Search results for "II error"
showing 9 items of 19 documents
A Unified Approach to Measuring Accuracy of Error Indicators
2014
In this paper, we present a unified approach to error indication for elliptic boundary value problems. We introduce two different definitions of the accuracy (weak and strong) and show that various indicators result from one principal relation. In particular, this relation generates all the main types of error indicators, which have already gained high popularity in numerical practice. Also, we discuss some new forms of indicators that follow from a posteriori error majorants of the functional type and compare them with other indicators. Finally, we discuss another question related to accuracy of error indicators for problems with incompletely known data.
Individual measurements and nested designs in aquaculture experiments: a simulation study
1998
Simple and nested models for analysis of variance (ANOVA) in aquaculture experiments were compared with the help of computer simulations. Simple models for analysing variables that are based on tank means, such as final weight and growth rate, were found to be sensitive to differences in the number of individual observations in each tank. In comparison to nested models that take into account individual measurements, the simple models were found to overestimate the F ratio and increase the risk of committing type I error, i.e., accepting a false alternative hypothesis. Further, nested models permit greater flexibility in experimental design, and allow more economical solutions within a given…
Detection of spatial disease clusters with LISA functions.
2011
Detection of disease clusters is an important tool in epidemiology that can help to identify risk factors associated with the disease and in understanding its etiology. In this article we propose a method for the detection of spatial clusters where the locations of a set of cases and a set of controls are available. The method is based on local indicators of spatial association functions (LISA functions), particularly on the development of a local version of the product density, which is a second-order characteristic of spatial point processes. The behavior of the method is evaluated and compared with Kulldorff's spatial scan statistic by means of a simulation study. It is shown that the LI…
Sample-size calculation and reestimation for a semiparametric analysis of recurrent event data taking robust standard errors into account
2014
In some clinical trials, the repeated occurrence of the same type of event is of primary interest and the Andersen-Gill model has been proposed to analyze recurrent event data. Existing methods to determine the required sample size for an Andersen-Gill analysis rely on the strong assumption that all heterogeneity in the individuals' risk to experience events can be explained by known covariates. In practice, however, this assumption might be violated due to unknown or unmeasured covariates affecting the time to events. In these situations, the use of a robust variance estimate in calculating the test statistic is highly recommended to assure the type I error rate, but this will in turn decr…
Tests for Differentiation in Gene Expression Using a Data-Driven Order or Weights for Hypotheses
2005
In the analysis of gene expression by microarrays there are usually few subjects, but high-dimensional data. By means of techniques, such as the theory of spherical tests or with suitable permutation tests, it is possible to sort the endpoints or to give weights to them according to specific criteria determined by the data while controlling the multiple type I error rate. The procedures developed so far are based on a sequential analysis of weighted p-values (corresponding to the endpoints), including the most extreme situation of weighting leading to a complete order of p-values. When the data for the endpoints have approximately equal variances, these procedures show good power properties…
Power and Type I Error of the Mean and Covariance Structure Analysis Model for Detecting Differential Item Functioning in Graded Response Items.
2016
In this simulation study, we investigate the power and Type I error rate of a procedure based on the mean and covariance structure analysis (MACS) model in detecting differential item functioning (DIF) of graded response items with five response categories. The following factors were manipulated: type of DIF (uniform and non-uniform), DIF magnitude (low, medium and large), equality/inequality of latent trait distributions, sample size (100, 200, 400, and 800) and equality or inequality of the sample sizes across groups. The simulated test was made up of 10 items, of which only 1 contained DIF. One hundred replications were generated for each simulated condition. Results indicate that the MA…
The Power of Word-Frequency Based Alignment-Free Functions: a Comprehensive Large-Scale Experimental Analysis
2021
Abstract Motivation Alignment-free (AF) distance/similarity functions are a key tool for sequence analysis. Experimental studies on real datasets abound and, to some extent, there are also studies regarding their control of false positive rate (Type I error). However, assessment of their power, i.e. their ability to identify true similarity, has been limited to some members of the D2 family. The corresponding experimental studies have concentrated on short sequences, a scenario no longer adequate for current applications, where sequence lengths may vary considerably. Such a State of the Art is methodologically problematic, since information regarding a key feature such as power is either mi…
Adaptive Modifications of Hypotheses After an Interim Analysis
2001
It is investigated how one can modify hypotheses in a trial after an interim analysis such that the type I error rate is controlled. If only a global statement is desired, a solution was given by Bauer (1989). For a general multiple testing problem, Kieser, Bauer and Lehmacher (1999) and Bauer and Kieser (1999) gave solutions, by means of which the initial set of hypotheses can be reduced after the interim analysis. The same techniques can be applied to obtain more flexible strategies, as changing weights of hypotheses, changing an a priori order, or even including new hypotheses. It is emphasized that the application of these methods requires very careful planning of a trial as well as a c…
Analysis of Educational Frequency Data from a Complex Sample Survey
1991
Abstract Some recent methods are presented for analyzing categorial data from complex surveys involving clustering familiar in educational research where e.g. teaching groups are used as sample clusters. The methods are introduced through a discussion of the test of independence on a two‐way table and the analysis of a two‐way table using logistic regression models. The analyses are illustrated using data from the First National Assessment of the Finnish Comprehensive School 1979. The primary focus of the paper is on the methods that provide first‐order corrections to standard multinomial‐based chi‐square tests by taking account of survey design effects. Both first‐ and second‐order correct…