Arguing About the Effectiveness of Assessments for the Classroom

Approaches to test score use and test purpose lack the well-developed methodological guidelines and established sources of evidence available for intended score interpretation. We argue in this paper that this lack fails to reflect the ultimate purpose of a test score—to help solve an important problem faced by intended test users. We explore the treatment of intended test purpose and test score use under the chain of assumption/inferences perspective identified within an argument-based approach to validity. Next, we revisit the notion of test score use and argue that, at least for classroom assessments based on complex constructs, such as learning progressions in math and science, test score use can be more effectively conceptualized as part of a potential solution to solving a problem, or “job-to-be-done.”. We argue for shifting from the definition of validity to the concept of effectiveness. Finally, we illustrate an argument- based approach to test score effectiveness by contrasting effectiveness arguments for interim assessments based on a conventional test blueprint or a test blueprint augmented with learning progressions.     

The interpretation and use of stability data in the certification of reference materials

 Stability tests are carried out on candidate reference materials in order to ascertain that the certification values continue to be valid a reasonable time after completion of the certification analysis. These tests are also used for recommending storage conditions, as well as the duration of storage before certification values need be rechecked. BCR (Community Bureau of Reference) reference materials do not normally have an expiry date, but rely on stability monitoring throughout the lifetime of the certified material. The 1997 version of the BCR Guidelines for the production and certification of reference materials does, however, take into account the necessity of limiting the validity of a certification, when degradation of the material during storage cannot be ignored. This paper discusses an example of significant degradation taking place between the time of completion of the certification analysis and the issue of a formal certificate. Various options are presented together with an account of their influence on the certified values and their uncertainties. Received: 3 October 1997 · Accepted: 3 November 1997     

Building confidence in models for multiple audiences: The modelling cascade

This paper reports on a model building process developed to enable multiple audiences, particularly non-experts, to appreciate the validity of the models being built and their outcomes. The process is a four stage reversible cascade. This cascade provides a structured, auditable/transparent, formalized process from “real world” interviews generating a rich qualitative model through two intermediate steps before arriving at a quantitative simulation model. There are a number of advantages of the cascade process including; achieving comprehensiveness, developing organizational learning, testing the veracity of multiple perspectives, modeling transparency, achieving common understanding across many audiences and promoting confidence building in the models. The paper, based on extensive work with organizations, discusses both the cascade process and its inherent benefits.     

Accreditation of sampling activities

Since the introduction of ISO/IEC 17025 it is a requirement for all accredited laboratories to include sampling in their quality statements. It is well understood that sampling and handling of the sample are key factors in the validity of a result. The fact that many laboratories worldwide are not involved in sampling poses a challenge to accreditors liability. This article describes the Israel Laboratory Accreditation Authoritys (ISRAC) and other accreditors approaches to sampling.Presented at the Second International Conference on Metrology—Trends and Applications in Calibration and Testing Laboratories, 4–6 November 2003, Eilat, Israel.     

关于聚类有效性函数熵公式HP（u,c）

对文[1]提出的聚类有效性函数HP(u,c）作了一定的理论分析,并就文[1]使用的数据及其他数据进行了计算机模拟。模拟结果显示：HP（u,c) 作为FCM算法的聚类有效性函数是不合适的。     

An analysis of chaos-based security solution for fingerprint data

Recently, an engineering report on chaos-based security solution has been proposed for fingerprint data during communication and transmission (IEEE Trans. Instrum. Meas. 61 (April (4)) (2012) 876–887). It has been claimed that experimental results and security analysis demonstrate the efficiency of the security solution in this report. However, from a scientific perspective, we give a validity analysis. Firstly, we demonstrate that the reversibility of integer reversible hidden transform (RHT) cannot be guaranteed under the current constraint condition in the original paper and then counterexamples are given to verify demonstration. In addition, in its experiment and performance analysis parts, there also exist several problems. Finally, we put forward some suggestive remarks on the designing of security solution for fingerprint data.     

Introducing validity in fuzzy probability for judicial decision-making

Since the Age of Enlightenment, most philosophers have associated reasoning with the rules of probability and logic. This association has been enhanced over the years and now incorporates the theory of fuzzy logic as a complement to the probability theory, leading to the concept of fuzzy probability. Our insight, here, is integrating the concept of validity into the notion of fuzzy probability within an extended fuzzy logic (FLe) framework keeping with the notion of collective intelligence. In this regard, we propose a novel framework of possibility–probability–validity distribution (PPVD). The proposed distribution is applied to a real world setting of actual judicial cases to examine the role of validity measures in automated judicial decision-making within a fuzzy probabilistic framework. We compute valid fuzzy probability of conviction and acquittal based on different factors. This determines a possible overall hypothesis for the decision of a case, which is valid only to a degree. Validity is computed by aggregating validities of all the involved factors that are obtained from a factor vocabulary based on the empirical data. We then map the combined validity based on the Jaccard similarity measure into linguistic forms, so that a human can understand the results. Then PPVDs that are obtained based on the relevant factors in the given case yield the final valid fuzzy probabilities for conviction and acquittal. Finally, the judge has to make a decision; we therefore provide a numerical measure. Our approach supports the proposed hypothesis within the three-dimensional contexts of probability, possibility, and validity to improve the ability to solve problems with incomplete, unreliable, or ambiguous information to deliver a more reliable decision.     

What do mathematicians mean by proof? A comparative-judgement study of students’ and mathematicians’ views

We present a study in which mathematicians and undergraduate students were asked to explain in writing what mathematicians mean by proof. The 175 responses were evaluated using comparative judgement: mathematicians compared pairs of responses and their judgements were used to construct a scaled rank order. We provide evidence establishing the reliability, divergent validity and content validity of this approach to investigating individuals’ written conceptions of mathematical proof. In doing so, we compare the quality of student and mathematician responses and identify which features the judges collectively valued. Substantively, our findings reveal that despite the variety of views in the literature, mathematicians broadly agree on what people should say when asked what mathematicians mean by proof. Methodologically, we provide evidence that comparative judgement could have an important role to play in investigating conceptions of mathematical ideas, and conjecture that similar methods could be productive in evaluating individuals’ more general (mathematical) beliefs.     

On the classification of first order Gödel logics

We characterize the recursively enumerable first order Gödel logics with △ with respect to validity and non-satisfiability. The finitely valued and four infinitely valued Gödel logics with △ are recursively enumerable, not-satisfiability is recursively enumerable if validity is recursively enumerable. This is in contrast to first order Gödel logics without △, where validity is recursively enumerable for finitely valued and two infinitely valued Gödel logics, not-satisfiability is recursively enumerable if validity is recursively enumerable or 0 isolated in the truth value set.