scholarly journals Improved procedures and computer programs for equivalence assessment of correlation coefficients

PLoS ONE ◽  
2021 ◽  
Vol 16 (5) ◽  
pp. e0252323
Author(s):  
Gwowen Shieh
Keyword(s):  
Correlation Coefficient ◽  
Type I Error ◽  
Reference Range ◽  
Correlation Coefficients ◽  
Sample Size Determination ◽  
Power Calculation ◽  
Type I ◽  
Significance Tests ◽  
Equivalence Tests ◽  
Essential Problem

The correlation coefficient is the most commonly used measure for summarizing the magnitude and direction of linear relationship between two response variables. Considerable literature has been devoted to the inference procedures for significance tests and confidence intervals of correlations. However, the essential problem of evaluating correlation equivalence has not been adequately examined. For the purpose of expanding the usefulness of correlational techniques, this article focuses on the Pearson product-moment correlation coefficient and the Fisher’s z transformation for developing equivalence procedures of correlation coefficients. Equivalence tests are proposed to assess whether a correlation coefficient is within a designated reference range for declaring equivalence decisions. The important aspects of Type I error rate, power calculation, and sample size determination are also considered. Special emphasis is given to clarify the nature and deficiency of the two one-sided tests for detecting a lack of association. The findings demonstrate the inappropriateness of existing methods for equivalence appraisal and validate the suggested techniques as reliable and primary tools in correlation analysis.

scholarly journals Generalized additive models and inflated type I error rates of smoother significance tests

2011 ◽  
Vol 55 (1) ◽  
pp. 366-374 ◽  
Author(s):  
Robin L. Young ◽  
Janice Weinberg ◽  
Verónica Vieira ◽  
Al Ozonoff ◽  
Thomas F. Webster
Keyword(s):  
Type I Error ◽  
Generalized Additive Models ◽  
Error Rates ◽  
Additive Models ◽  
Type I ◽  
Significance Tests ◽  
Type I Error Rates ◽  
Inflated Type

scholarly journals Not so different in present attitudes and behaviour, but expected future membership: A technical replication of a study of party youth in six European democracies

2018 ◽  
Vol 5 (1) ◽  
pp. 205316801876487
Author(s):  
Lion Behrens ◽  
Ingo Rohlfing
Keyword(s):  
Multiple Testing ◽  
Type I Error ◽  
Statistical Significance ◽  
Original Study ◽  
Pairwise Comparisons ◽  
Type I ◽  
Significance Tests ◽  
Party Members ◽  
Original Survey ◽  
Technical Replication

Based on the statistical analysis of an original survey of young party members from six European democracies, a study concluded that three types of young members differed systematically regarding their membership objectives, activism, efficacy and perceptions of the party and self-perceived political future. We performed a technical replication of the original study, correcting four deficiencies, which led us to a different conclusion. First, we discuss substantive significance in addition to statistical significance. Second, we ran significance tests on all comparisons instead of limiting them to an arbitrary subset. Third, we performed pairwise comparisons between the three types of members instead of using pooled groups. Fourth, we avoided the inflation of the type-I error rate due to multiple testing by using the Bonferroni–Holm correction. We found that most of the differences between the types lacked substantive significance, and that statistical significance only coherently distinguished the types of members in their future membership, but not in their present behaviour and attitudes.

Use of interval estimations in design and evaluation of multiregional clinical trials with continuous outcomes

2018 ◽  
Vol 28 (7) ◽  
pp. 2179-2195 ◽  
Author(s):  
Chieh Chiang ◽  
Chin-Fu Hsiao
Keyword(s):  
Clinical Trials ◽  
Sample Size ◽  
Type I Error ◽  
Interval Estimation ◽  
Error Rates ◽  
New Drugs ◽  
Sample Size Determination ◽  
Type I ◽  
Size Determination ◽  
Interval Estimators

Multiregional clinical trials have been accepted in recent years as a useful means of accelerating the development of new drugs and abridging their approval time. The statistical properties of multiregional clinical trials are being widely discussed. In practice, variance of a continuous response may be different from region to region, but it leads to the assessment of the efficacy response falling into a Behrens–Fisher problem—there is no exact testing or interval estimator for mean difference with unequal variances. As a solution, this study applies interval estimations of the efficacy response based on Howe’s, Cochran–Cox’s, and Satterthwaite’s approximations, which have been shown to have well-controlled type I error rates. However, the traditional sample size determination cannot be applied to the interval estimators. The sample size determination to achieve a desired power based on these interval estimators is then presented. Moreover, the consistency criteria suggested by the Japanese Ministry of Health, Labour and Welfare guidance to decide whether the overall results from the multiregional clinical trial obtained via the proposed interval estimation were also applied. A real example is used to illustrate the proposed method. The results of simulation studies indicate that the proposed method can correctly determine the required sample size and evaluate the assurance probability of the consistency criteria.

scholarly journals MINIMIZATION OF RISK OF THE ERRONEOUS DECISION IN THE ASSESSMENT OF THE IMPORTANCE OF STATISTICAL RELATIONS OF TECHNICAL AND ECONOMIC INDICATORS OF THE OBJECTS OF ELECTRIC POWER SYSTEMS

2018 ◽  
Vol 61 (3) ◽  
pp. 193-206 ◽  
Author(s):  
E. M. Farhadzadeh ◽  
A. Z. Muradaliyev ◽  
Yu. Z. Farzaliyev ◽  
T. K. Rafiyeva ◽  
S. A. Abdullayeva
Keyword(s):  
Power Systems ◽  
Electric Power ◽  
Type I Error ◽  
Correlation Coefficients ◽  
Electric Power Systems ◽  
Critical Values ◽  
Economic Indicators ◽  
Type I ◽  
Type Ii ◽  
Technical And Economic Indicators

Improving the reliability of decisions taken in the organization of maintenance and repair of electric power systems is one of the most important and difficult problems. It is important because erroneous solutions lead, first of all, to an increase in operating costs. The difficulty in solving this problem is associated with the lack of appropriate methods to reduce the risk of erroneous decisions. The article presents one of the aspects of this problem, i.e. improving the reliability of the decision on the nature of the relationship of technical and economic indicators of electric power systems. Traditionally, increase of reliability of the decision is reached by reduction of a Type I error. Usually it is accepted to be equal to 5%, occasionally – to 1%, and at researches – even to 0.5 %. The corresponding critical values of correlation coefficients are given in mathematics reference books. This method implicitly assumes that the consequences of a Type I error significantly exceed the consequences of Type II errors, and the distribution of correlation coefficients corresponds to the normal law. Therefore, the risk of an erroneous decision concerning the absence of a significant statistical relation is not controlled. But even if there is a wish to estimate the Type II error, it is almost impossible to fulfill it, because there are no critical values for correlation coefficients of dependent samples. No less relevant is the problem of deciding on the statistical relationship between technical and economic indicators in conditions of equality of consequences of erroneous decisions, i.e. it is necessary to take into account both a Type I error and a Type II error. To overcome the mentioned difficulties a new method for estimating the critical values of correlation coefficients has been developed. The novelty consists in the application of fiducial approach; the calculation of critical values are fulfilled with the aid of computer technologies of simulation of possible realizations of the correlation coefficients for the two assumptions, viz. technical and economic indicators of the independent and dependent; simulation is fulfilled with the method of solving the “inverse problem”, which enables the possible implementation of the correlation coefficients for the really dependent and independent samples of random variables at a given sample size; the developed algorithms and programs for calculation made it possible to obtain the critical values of correlation coefficients for independent and dependent samples; in conditions of the sameness of the consequences of erroneous decisions it is proposed to make a decision not based on critical value but based on the boundary values of the correlation coefficients that correspond to the minimum total risk of erroneous decisions; the exemplification of the recommendations application was made on example of technical and economic parameters of boilers of power units of 300 MWt. The significant impact of the availability of interrelated technical and economic indicators on the result of the ranking of boiler plants by the reliability and efficiency of their work is demonstrated.

scholarly journals A novel approach to sample size determination of clinical trials for rare diseases assuming symmetry

2019 ◽  
Author(s):  
Emma Wang ◽  
Bernard North ◽  
Peter Sasieni
Keyword(s):  
Clinical Trials ◽  
Hypothesis Testing ◽  
Rare Diseases ◽  
Statistical Power ◽  
Type I Error ◽  
Standard Of Care ◽  
Testing Procedure ◽  
Sample Size Determination ◽  
Type I ◽  
Number Of Patients

Abstract Abstract Background Rare and uncommon diseases are difficult to study in clinical trials due to limited recruitment. If the incidence of the disease is very low, international collaboration can only solve the problem to a certain extent. A consequence is a disproportionately high number of deaths from rare diseases, due to unclear knowledge of the best way to treat patients suffering from these diseases. Hypothesis testing using the conventional Type I error in conjunction with the number of patients who can realistically be enrolled for a rare disease, would cause the trial to be severely underpowered. Methods Our proposed method recognises these pragmatic limitations and suggests a new testing procedure, wherein conclusion of efficacy of one arm is grounded in robust evidence of non-inferiority in the endpoint of interest, and reasonable evidence of superiority, over the other arm. Results Simulations were conducted to illustrate the gains in statistical power compared with conventional hypothesis testing in several statistical settings as well as the example of clinical trials for Merkel cell carcinoma, a rare skin tumour. Conclusions Our proposed analysis method enables conducting clinical trials for rare diseases, potentially leading to better standard of care for patients suffering from rare diseases

A Forum for Researchers

1977 ◽  
Vol 8 (1) ◽  
pp. 74-80
Author(s):  
Randy Ellsworth ◽  
Richard L. Isakson ◽  
Kenneth J. Travers
Keyword(s):  
Correlation Coefficient ◽  
Null Hypothesis ◽  
Type I Error ◽  
Type I ◽  
Original Experiment ◽  
Research Results ◽  
Replication Studies ◽  
Interest In Research ◽  
Rule Out

Eastman's (1975) recent expression in the JRME of concern over so few replication studies is a concern that should be shared by all who have an interest in research. Replication is critical in assessing the “significance” of research results. A correlation coefficient of .20, which is statistically significant at the .01 level, will be much more “significant” if we can demonstrate by replication that the same result occurs again and again. By replicating, we help rule out the possibility that a Type I error (we rejected the null hypothesis when it was true) occurred in the original experiment. Furthermore, by independently replicating with different subjects, at different times and places, we also are helping to increase the generalizability of any “significant” results we do obtain.

Sample size calculation for agreement between two raters with binary endpoints using exact tests

2016 ◽  
Vol 27 (7) ◽  
pp. 2132-2141 ◽  
Author(s):  
Guogen Shan
Keyword(s):  
Sample Size ◽  
Error Control ◽  
Type I Error ◽  
Sample Size Calculation ◽  
Sample Size Determination ◽  
Type I ◽  
Test Statistic ◽  
Testing Procedures ◽  
Alternative Hypotheses ◽  
The One

In an agreement test between two raters with binary endpoints, existing methods for sample size calculation are always based on asymptotic approaches that use limiting distributions of a test statistic under null and alternative hypotheses. These calculated sample sizes may be not reliable due to the unsatisfactory type I error control of asymptotic approaches. We propose a new sample size calculation based on exact approaches which control for the type I error rate. The two exact approaches are considered: one approach based on maximization and the other based on estimation and maximization. We found that the latter approach is generally more powerful than the one based on maximization. Therefore, we present the sample size calculation based on estimation and maximization. A real example from a clinical trial to diagnose low back pain of patients is used to illustrate the two exact testing procedures and sample size determination.

scholarly journals Methods for dealing with unequal cluster sizes in cluster randomized trials: A scoping review

PLoS ONE ◽  
2021 ◽  
Vol 16 (7) ◽  
pp. e0255389
Author(s):  
Denghuang Zhan ◽  
Liang Xu ◽  
Yongdong Ouyang ◽  
Richard Sawatzky ◽  
Hubert Wong
Keyword(s):  
Scoping Review ◽  
Cluster Size ◽  
Trial Design ◽  
Type I Error ◽  
Binary Outcomes ◽  
Power Calculation ◽  
Type I ◽  
Cluster Randomized ◽  
Parameter Values ◽  
Unequal Cluster

In a cluster-randomized trial (CRT), the number of participants enrolled often varies across clusters. This variation should be considered during both trial design and data analysis to ensure statistical performance goals are achieved. Most methodological literature on the CRT design has assumed equal cluster sizes. This scoping review focuses on methodology for unequal cluster size CRTs. EMBASE, Medline, Google Scholar, MathSciNet and Web of Science databases were searched to identify English-language articles reporting on methodology for unequal cluster size CRTs published until March 2021. We extracted data on the focus of the paper (power calculation, Type I error etc.), the type of CRT, the type and the range of parameter values investigated (number of clusters, mean cluster size, cluster size coefficient of variation, intra-cluster correlation coefficient, etc.), and the main conclusions. Seventy-nine of 5032 identified papers met the inclusion criteria. Papers primarily focused on the parallel-arm CRT (p-CRT, n = 60, 76%) and the stepped-wedge CRT (n = 14, 18%). Roughly 75% of the papers addressed trial design issues (sample size/power calculation) while 25% focused on analysis considerations (Type I error, bias, etc.). The ranges of parameter values explored varied substantially across different studies. Methods for accounting for unequal cluster sizes in the p-CRT have been investigated extensively for Gaussian and binary outcomes. Synthesizing the findings of these works is difficult as the magnitude of impact of the unequal cluster sizes varies substantially across the combinations and ranges of input parameters. Limited investigations have been done for other combinations of a CRT design by outcome type, particularly methodology involving binary outcomes—the most commonly used type of primary outcome in trials. The paucity of methodological papers outside of the p-CRT with Gaussian or binary outcomes highlights the need for further methodological development to fill the gaps.

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