Applied Statistics Education and Research Collaboration (ASEARC) - Conference Papers

Systems theory and improving healthcare

Peter Howley — Mon, 05 Mar 2012 17:31:08 PST

The accreditation and quality measurement and reporting systems in health care organisations are believed to influence patient safety and quality of care. In order to gain knowledge about the effects of these two systems, an holistic healthcare systems relationship model was recently constructed and a series of adaptive-control studies developed to explore relationships between segments within the systems relationship model.

This paper describes where we’ve been, where we are and where we’re headed: the studies, the models, the supporting research and the systems theory-based approach encompassing the current direction.

Threshold Autoregressive Models in Finance: A Comparative Approach

David Gibson — Mon, 05 Mar 2012 17:28:18 PST

Financial instruments are known to exhibit abrupt and dramatic changes in behaviour. This paper investigates the relative efficacy of two-regime threshold autoregressive (TAR) models and smooth threshold autoregressive (STAR) models, applied successfully to econometric dynamics, in the finance domain. The nature of this class of models is explored in relation to the conventional linear modeling approach, with reference to simulated data and real stock return indices.

Is the Basis of the Stock Index Futures Markets Nonlinear?

Heni Puspaningrum — Mon, 05 Mar 2012 17:26:05 PST

A considerable amount of papers use a cost-carry model in modelling the relationship between future and spot index prices. The cost-carry model defines basis, bt;T , at time t and maturity date of the future contract at T as bt;T = ft � st = r(T � t), where ft, st and r denote the log of future prices, the log of spot index prices and the difference between interest rate and dividend rate, respectively. Using daily data time series on future contracts of the S&P 500 index and the FTSE 100 index, as well as the price levels of the corresponding underlying cash indices over the sample period from January 1, 1988 to December 31, 1998, [1] argued that there is significant nonlinearity in the dynamics of the basis due to the existence of transaction costs or agents heterogeneity. They found that the basis follows a nonlinear stationary ESTAR (Exponential Smooth Transition Autoregressive) model. However, based on the study with the S&P 500 data series from January 1, 1998 to December 31, 2009, we conclude that there is no significant difference between a linear AR(p) model and a nonlinear STAR model in fitting the data.

Prior Sensitivity Analysis for a Hierarchical Model

Junaidi — Mon, 05 Mar 2012 17:23:18 PST

Meta-analysis can be presented in the Frequentist or Bayesian framework. Based on the model of DuMouchel, a simulation study is conducted which fixes the overall mean and variance-covariance matrix to generate estimates of the true mean effect. These estimates will be compared to the true effect to assess bias. A sensitivity analysis, to measure the robustness of results to the selection of prior distributions, is conducted by employing Uniform and Pareto distributions for the variance components, the t-distribution for the overall mean component and a combination of priors for both variance and mean components respectively. Results were more sensitive when the prior was changed only on the overall mean component.

Advice for the potential statistical consultant

Ken Russell — Mon, 05 Mar 2012 17:20:09 PST

Many of those who have never practised statistical consulting seem to view it from one of two extremes: a trivial exercise that any statistician could do, or an extremely difficult task occasioning extreme anxiety. Of course, the truth is that it lies somewhere in between. I will consider various aspects of statistical consulting, including the characteristics of a successful consultation, the necessary knowledge, skills and attributes of the consultant, things to do and not to do, and the pleasures and frustrations that one can gain from consulting.

Bootstrap confidence intervals for Mean Average Precision

Laurence Park — Mon, 05 Mar 2012 17:18:30 PST

Due to the unconstrained nature of language, search engines (such as the Google search engine) are developed and compared by obtaining a document set, a sample set of queries and the associated relevance judgments for the queries on the document set. The de facto standard function used to measure the accuracy of each search engine on the test data is called mean Average Precision (AP). It is common practice to report mean AP scores and the results of paired significance tests against baseline search engines, but the confidence in the mean AP score is never reported. In this article, we investigate the utility of bootstrap confidence intervals for mean AP. We find that our Standardised logit bootstrap confidence intervals are very accurate for all levels of confidence examined and sample sizes.

Assessing Poisson and Logistic Regression Models Using Smooth Tests

Paul Rippon — Mon, 05 Mar 2012 17:16:29 PST

The smooth testing approach described in [2] has been used to develop a test of the distributional assumption for generalized linear models. Application of the test to help assess Poisson and logistic regression models is discussed. Power is compared to other common tests.

Smooth Tests of Fit for a Mixture of Two Poisson Distributions

John Best — Mon, 05 Mar 2012 17:13:13 PST

In this note smooth tests of fit for a mixture of two Poisson distributions are derived and compared with a traditional Pearson chi-squared test. The tests are illustrated with a classic data set of deaths per day of women over 80 as recorded in the London Times for the years 1910 to 1912.

Were Clopper & Pearson (1934) too careful?

Frank Tuyl — Mon, 05 Mar 2012 17:08:11 PST

The ‘exact’ interval due to Clopper & Pearson is often considered to be the gold standard for estimating the binomial parameter. However, for practical purposes it is also often considered to be too conservative, when mean rather than minimum coverage close to nominal could be more appropriate. It is argued that (1) in their article, Clopper & Pearson themselves changed between these two criteria, and (2) ‘approximate’ is indeed better than ‘exact’.

Clickers in an introductory statistics course

Alice Richardson — Mon, 05 Mar 2012 17:06:13 PST

This paper reports on a pilot study of the use of an student response system, commonly known as clickers, in an introductory statistics course. Early results show a small but significant increase in grades following the introduction of clickers. A Statistics Concept Inventory (SCI) was also used to assess students’ understanding of the course concepts. The usefulness of the SCI was partially supported, as many questions were better answered by more able students.

An early ASEARC-taught subject: has it been a success?

Carole Birrell — Mon, 05 Mar 2012 16:53:34 PST

The Applied Statistics Education and Research Collaboration (ASEARC) aims to “involve joint development and delivery of subjects and courses. : : : There would be effciency benefits involved in sharing subjects. There would also be significant benefits in : : : students accessing subjects that would otherwise not be available to them, developed and presented by experts who would not usually be accessible. In parallel with the subject review the technological and administrative environment will also be assessed : : : ”

A 300-level subject covering Sample Surveys and Experimental Design has now been taught jointly to the Universities of Wollongong and Newcastle for two years, first using video-conferencing and then the Access Grid. In each year, the subject was delivered by the same two lecturers.

We provide an initial review of the subject. We discuss its organisation, the use of the technology, changes in our teaching and administrative styles needed to cope with this mode of delivery, feedback from students, and our reaction to all of these. An overview of the subject results is given.

The Odds Ratio and Aggregate Data: The 2×2 Contingency Table

Eric Beh — Mon, 05 Mar 2012 16:50:45 PST

The odds ratio remains one of the simplest of measures for quantifying the association structure between two dichotomous variables. Its use is especially applicable when the cell values of a 2× 2 contingency table are known. However, there are cases where this information is not known. This may be due to reasons of confidentiality or because the data was not collected at the time of the study. Therefore one must resort to considering other means of quantifying the association between the variables. One strategy is to consider the aggregate association index (AAI) proposed by [1]. This paper will explore the characteristics of the AAI when considering the odds ratio of the 2× 2 contingency table.

Nonparametric Tests for Two Factor Designs

John Rayner — Mon, 05 Mar 2012 16:48:57 PST

We show how to construct nonparametric tests for two factor designs. These tests depend on whether or not the factors are ordered. Pearson’s X2 statistic is decomposed into components of orders 1, 2, ... . These components may be further decomposed, the decomposition depending on the design. If neither factor is ordered, the components reflect linear, quadratic etc main and interaction effects. The approach is demonstrated with reference to the latin squares design.

Two-Sample Testing for Equality of Variances

David Allingham — Mon, 05 Mar 2012 16:45:53 PST

To test for equality of variances given two independent random samples from univariate normal populations, popular choices would be the two-sample F test and Levene’s test. The latter is a nonparametric test while the former is parametric: it is the likelihood ratio test, and also a Wald test. Another Wald test of interest is based on the difference in the sample variances. We give a nonparametric analogue of this test and call it the R test. The R, F and Levene tests are compared in an indicative empirical study.

For moderate sample sizes when assuming normality the R test is nearly as powerful as the F test and nearly as robust as Levene’s test. It is also an appropriate test for testing equality of variances without the assumption of normality, and so it can be strongly recommended.

Contextual Effects in Modeling for Small Domains

Mohammad-Reza Namazi-Rad — Mon, 05 Mar 2012 16:42:02 PST

During last two decades, different Small Area Estimation (SAE) methods have been proposed to overcome the challenge of finding reliable small area estimates. This happens a lot that the required data for various research purposes are available at different levels. Based on availability of data, individual-level or aggregated-level models are implied in SAE. However, the estimated values for model parameters obtained from individual-level analysis can be different from the one obtained based on analysis of aggregate data. Generally, this is referred to as the ecological fallacy. This happens due to some substantial contextual or area-level effects in the covariates. To have a good interpretation of available data, possible contextual effects must be carefully included, measured, and accounted for in statistical models for calculating reliable estimates. Ignoring these effects leads to misleading results. The main advantage of contextual models is to help statisticians in studying aggregated-level data without concerning about the issue of ecological fallacy. In this paper, synthetic estimators and Empirical Best Linear Unbiased Predictors (EBLUPs) are studied based on different levels of linear mixed models. Using a numerical simulation study, the key role of contextual area-level effects is examined for model selection in SAE.

Finding the Best ARIMA Model to Forecast Daily Peak Electricity Demand

Mohamad As'ad — Sun, 04 Mar 2012 19:56:13 PST

Time series models of peak daily electricity demand (June 2010-May 2011) are constructed using half hourly demand data from New South Wales, Australia. We are interested in predicting the peak electricity demand for the first seven days of June 2011 starting from 31 the May 2011. How much of the past data should be used for constructing an appropriate model which is able to provide a better forecast for the peak demand? Four appropriate ARIMA (autoregressive integrated moving average) models based past three, six, nine and twelve months of data are considered. Using RMSE (root mean square error) and MAPE (mean absolute percentage error) to measure forecast accuracy, it is shown that the ARIMA model build based on past three months data is the best model in term of forecasting two to seven days ahead and ARIMA model based on past six months data is the best model to forecast one day ahead.

Estimation in Autoregressive Population Models

Thomas Suesse — Sun, 04 Mar 2012 19:54:06 PST

Autoregressive (AR) models for spatial and social interaction have been proposed by many authors. A sample of units is obtained and the model is applied to this sample. Estimation methods such as the maximum likelihood method (ML) have been employed and investigated in the literature. The main assumption is that a response depends on other responses, when these units interact. Some of those units will be in the sample and some in the non-sample. Therefore the model should apply to the whole population rather to the sample only. Under such a population model, the marginal model for the responses of the sample is generally not of the same form and depends on covariates and interactions of non-sample units. Standard estimation methods using the sample information only are inappropriate. In this paper we investigate the performance of the standard ML method and a modified ML version that is based on the population model. Due to the population size, we also consider an approximate ML method. The results show that the standard ML method yields biased estimates and the modified ML version along with the approximate method perform far better.

Evaluating the Use of Worked Examples and Problem Solving Methods in Teaching Mathematics for ESL Students at the Tertiary Level

Ali Algarni — Sun, 04 Mar 2012 19:50:47 PST

This study presents an overview of the baseline attitudes of King Abdul-Aziz, University, Jeddah, Saudi Arabia (KAU) students to various methods used in mathematics teaching when being taught mathematics in a second language. Seventy male undergraduate students who were enrolled in the first year mathematics subject MATH132 at the KAU were asked to participate in the survey. The results showed that there were differences between the perceived effectiveness of the use of worked examples and problem solving in teaching of mathematics for ESL at tertiary level. Furthermore, the study found that the ESL students who rate their mathematics ability as low prefer to study mathematics using worked examples while the students who rate their mathematics ability as high prefer problem solving or a mixture of problem solving and worked examples. Comments from students who prefer worked examples include their experience of a reduction in anxiety whereas for students who prefer problem solving, comments suggest they experience an increase in confidence. This suggests an effective teaching strategy would be to scaffold from worked examples to problem solving and through this benefitting both weak and more able students.

Minimizing sample overlap with surveys using different geographic units

Kevin Lu — Sun, 04 Mar 2012 19:47:15 PST

The ABS runs Australia-wide population surveys using area-based multi-stage designs. One challenge for the ABS and other National Statistical Organizations is to avoid returning to areas selected in other recent surveys so that households are not overburdened with multiple surveys, while ensuring areas have the correct unconditional probabilities of selection for the survey to represent all of the country. There is a well-known method to choose primary-stage units in a way that minimizes overlap and leaves the unconditional probabilities of selection unchanged. However, this method cannot simply be applied when the primary-stage units in the current survey are geographically di erent from those used in previous surveys. We develop two extensions to the existing approach for an ABS household survey facing this challenge. The first method uses simulations as part of computing conditional probabilities of selection, while the second uses a weighted average of conditional probabilities applied on the geographic intersections of the previous and current primary-stage units. We show that both methods preserve the unconditional probability of selection, but do not achieve the same levels of overlap.

The Aggregate Association Index and its Application in the 1893 New Zealand Election

Tran Duy — Sun, 04 Mar 2012 19:43:56 PST

Politics and gender have always been a hot topic for at least four decades, especially for politicians, social scientists, feminists and historians. Numerous statistical methods have been developed to try to establish and understand if any difference occurs between men’s and women’s voting patterns. However, due to confidentiality issues or policies in many real-life situations, only aggregate information is often available. As a result, a significant amount of valuable information about politics and gender may have been lost over the years.

The objective of this paper is to consider the development and application of a new method called Aggregate Association Index (AAI), which can be applied in such situations of gendered aggregate political data. Moreover, these two aspects of the AAI shall be examined by considering the New Zealand election data in 1893 and this may well help us establish the future development for the index.