scholarly journals N = 1 Designs: The Failure of ANOVA-Based Tests

1983 ◽  
Vol 8 (4) ◽  
pp. 289-309 ◽  
Author(s):  
Larry E. Toothaker ◽  
Martha Banz ◽  
Cindy Noble ◽  
Jill Camp ◽  
Diana Davis
Keyword(s):  
Serial Correlation ◽  
Type I Error ◽  
Single Subject ◽  
Type I ◽  
Phase Lag ◽  
Exponential Distributions ◽  
Preliminary Testing ◽  
Single Subject Research ◽  
The One ◽  
One Way Anova

Several methods have been proposed for the analysis of data from single-subject research settings. This research focuses on the modifications of ANOVA-based tests proposed by Shine and Bower, a procedure that precedes the ANOVA F test by preliminary testing of within-phase lag one serial correlation and the one-way ANOVA as presented by Gentile, Roden and Klein. Monte Carlo simulation is used to investigate these tests with respect to robustness and power. Each test was analyzed under various patterns of serial correlation, various patterns of phase and trial means, normal and exponential distributions, and equal and unequal phase variances. The findings indicate that the probability of a Type I error for these ANOVA-based tests is seriously inflated by nonzero serial correlation. These tests, therefore, cannot be recommended for use with data that have nonzero serial correlation.

Summarizing Monte Carlo Results in Methodological Research: The One- and Two-Factor Fixed Effects ANOVA Cases

1992 ◽  
Vol 17 (4) ◽  
pp. 315-339 ◽  
Author(s):  
Michael R. Harwell ◽  
Elaine N. Rubinstein ◽  
William S. Hayes ◽  
Corley C. Olds
Keyword(s):  
Monte Carlo ◽  
Error Rate ◽  
Fixed Effects ◽  
Type I Error ◽  
Type I ◽  
F Test ◽  
Unequal Variances ◽  
Type I Error Rate ◽  
Monte Carlo Studies ◽  
The One

Meta-analytic methods were used to integrate the findings of a sample of Monte Carlo studies of the robustness of the F test in the one- and two-factor fixed effects ANOVA models. Monte Carlo results for the Welch (1947) and Kruskal-Wallis (Kruskal & Wallis, 1952) tests were also analyzed. The meta-analytic results provided strong support for the robustness of the Type I error rate of the F test when certain assumptions were violated. The F test also showed excellent power properties. However, the Type I error rate of the F test was sensitive to unequal variances, even when sample sizes were equal. The error rate of the Welch test was insensitive to unequal variances when the population distribution was normal, but nonnormal distributions tended to inflate its error rate and to depress its power. Meta-analytic and exact statistical theory results were used to summarize the effects of assumption violations for the tests.

Misspecification of the random effect structure: Implications for the linear mixed model

2020 ◽  
Author(s):  
Brandon LeBeau
Keyword(s):  
Fixed Effects ◽  
Serial Correlation ◽  
Mixed Model ◽  
Linear Mixed Model ◽  
Type I Error ◽  
Random Effect ◽  
Correlated Data ◽  
Unbiased Estimation ◽  
Type I ◽  
Nested Data

<p>The linear mixed model is a commonly used model for longitudinal or nested data due to its ability to account for the dependency of nested data. Researchers typically rely on the random effects to adequately account for the dependency due to correlated data, however serial correlation can also be used. If the random effect structure is misspecified (perhaps due to convergence problems), can the addition of serial correlation overcome this misspecification and allow for unbiased estimation and accurate inferences? This study explored this question with a simulation. Simulation results show that the fixed effects are unbiased, however inflation of the empirical type I error rate occurs when a random effect is missing from the model. Implications for applied researchers are discussed.</p>

Designing variable control charts under failure censoring reliability tests with replacement

2020 ◽  
Vol 42 (15) ◽  
pp. 3002-3011
Author(s):  
Hasan Rasay ◽  
Hossein Arshad
Keyword(s):  
Control Charts ◽  
Type I Error ◽  
Average Run Length ◽  
Quality Characteristic ◽  
Erlang Distribution ◽  
Type I ◽  
Chi Square ◽  
Variable Control ◽  
Specific Distribution ◽  
The One

There exist many processes where the quality characteristic does not follow a normal distribution, and the conditions for the application of central limit theorem are not satisfied; for example, because collecting data in a subgroup is impossible or the distribution is highly skewed. Thus, researchers have developed the control charts according to the specific distribution that models the quality characteristic. In this paper, some control charts are designed to monitor an exponentially distributed lifetime. The life testing is conducted according to the failure censoring while during the test; once observing a failure item, it is replaced by a new one so that the total number of items inspected during the test remains constant. Under the condition of the test, it is discussed that the elapsed time until observing the r’th failure has Erlang distribution. According to the relation of Erlang and chi-square distributions, the chart limits are computed to satisfy a specified value of type I error. Examples are presented and the curves of average run length are derived for the one-sided and two-sided control charts. Also, a comparative study is conducted to show the performance and superiority of the proposed control charts.

scholarly journals An efficient genome-wide association test for mixed binary and continuous phenotypes with applications to substance abuse research

2016 ◽  
Vol 27 (3) ◽  
pp. 905-919
Author(s):  
Anne Buu ◽  
L Keoki Williams ◽  
James J Yang
Keyword(s):  
Type I Error ◽  
Empirical Distribution ◽  
Genetic Effect ◽  
Association Test ◽  
Genome Wide Association ◽  
Type I ◽  
Multiple Phenotypes ◽  
Power Of The Test ◽  
Genome Wide ◽  
The One

We propose a new genome-wide association test for mixed binary and continuous phenotypes that uses an efficient numerical method to estimate the empirical distribution of the Fisher’s combination statistic under the null hypothesis. Our simulation study shows that the proposed method controls the type I error rate and also maintains its power at the level of the permutation method. More importantly, the computational efficiency of the proposed method is much higher than the one of the permutation method. The simulation results also indicate that the power of the test increases when the genetic effect increases, the minor allele frequency increases, and the correlation between responses decreases. The statistical analysis on the database of the Study of Addiction: Genetics and Environment demonstrates that the proposed method combining multiple phenotypes can increase the power of identifying markers that may not be, otherwise, chosen using marginal tests.

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.

Fitting a Serial Correlation Pattern to Repeated Observations

1991 ◽  
Vol 16 (1) ◽  
pp. 53-76
Author(s):  
Lynne K. Edwards
Keyword(s):  
Correction Factor ◽  
Serial Correlation ◽  
Degrees Of Freedom ◽  
Type I Error ◽  
Error Rates ◽  
Stationary Time Series ◽  
Type I ◽  
Correlation Pattern ◽  
Time Effects ◽  
Repeated Observations

When repeated observations are taken at equal time intervals, a simple form of a stationary time series structure may be fitted to the observations. Wallenstein and Fleiss (1979) have shown that the degrees-of-freedom correction factor for time effects has a higher lowerbound for data with a serial correlation pattern (or a simplex pattern) than for data without such a structure. The reanalysis of the example data found in Hearne, Clark, and Hatch (1983) indicated that the correction factor from a patterned matrix could be smaller than the counterpart without fitting a simplex pattern. First, an example from education was used to illustrate the computational steps in obtaining these two correction factors. Second, a simulation study was conducted to determine the conditions under which fitting a simplex pattern would be advantageous over not assuming such a pattern. Fitting a serial correlation pattern did not always produce more powerful tests of time effects than not assuming such a pattern. This was particularly true when correlations were high (ρ > .50). Furthermore, it inflated Type I error rates when the simplex shypothesis was not warranted. Indiscriminately fitting a serial correlation pattern should be discouraged.

An improved one-sample log-rank test

2020 ◽  
Vol 29 (10) ◽  
pp. 2814-2829
Author(s):  
Laura Kerschke ◽  
Andreas Faldum ◽  
Rene Schmidt
Keyword(s):  
Sample Size ◽  
Type I Error ◽  
Survival Curve ◽  
Rank Test ◽  
Rank Statistic ◽  
Type I ◽  
Time To Event ◽  
Log Rank Test ◽  
Alternative Approach ◽  
The One

The one-sample log-rank test allows to compare the survival of a single sample with a prefixed reference survival curve. It naturally applies in single-arm phase IIa trials with time-to-event endpoint. Several authors have described that the original one-sample log-rank test is conservative when sample size is small and have proposed strategies to correct the conservativeness. Here, we propose an alternative approach to improve the one-sample log-rank test. Our new one-sample log-rank statistic is based on the unique transformation of the underlying counting process martingale such that the moments of the limiting normal distribution have no shared parameters. Simulation results show that the new one-sample log-rank test gives type I error rate and power close to the nominal levels also when sample size is small, while relevantly reducing the required sample size to achieve the desired power as compared to current approaches to design studies to compare the survival outcome of a sample with a reference.

scholarly journals Comparison of Some Robust Wilks’ Statistics for the One-Way Multivariate Analysis of Variance (MANOVA )

2019 ◽  
Vol 11 (2) ◽  
pp. 42-58
Author(s):  
Abdullah A. Ameen ◽  
Osama H. Abbas
Keyword(s):  
Multivariate Analysis ◽  
Analysis Of Variance ◽  
Type I Error ◽  
Error Rates ◽  
Type I ◽  
Test Statistics ◽  
Multivariate Analysis Of Variance ◽  
Power Of The Test ◽  
Monte Carlo Studies ◽  
The One

The classicalWilks' statistic is mostly used to test hypothesesin the one-way multivariate analysis of variance (MANOVA), which is highly sensitive to the effects of outliers. The non-robustness of the test statistics based on normal theory has led many authors to examine various options.In this paper, we presented a robust version of the Wilks' statistic and constructed its approximate distribution.A comparison was made between the proposed statistics and some Wilks' statistics. The Monte Carlo studies are used to obtain performance assessment of test statistics in different data sets.Moreover, the results of the type I error rate and the power of test were considered as statistical tools to compare test statistics.The study reveals that, under normally distributed, the type I error rates for the classical and the proposedWilks' statistics are close to the true significance levels, and the power of the test statistics are so close. In addition, in the case of contaminated distribution, the proposed statistic is the best.  

scholarly journals An optimal kernel-based method for gene set association analysis

2018 ◽  
Author(s):  
Tao He ◽  
Shaoyu Li ◽  
Ping-Shou Zhong ◽  
Yuehua Cui
Keyword(s):  
Genetic Variants ◽  
Complex Traits ◽  
Type I Error ◽  
Association Studies ◽  
P Value ◽  
Systematic Effect ◽  
Type I ◽  
Genome Wide Association Studies ◽  
Optimal Kernel ◽  
The One

ABSTRACTSingle-variant based genome-wide association studies have successfully detected many genetic variants that are associated with many complex traits. However, their power is limited due to weak marginal signals and ignoring potential complex interactions among genetic variants. Set-based strategy was proposed to provide a remedy where multiple genetic variants in a given set (e.g., gene or pathway) are jointly evaluated, so that the systematic effect of the set is considered. Among many, the kernel-based testing (KBT) framework is one of the most popular and powerful methods in set-based association studies. Given a set of candidate kernels, method has been proposed to choose the one with the smallest p-value. Such a method, however, can yield inflated type I error, especially when the number of variants in a set is large. Alternatively one can get p-values by permutations which, however, could be very time consuming. In this work, we proposed an efficient testing procedure that can not only control type I error rate but also generate power close to the one obtained under the optimal kernel. Our method is built upon the KBT framework and is based on asymptotic results under a high-dimensional setting. Hence it can efficiently deal with the case where the number of variants in a set is much larger than the sample size. Both simulation and real data analysis demonstrate the advantages of the method compared with its counterparts.

An analysis of the type I error in the one sample Student t-test

1978 ◽  
Vol 7 (6) ◽  
pp. 593-603 ◽  
Author(s):  
Richard H. Browne ◽  
D. B. Owen ◽  
Faming Ju
Keyword(s):  
Type I Error ◽  
T Test ◽  
Type I ◽  
The One
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