge. Finally, it was found that for relatively complex problems, solution times and time to judge computability were longer if nonsense formulas were learned in separate sets than if they were learned in a single set; however, no such effect was found with meaningful formulas. It was concluded that learning conditions influenced the integration of cognitive structure in the case of nonsense formulas, while subjects were able to adjust organization of the meaningful formulas.     

Frame Based Formulas for Intermediate Logics

In this paper we define the notion of frame based formulas. We show that the well-known examples of formulas arising from a finite frame, such as the Jankov-de Jongh formulas, subframe formulas and cofinal subframe formulas, are all particular cases of the frame based formulas. We give a criterion for an intermediate logic to be axiomatizable by frame based formulas and use this criterion to obtain a simple proof that every locally tabular intermediate logic is axiomatizable by Jankov-de Jongh formulas. We also show that not every intermediate logic is axiomatizable by frame based formulas. Presented by Johan van Benthem     

The relative error magnitude in three measures of change

Formulas for the standard error of measurement of three measures of change—simple difference scores, residualized difference scores, and the measure introduced by Tucker, Damarin, and Messick—are derived. Equating these formulas by pairs yields additional explicit formulas which provide a practical guide for determining the relative error of the three measures in any pretest-posttest design. The functional relationship between the standard error of measurement and the correlation between pretest and posttest observed scores remains essentially the same for each of the three measures despite variations in other test parameters (reliability coefficients, standard deviations), even when pretest and posttest errors of measurement are correlated.     

Generalized sample size determination formulas for experimental research with hierarchical data

Hierarchical data sets arise when the data for lower units (e.g., individuals such as students, clients, and citizens) are nested within higher units (e.g., groups such as classes, hospitals, and regions). In data collection for experimental research, estimating the required sample size beforehand is a fundamental question for obtaining sufficient statistical power and precision of the focused parameters. The present research extends previous research from Heo and Leon (2008) and Usami (2011b), by deriving closed-form formulas for determining the required sample size to test effects in experimental research with hierarchical data, and by focusing on both multisite-randomized trials (MRTs) and cluster-randomized trials (CRTs). These formulas consider both statistical power and the width of the confidence interval of a standardized effect size, on the basis of estimates from a random-intercept model for three-level data that considers both balanced and unbalanced designs. These formulas also address some important results, such as the lower bounds of the needed units at the highest levels.     

Readability of Three Adult Personality Tests: Basic Personality Inventory,Jackson Personality Inventory,and Personality Research Form-E

Three personality tests, the Basic Personality Inventory (BPI), the Jackson Personality Inventory (JPI), and the Personality Research Form-E (PRF-E) were evaluated for readability using a number of indices. Sentence length, word length, sentence type, and four readability formulas indicated that the readability of the BPI, JPI, and PRF-E would not impede the administration or interpretation of these tests in broad segments of the population.     

The measurement of reliability of social relations components from round‐robin designs

The social relations model (SRM) is a useful tool for measuring relationship effects, defined as the unique perceptions or behaviors of 2 people. The sources of variance in SRM studies are persons (actors and partners), groups, and items; the relationship effect is defined as the actor–partner interaction. By removing variance because of persons and groups, a measure of a “pure” relationship effect is obtained. In this article, generalizability theory (G Theory) is applied to estimate the reliability of SRM components from round‐robin data structures. Using G Theory, reliability formulas for actor, partner, group, and relationship are developed and interpretations for the reliability estimates are provided. The authors also discuss how these formulas can be used in both planning and interpreting results from relationship research.     

可满足性问题的归约技术

通过一个恰当的归约变换,可以将一个CNF公式变换为另一个具有某种特殊结构或性质的公式,使其两者具有相同的可满足性。一个典型的归约是将一般的CNF公式变换为3．GVF公式。通过构造一些恰当的工具,可以将公式类变换为所要求的正则类。极小不可满足公式具有一个临界特征,公式本身不可满足,从原始公式中删去任意一个子句后得到的公式可满足。我们提供了一种归约技术,通过构造恰当的极小不可满足公式作为工具,将公式类变换为具有正则结构的公式类。研究正则结构的公式的复杂性及性质很有意义。如,将一个从3．CNF公式变换为（3,4）一CNF公式,这里（3,4）一CNF公式是指公式中每个子句的长度恰为3,每个变元出现的次数恰为4。因此,（3,4）．SAT是一个NP．完全问题,并且正N-部图的诸多良好性质对于研究正则结构的SAT问题具有许多潜在的作用。     

Hintikka’s Independence-Friendly Logic Meets Nelson’s Realizability

Inspired by Hintikka’s ideas on constructivism, we are going to ‘effectivize’ the game-theoretic semantics (abbreviated GTS) for independence-friendly first-order logic (IF-FOL), but in a somewhat different way than he did in the monograph ‘The Principles of Mathematics Revisited’. First we show that Nelson’s realizability interpretation—which extends the famous Kleene’s realizability interpretation by adding ‘strong negation’—restricted to the implication-free first-order formulas can be viewed as an effective version of GTS for FOL. Then we propose a realizability interpretation for IF-FOL, inspired by the so-called ‘trump semantics’ which was discovered by Hodges, and show that this trump realizability interpretation can be viewed as an effective version of GTS for IF-FOL. Finally we prove that the trump realizability interpretation for IF-FOL appropriately generalises Nelson’s restricted realizability interpretation for the implication-free first-order formulas.     

Reliability formulas for noncompleted or speeded tests

New formulas are developed to give lower bounds to the reliability of a test, whether or not all respondents attempt all items. The formulas apply in particular, then, to completed tests, pure speed tests, pure power tests, and any mixture of speed and power. For the case of completed tests, the formulas give the same answer as certain standard ones; for noncompleted tests the formulas give a correct answer where previous standard formulas are inappropriate. The formulas hold both in the sense of retest reliability and of parallel tests.This research was facilitated by an uncommitted grant-in-aid to the writer from the Behavioral Sciences Division of the Ford Foundation.     

Measuring coherence using LP-models

This paper introduces a technique for measuring the degree of (in)coherence of inconsistent sets of propositional formulas. The coherence of these sets of formulas is calculated using the minimal models of those sets in G. Priest's Logic of Paradox. The compatibility of the information expressed by a set of formulas with the background or domain knowledge can also be measured with this technique. In this way, Hunter's objections to many-valued paraconsistent logics as instruments for measuring (in)coherence are addressed.     

A Bayesian hierarchical model for the measurement of working memory capacity

Working memory is the memory system that allows for conscious storage and manipulation of information. The capacity of working memory is extremely limited. Measurements of this limit, and what affects it, are critical to understanding working memory. Cowan (2001) and Pashler (1988) suggested applying multinomial tree models to data from change detection paradigms in order to estimate working memory capacity. Both Pashler and Cowan suggested simple formulas for estimating capacity with these models. However, in many cases, these simple formulas are inadequate, and may lead to inefficient or biased estimation of working memory capacity. I propose a Bayesian hierarchical alternative to the Pashler and Cowan formulas, and show that the hierarchical model outperforms the traditional formulas. The models are easy to use and appropriate for a wide range of experimental designs. An easy-to-use graphical user interface for fitting the hierarchical model to data is available.     

Coherence and Computational Complexity of Quantifier-free Dependence Logic Formulas

We study the computational complexity of the model checking problem for quantifier-free dependence logic ${(\mathcal{D})}$ formulas. We characterize three thresholds in the complexity: logarithmic space (LOGSPACE), non-deterministic logarithmic space (NL) and non-deterministic polynomial time (NP).     

A general possible worlds framework for reasoning about knowledge and belief

In this paper non-normal worlds semantics is presented as a basic, general, and unifying approach to epistemic logic. The semantical framework of non-normal worlds is compared to the model theories of several logics for knowledge and belief that were recently developed in Artificial Intelligence (AI). It is shown that every model for implicit and explicit belief (Levesque), for awareness, general awareness, and local reasoning (Fagin and Halpern), and for awareness and principles (van der Hoek and Meyer) induces a non-normal worlds model validating precisely the same formulas (of the language in question).     

Modal Horn Classes

This paper deals with modal Horn formulas. It contains a characterization of the classes of models definable by modal universal Horn formulas as well as a preservation result for modal universal Horn formulas. This revised version was published online in June 2006 with corrections to the Cover Date.