Testing Variability in the Two-Sample Case

A number of robust methods for testing variability have been reported in previous literature. An examination of these procedures for a wide variety of populations confirms their general robustness. Shoemaker's improvement of the F test extends that test use to a realistic variety of population shapes. However, a combination of the Brown–Forsythe and O'Brien methods based on testing kurtosis is shown to be conservative for a wide range of sample sizes and population distributions. The composite test is also shown to be more powerful in most conditions than other conservative procedures.     

A robust test for asymptotic independence of bivariate extremes

We show that the existing tests for asymptotic independence are sensitive to outliers. A robust test is proposed. The new test is made stable under contamination through a shrinkage scheme. Simulations show that the new test performs well in the presence of contaminated data while maintaining good properties when there is no contamination. An application to real data shows the added value of our new robust approach.     

Estimation of the Proportion of Defective Units by Using Group Testing Under the Existence of a Threshold of Detection

Group testing procedures, in which groups containing several units are tested without testing each unit, are widely used as cost-effective procedures in estimating the proportion of defective units in a population. A problem arises when we apply these procedures to the detection of genetically modified organisms (GMOs), because the analytical instrument for detecting GMOs has a threshold of detection. If the group size (i.e., the number of units within a group) is large, the GMOs in a group are not detected due to the dilution even if the group contains one unit of GMOs. Thus, most people conventionally use a small group size (which we call conventional group size) so that they can surely detect the existence of defective units if at least one unit of GMOs is included in the group. However, we show that we can estimate the proportion of defective units for any group size even if a threshold of detection exists; the estimate of the proportion of defective units is easily obtained by using functions implemented in a spreadsheet. Then, we show that the conventional group size is not always optimal in controlling a consumer's risk, because such a group size requires a larger number of groups for testing.     

Statistical Certification of Software Systems

Common software release procedures based on statistical techniques try to optimize the trade-off between further testing costs and costs due to remaining errors. We propose new software release procedures where the aim is to certify with a certain confidence level that the software does not contain errors. The underlying model is a discrete time model similar to the geometric Moranda model. The decisions are based on a mix of classical and Bayesian approaches to sequential testing and do not require any assumption on the initial number of errors.     

A Revisit to the Behrens–Fisher Problem: Comparison of Five Test Methods

We revisit the well-known Behrens–Fisher problem and apply a newly developed ‘Computational Approach Test’ (CAT) to test the equality of two population means where the populations are assumed to be normal with unknown and possibly unequal variances. An advantage of the CAT is that it does not require the explicit knowledge of the sampling distribution of the test statistic. The CAT is then compared with three widely accepted tests—Welch–Satterthwaite test (WST), Cochran–Cox test (CCT), ‘Generalized p-value’ test (GPT)—and a recently suggested test based on the jackknife procedure, called Singh–Saxena–Srivastava test (SSST). Further, model robustness of these five tests are studied when the data actually came from t-distributions, but wrongly perceived as normal ones. Our detailed study based on a comprehensive simulation indicate some interesting results including the facts that the GPT is quite conservative, and the SSST is not as good as it has been claimed in the literature. To the best of our knowledge, the trends observed in our study have not been reported earlier in the existing literature.     

Testing the Equality of the Noncentrality Parameters of Two Noncentral t-Distributions with Identical Degrees of Freedom

The problem of testing the equality of the noncentrality parameters of two noncentral t-distributions with identical degrees of freedom is considered, which arises from the comparison of two signal-to-noise ratios for simple linear regression models. A test procedure is derived that is guaranteed to maintain Type I error while having only minimal amounts of conservativeness, and comparisons are made with several other approaches to this problem based on variance stabilizing transformations. The new procedure derived in this article is shown to have good properties and will be useful for practitioners.     

Tests for homogeneity of risk differences in stratified design with correlated bilateral data

ABSTRACT

Correlated bilateral data arise from stratified studies involving paired body organs in a subject. When it is desirable to conduct inference on the scale of risk difference, one needs first to assess the assumption of homogeneity in risk differences across strata. For testing homogeneity of risk differences, we herein propose eight methods derived respectively from weighted-least-squares (WLS), the Mantel-Haenszel (MH) estimator, the WLS method in combination with inverse hyperbolic tangent transformation, and the test statistics based on their log-transformation, the modified Score test statistic and Likelihood ratio test statistic. Simulation results showed that four of the tests perform well in general, with the tests based on the WLS method and inverse hyperbolic tangent transformation always performing satisfactorily even under small sample size designs. The methods are illustrated with a dataset.     

Modeling of Discrete HNBUE Class with Hypothesis Testing Application

A new model is proposed to test whether an equipment whose life is measured in discrete time units fails due to uncontrollable chance factors alone against the alternatives that it degrades over time in the sense of discrete HNBUE (harmonic new better than used in expectation) aging. The test is shown to be consistent and the asymptotic distribution of the test statistic has been obtained. The critical points and the power of the test against various alternatives from discrete HNBUE class have been studied by means of simulation. Finally, the test is applied to a discrete reliability data to examine the performance.     

Testing the feasibility of a value‐added model of school quality in a low‐income country

Value‐added models (VAMS) are commonly used in high‐income countries for measuring the quality of teachers and schools, on the grounds that they are a fairer reflection of true quality than simple average test scores, as they account for differences in student intake. Not accounting for student's prior test scores can give a misleading impression of school quality. In this article, we adapt the current VAM of secondary school quality to the Ugandan context, and test its robustness. Using official test score data from Uganda, we test the robustness of the model to a range of different empirical specifications, including sensitivity to the inclusion of controls for student socioeconomic status. We find that the model is robust to a variety of different specifications and control variables. The VAM is low cost and has the potential to provide a clearer signal to parents, teachers, schools, and policy‐makers about how much learning is actually happening in different schools. This approach could be carried out at low cost in a wide range of low‐income countries that have similar testing regimes.