The impact of contingency factors on validation of problem structuring methods

Although much has been written about validating Decision support systems andother ‘hard’ OR models, less has been written about validating‘soft’ OR models. This article seeks to determine which contingencyfactors known to influence DSS validation are also important factors influencingproblem structuring methods (PSM) validation. In addition, after consultationwith PSM experts other contingency factors influencing PSM validation areproposed. Evidence from these PSM experts concerning the levels of influence ofthese factors is used to support proposals for a contingency approach to PSMvalidation.     

A survey of contingency factors affecting the validation of end-user spreadsheet-based decision support systems

Decision support systems have become widespread in recent years. However, most of these systems are not carefully validated and this has led in some cases to serious errors. One of the principal reasons for the lack of validity is the lack of an operationalised validation methodology. A simplified validity framework has already been developed by the authors as the first part of a 3-phase approach towards devising a practical validation methodology. This paper describes the second phase, reporting as it does on a survey that has been undertaken to unearth the contingency factors that influence how the process of validation, employing the validity framework, will be carried out for a particular kind of decision support system—one involving a spreadsheet model.     

Computational thinking and constructionism: creating difference equations in spreadsheets

The invention of the computer has led to the establishment of a new research paradigm, computation, which has recently become more and more popular in scientific exploration. However, computation is not well represented in high school and university curricula in science and engineering, although it applies to a wide range of disciplines beyond computer science and software engineering. In light of the increasing need to provide students with computational education, this paper presents a novel way to develop computational thinking among students. The proposed approach is based on the implementation of Papert's theory of constructionism in electronic spreadsheets. In this approach, students build their knowledge while constructing the difference equation that describes a physical (or engineering) phenomenon, based on specific cases investigated in the spreadsheet. The method does not require the students to write code or perform complex calculations in the spreadsheet and makes it possible to teach advanced subjects at a relatively early stage. The method is demonstrated through contents taken from the secondary and tertiary curricula in mechanics and electromagnetism.     

Counting subsets of contingency tables

We describe multistage Markov chain Monte Carlo (MSMCMC) procedures which, in addition to estimating the total number of contingency tables with given positive row and column sums, estimate the number, $Q$ , and the proportion, $P$ , of those tables that satisfy an additional, possibly, nonlinear constraint. Three Options, A, B, and C, are studied. Options A and B exploit locally optimal statistical properties whereas judicious assignment of a particular parameter of Option C allows estimation with approximately minimal standard error. Ten examples of varying dimensions and total entries illustrate and compare the procedures, where $Q$ and $P$ denote the number and proportion of chi-squared statistics less than a given value. For both small and large dimensional tables, the comparisons favor Options A and B for moderate $P$ and Option C for small $P$ . Additional comparison with sequential importance sampling estimates favors the latter for small dimensional tables and moderate $P$ but favors Option C for large dimensional tables for both small and moderate $P$ . The proposed options extend an earlier MSMCMC technique for estimating total count and, in principle, can be further extended to incorporate additional constraints.     

Solution to projectile motion with quadratic drag and graphing the trajectory in spreadsheets

This note gives the analytical solution to projectile motion with quadratic drag by decomposing the velocity vector to x, y coordinate directions. The solution is given by definite integrals. First, the impact angle is estimated from above, then the projectile coordinates are computed, and the trajectory is graphed at various launch angles and speed using an interactive Excel application.     

影响中学生数学成绩因素的通径分析

用绵阳市 6 0 0名初中学生构成样本 ,采用J¨oreskog提出的线性结构方程式模型理论 ,以及J¨oreskog和S¨orbom开发的软件系统LIREL8.3对调查的资料进行分析。结果表明 :用 2 0个显在变量和 10个隐在变量研究影响中学生数学成绩的因素 ,最后有 13个显在变量入选构成外生模型 ,有 7个隐在变量变量入选构成内生模型。Homeback、Attitud、Views、EQ、IQ和Class这 6个内生的隐在变量对中学生的数学成绩均存在不同程度的影响 ,其中以Attitud、Homeback、IQ和EQ对数学成绩的贡献最大。内生模型中 6个内生的隐在变量的R2 的平均值为 0 .2 0 ,该模型中数学成绩(Mathachi)这一变量中可预测的方差占到了 4 1% (R2 =0 .4 1) ,将这两者结合起来考虑 ,所建立的模型应当是比较有说服力的。     

非主观因素对小学生学习成绩影响的方差分析

本文采用非参数的方差分析方法,结合实际调查数据,初步探讨了性别、家庭类型、入学年龄等非主观因素对小学生学习成绩的影响。结果表明这些非主观因素对小学生的学习成绩是有显著影响的。     

An ordering of dependence for contingency tables

A majorization ordering is defined on matrices with the same row and column sums. This ordering is used as an ordering of dependence for contingency tables. Results are derived for maximal and minimal matrices with respect to the majorization ordering. This theory can be used to maximize and minimize Schur concave functions defined over matrices, when there are row and column sum constraints; in this paper, it is applied to the algorithm of Mehta and Patel (1983) for finding the P-value of Fisher's exact test.     

Clustering of contingency table and mixture model

Basing cluster analysis on mixture models has become a classical and powerful approach. It enables some classical criteria such as the well-known k-means criterion to be explained. To classify the rows or the columns of a contingency table, an adapted version of k-means known as Mndki2, which uses the chi-square distance, can be used. Unfortunately, this simple, effective method which can be used jointly with correspondence analysis based on the same representation of the data, cannot be associated with a mixture model in the same way as the classical k-means algorithm. In this paper we show that the Mndki2 algorithm can be viewed as an approximation of a classifying version of the EM algorithm for a mixture of multinomial distributions. A comparison of the algorithms belonging in this context are experimentally investigated using Monte Carlo simulations.     

试论影响学生提出数学问题的因素

影响学生提出数学问题的因素包括传统文化因素、学校内部因素、教师因素、学生因素．     

Characterizing optimal sampling of binary contingency tables via the configuration model

A binary contingency table is an m × n array of binary entries with row sums r = (r₁, …, r_m) and column sums c = (c₁, …, c_n). The configuration model generates a contingency table by considering r_i tokens of type 1 for each row i and c_j tokens of type 2 for each column j, and then taking a uniformly random pairing between type‐1 and type‐2 tokens. We give a necessary and sufficient condition so that the probability that the configuration model outputs a binary contingency table remains bounded away from 0 as \begin{align*}N=\sum_{i=1}^m r_i=\sum_{j=1}^n c_j\end{align*} goes to ∞. Our finding shows surprising differences from recent results for binary symmetric contingency tables. © 2012 Wiley Periodicals, Inc. Random Struct. Alg., 2012     

An alternative tactic to deal with the contingency of driver absenteeism

On any given workday, unexpected absence of drivers calls for emergency operational tactics to ensure completion of planned deliveries of merchandise to customers. A typical tactic in the workforce scheduling literature is to rely exclusively on a pool of workers who were not scheduled for work; that is, full-time off-duty drivers and part-time drivers. Concerns about the expense of maintaining a staff of part-timers prompt consideration of alternative tactics. This study proposes one such alternative. It minimizes the part-time pool by reassigning routes among drivers who show for work. In multi-route vehicle routing problems, the prospect of this alternative arises because cost-minimizing patterns of travel distances across routes often allow one driver to do extra work by handling more than one route (subject to time-window and workload constraints). By considering costs such as overtime rates when drivers perform extra (emergency) driving duties and the cost to maintain part-time staff, this study tests the efficacy of the aforementioned alternative. Its efficacy is confirmed by the fact that it is less costly than the typical tactic: while the typical tactic adds just over 22% to driver payroll, the proposed alternative adds a noticeably smaller cost of just under 15%.     

列联表分析及在SPSS中的实现

本文首先介绍了列联表的一致性与独立性检验、相关分析、某些特殊统计量等内容 ,然后说明了上述分析在SPSS9.0中的实现 ,并最终结合实例进行了应用     

A practical method of determining project risk contingency budgets

Given a collection of accepted risks with corresponding impacts and probabilities over the life of a project (or a relevant portion), a method to estimate the total potential impact at a given certainty is presented. Project sponsors and managers can decide their risk tolerance and set aside corresponding contingency funds. This analytic method uses a binomial distribution with a probability equal to the risks’ average probability. At a desired statistical confidence level, the number of risks to consider is determined, and risks are ranked in descending order of either impact or expected value of impact. The ranked risks’ impacts are then summed over the specified number of risks, leading to an appropriate contingency budget. The budget found with this method compares extremely well with the one ascertained from numerical simulations of the risk occurrences.     

Comparing multi-dimensional contingency fit to financial performance of organizations

In theory, it is widely accepted that an organization’s optimal structure is contingent upon various situational factors such as market conditions, nature of work and properties of technology. In practice, providing practical advice based on this understanding has been difficult. This paper demonstrates that it is possible to find a correlation between financial performance, as measured by growth in Return on Assets, and degree of compliance with the recommendations of the contingency theory model known as Interaction Value Analysis (IVA). IVA is based on an abstract theoretical representation of organizational work as a series of value-adding interactions among rational value-maximizing agents. Six different dimensions of an organization’s situation are represented as parameters of the equation that sums up the value added by all interactions within the organization. This “Multi-dimensional” approach is contrasted with the “Multi-contingency” model, which aggregates the effects of multiple contingent-design rules without considering how the rules overlap or otherwise influence one another. The success of the six-parameter IVA model in partially predicting financial performance is an inducement to expand IVA to include more of the parameters included in the Multi-contingency model.     

Tests for the marginal probabilities in the two-way contingency table under restricted alternatives

Testing hypotheses on the marginal probabilities of a two-way contingency table is discussed. Three statistics are considered for testing the hypothesis of specified probabilities in the margins against alternatives with certain kind of order restriction. The properties of these statistics are discussed and their asymptotic behaviors are compared in depth. An appliction which motivated the consideration of the original testing problem is illustrated with a practical data.     

Validation of association

Recognizing, quantifying and visualizing associations between two variables is increasingly important. This paper investigates how a new function-valued measure of dependence, the quantile dependence function, can be used to construct tests for independence and to provide an easily interpretable diagnostic plot of existing departures from the null model. The dependence function is designed to detect general dependence structure between variables in quantiles of the joint distribution. It gives an insight into how the dependence structure changes in different parts of the joint distribution. We define new estimators of the dependence function, discuss some of their properties, and apply them to construct new tests of independence. Numerical evidence is given to the tests benefits against three recognized independence tests introduced in the previous years. In real-data analysis, we offer the use of our tests and the graphical presentation of the underlying dependence structure.     

The dependence structure of conditional probabilities in a contingency table

Conditional probability and statistical independence can be better explained with contingency tables. In this note some special cases of 2 X 2 contingency tables are considered. In turn an interesting insight into statistical dependence as well as independence of events is obtained.