scholarly journals BHEP Class of Tests for Multivariate Normality: An Empirical Comparison

2021 ◽  
pp. 185-195
Author(s):  
Mbanefo S. Madukaife
Keyword(s):  
Type I Error ◽  
Good Control ◽  
Multivariate Normality ◽  
Type I ◽  
Empirical Power ◽  
Empirical Comparison

This paper compares the empirical power performances of eight tests for multivariate normality classified under Baringhaus-Henze-Epps-Pulley (BHEP) class of tests. The tests are compared under eight different alternative distributions. The result shows that the eight statistics have good control over type-I-error. Also, some tests are more sensitive to distributional differences with respect to their power performances than others. Also, some tests are generally more powerful than others. The generally most powerful ones are therefore recommended.

Anova Tests for Homogeneity of Variance: Nonnormality and Unequal Samples

1977 ◽  
Vol 2 (3) ◽  
pp. 187-206 ◽  
Author(s):  
Charles G. Martin ◽  
Paul A. Games
Keyword(s):  
Error Rate ◽  
Type I Error ◽  
Type I ◽  
Empirical Comparison ◽  
Jackknife Test ◽  
Type I Error Rate ◽  
Power And Control ◽  
Homogeneity Of Variance ◽  
Test Use ◽  
And Control

This paper presents an exposition and an empirical comparison of two potentially useful tests for homogeneity of variance. Control of Type I error rate, P(EI), and power are investigated for three forms of the Box test and for two forms of the jackknife test with equal and unequal n's under conditions of normality and nonnormality. The Box test is shown to be robust to violations of the assumption of normality. The jackknife test is shown not to be robust. When n's are unequal, the problem of heterogeneous within-cell variances of the transformed values and unequal n's affects the jackknife and Box tests. Previously reported suggestions for selecting subsample sizes for the Box test are shown to be inappropriate, producing an inflated P(EI). Two procedures which alleviate this problem are presented for the Box test. Use of the jack-knife test with a reduced alpha is shown to provide power and control of P(EI) at approximately the same level as the Box test. Recommendations for the use of these techniques and computational examples of each are provided.

scholarly journals Model Error in Covariance Structure Models

Methodology ◽  
2008 ◽  
Vol 4 (4) ◽  
pp. 159-167 ◽  
Author(s):  
Donna L. Coffman
Keyword(s):  
Error Rate ◽  
Null Hypothesis ◽  
Type I Error ◽  
Sampling Error ◽  
Model Error ◽  
Type I ◽  
Empirical Power ◽  
Parameter Drift ◽  
Type I Error Rate ◽  
Close Fit

This study investigated the degree to which violation of the parameter drift assumption affects the Type I error rate for the test of close fit and the power analysis procedures proposed by MacCallum et al. (1996) for both the test of close fit and the test of exact fit. The parameter drift assumption states that as sample size increases both sampling error and model error (i.e., the degree to which the model is an approximation in the population) decrease. Model error was introduced using a procedure proposed by Cudeck and Browne (1992). The empirical power for both the test of close fit, in which the null hypothesis specifies that the root mean square error of approximation (RMSEA) ≤ 0.05, and the test of exact fit, in which the null hypothesis specifies that RMSEA = 0, is compared with the theoretical power computed using the MacCallum et al. (1996) procedure. The empirical power and the theoretical power for both the test of close fit and the test of exact fit are nearly identical under violations of the assumption. The results also indicated that the test of close fit maintains the nominal Type I error rate under violations of the assumption.

Stepwise and Simultaneous Multiple Comparison Procedures of Repeated Measures’ Means

1994 ◽  
Vol 19 (2) ◽  
pp. 127-162 ◽  
Author(s):  
H. J. Keselman
Keyword(s):  
Repeated Measures ◽  
Type I Error ◽  
Multiple Comparison ◽  
Multivariate Normality ◽  
Type I ◽  
Stepwise Procedures ◽  
Multiple Comparison Procedures ◽  
Multisample Sphericity

Stepwise multiple comparison procedures (MCPs) for repeated measures’ means based on the methods of Hayter (1986) , Hochberg (1988) , Peritz (1970) , Ryan (1960) - Welsch (1977a) , Shaffer (1979 , 1986) , and Welsch (1977a) were compared for their overall familywise rates of Type I error when multisample sphericity and multivariate normality were not satisfied. Robust stepwise procedures were identified by Keselman, Keselman, and Shaffer (1991) with respect to three definitions of power. On average, Welsh’s (1977a) step-up procedure was found to be the most powerful MCP.

scholarly journals Advice on comparing two independent samples of circular data in biology

2021 ◽  
Vol 11 (1) ◽  
Author(s):  
Lukas Landler ◽  
Graeme D. Ruxton ◽  
E. Pascal Malkemper
Keyword(s):  
Error Rate ◽  
Statistical Power ◽  
Type I Error ◽  
Statistical Treatment ◽  
Good Control ◽  
Circular Data ◽  
Type I ◽  
Trigonometric Functions ◽  
Biological Variables ◽  
Two Samples

AbstractMany biological variables are recorded on a circular scale and therefore need different statistical treatment. A common question that is asked of such circular data involves comparison between two groups: Are the populations from which the two samples are drawn differently distributed around the circle? We compared 18 tests for such situations (by simulation) in terms of both abilities to control Type-I error rate near the nominal value, and statistical power. We found that only eight tests offered good control of Type-I error in all our simulated situations. Of these eight, we were able to identify the Watson’s U2 test and a MANOVA approach, based on trigonometric functions of the data, as offering the best power in the overwhelming majority of our test circumstances. There was often little to choose between these tests in terms of power, and no situation where either of the remaining six tests offered substantially better power than either of these. Hence, we recommend the routine use of either Watson’s U2 test or MANOVA approach when comparing two samples of circular data.

scholarly journals Comparing two circular distributions: advice for effective implementation of statistical procedures in biology

2021 ◽  
Author(s):  
Lukas Landler ◽  
Graeme D Ruxton ◽  
Erich Pascal Malkemper
Keyword(s):  
Statistical Power ◽  
Type I Error ◽  
Statistical Treatment ◽  
Good Control ◽  
Time Of Day ◽  
Circular Data ◽  
Type I ◽  
Biological Variables ◽  
Circular Distributions ◽  
Two Samples

Many biological variables, often involving timings of events or directions, are recorded on a circular rather than linear scale, and need different statistical treatment for that reason. A common question that is asked of such circular data involves comparison between two groups or treatments: Are the populations from which the two samples drawn differently distributed around the circle? For example, we might ask whether the distribution of directions from which a stalking predator approaches its prey differs between sunny and cloudy conditions; or whether the time of day of mating attempts differs between lab mice subject to one of two hormone treatments. An array of statistical approaches to these questions have been developed. We compared 18 of these (by simulation) in terms of both abilities to control type I error rate near the nominal value, and statistical power. We found that only eight tests offered good control of type I error in all our test situations. Of these eight, we are able to identify Watsons U^2 test and MANOVA based on trigonometric functions of the data as offering the best power in the overwhelming majority of our test circumstances. There was often little to choose between these tests in terms of power, and no situation where either of the remaining six tests offered substantially better power than either of these. Hence, we recommend the routine use of either Watsons U^2 test or MANOVA when comparing two samples of circular data.

scholarly journals Modifying and Evaluating the Alexander-Govern Test Using Real Data

2015 ◽  
Vol 9 (12) ◽  
pp. 1
Author(s):  
Tobi Kingsley Ochuko ◽  
Suhaida Abdullah ◽  
Zakiyah Binti Zain ◽  
Sharipah Syed Soaad Yahaya
Keyword(s):  
Type I Error ◽  
Parametric Method ◽  
Real Life ◽  
Good Control ◽  
Error Rates ◽  
P Value ◽  
Type I ◽  
Central Tendency ◽  
Central Tendency Measure ◽  
Type I Error Rates

This study examines the use of independent group test of comparing two or more means by using parametric method, such as the Alexander-Govern (<em>AG</em>) test. The Alexander-Govern test is used for comparing two or more groups and is a better alternative compared to the James test, the Welch test and the <em>ANOVA</em>. This test has a good control of Type I error rates and gives a high power under variance heterogeneity for a normal data, but it is not robust for non-normal data. As a result, trimmed mean was applied on the test under non-normal data for two group condition. But this test could not control the Type I error rates, when the number of groups exceed two groups. As a result, the <em>MOM</em> estimator was introduced on the test, as its central tendency measure and is not influenced by the number of groups. But this estimator fails to give a good control of Type I error rates, under skewed heavy tailed distribution. In this study, the <em>AGWMOM </em>test was applied in Alexander-Govern test as its central tendency measure. To evaluate the capacity of the test, a real life data was used. Descriptive statistics, Tests of Normality and boxplots were used to determine the normality and non-normality of the independent groups. The results show that only the group middle is not normally distributed due extreme value in the data distribution. The results from the test statistic show that the <em>AGWMOM</em> test has a smaller p-value of 0.0000002869 that is less than 0.05, compared to the <em>AG</em> test that produced a p-value of 0.06982, that is greater than 0.05. Therefore, the <em>AGWMOM</em> test is considered to be significant, compared to the <em>AG</em> test.

scholarly journals Multiple Comparisons Using Composite Likelihood in Clustered Data

2016 ◽  
Vol 12 (2) ◽  
Author(s):  
Mahdis Azadbakhsh ◽  
Xin Gao ◽  
Hanna Jankowski
Keyword(s):  
Type I Error ◽  
Clustered Data ◽  
Likelihood Estimation ◽  
Good Control ◽  
Multiple Hypothesis Testing ◽  
Composite Likelihood ◽  
Multiple Comparison ◽  
Likelihood Method ◽  
Type I ◽  
Multiple Comparison Procedures

AbstractWe study the problem of multiple hypothesis testing for correlated clustered data. As the existing multiple comparison procedures based on maximum likelihood estimation could be computationally intensive, we propose to construct multiple comparison procedures based on composite likelihood method. The new test statistics account for the correlation structure within the clusters and are computationally convenient to compute. Simulation studies show that the composite likelihood based procedures maintain good control of the familywise type I error rate in the presence of intra-cluster correlation, whereas ignoring the correlation leads to erratic performance.

scholarly journals An Investigation of Chi-Square and Entropy Based Methods of Item-Fit Using Item Level Contamination in Item Response Theory

2020 ◽  
Vol 18 (2) ◽  
pp. 2-43
Author(s):  
William R. Dardick ◽  
Brandi A. Weiss
Keyword(s):  
Item Response Theory ◽  
Item Response ◽  
Type I Error ◽  
Type I ◽  
Power Performance ◽  
Empirical Power ◽  
Response Theory ◽  
Chi Square ◽  
Item Fit ◽  
Item Level

New variants of entropy as measures of item-fit in item response theory are investigated. Monte Carlo simulation(s) examine aberrant conditions of item-level misfit to evaluate relative (compare EMRj, X2, G2, S-X2, and PV-Q1) and absolute (Type I error and empirical power) performance. EMRj has utility in discovering misfit.

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