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Levene's Test (levene + test)

Distribution by Scientific Domains
Mathematics and Statistics75%

Selected Abstracts

Levene Tests of Homogeneity of Variance for General Block and Treatment Designs

BIOMETRICS, Issue 1 2002
Michael E. O'Neill
Summary. This article develops a weighted least squares version of Levene's test of homogeneity of variance for a general design, available both for univariate and multivariate situations. When the design is balanced, the univariate and two common multivariate test statistics turn out to be proportional to the corresponding ordinary least squares test statistics obtained from an analysis of variance of the absolute values of the standardized mean-based residuals from the original analysis of the data. The constant of proportionality is simply a design-dependent multiplier (which does not necessarily tend to unity). Explicit results are presented for randomized block and Latin square designs and are illustrated for factorial treatment designs and split-plot experiments. The distribution of the univariate test statistic is close to a standard F -distribution, although it can be slightly underdispersed. For a complex design, the test assesses homogeneity of variance across blocks, treatments, or treatment factors and offers an objective interpretation of residual plots. [source]

Bootstrap calibration to improve the reliability of tests to compare sample means and variances

ENVIRONMETRICS, Issue 8 2001
R. I. C. Chris Francis
Abstract The comparison of several sample means to see whether they differ significantly is a common analysis, which is not straightforward when the samples may be from non-normal distributions with different variances. A recent study found that a randomization test that attempts to approximate the distribution of F -statistics from one- and two-factor analysis of variance in the presence of unequal population variances was the best of 12 alternative tests considered. However, it sometimes suffered from excess size with data from extremely non-normal distributions. In the present article a method for improving the robustness of the test by bootstrap calibration is described for one-factor analysis of variance, and shown to be effective by a simulation study. The method is also applied with Levene's test for unequal variance by randomization. In this case the test is very robust without calibration, and calibration does not improve it. Copyright © 2001 John Wiley & Sons, Ltd. [source]

Evaluation of canal filling after using two warm vertical gutta-percha compaction techniques in vivo: a preliminary study

INTERNATIONAL ENDODONTIC JOURNAL, Issue 7 2006
M. Venturi
Abstract Aim, To evaluate the quality of root canal filling when comparing two warm gutta-percha filling techniques in vivo. Methodology, Human teeth were randomly divided into two equal groups, with 30 canals each. The root canals were shaped by hand and ProFile 0.04 rotary instruments to size 20,40 at the end-point and then filled with gutta-percha cones and AH-Plus. In group A, a traditional warm vertical compaction technique was performed using the Touch'n Heat, and back-filling with the Obtura II. In group B, a modified warm vertical compaction technique was used: small amounts of gutta-percha were removed, and the remaining most apical 3 mm were compacted with a 1 mm movement; then thermomechanical back-filling was performed. The teeth were extracted, stored in dye, cleared, and the distance between the apex and apical limit of the filling, linear dye penetration, and voids were measured from the buccal, lingual, mesial and distal perspective. The homogeneity of variance and means was verified using Levene's test and t -test. anova and Dunnett post hoc test were used to establish the significance and to analyse the effects through multiple comparisons. Results, Compared with the specimens of group A, the specimens of group B exhibited less mean linear dye penetration (P < 0.05), smaller void length (P , 0.05) and maximal width (P , 0.05) when examined in all four views, and a more precise filling when viewed from the buccal aspect (P < 0.05). Conclusions, The modified warm vertical compaction technique with apical back-filling produced a more effective and precise three-dimensional filling. [source]

Levene Tests of Homogeneity of Variance for General Block and Treatment Designs

BIOMETRICS, Issue 1 2002
Michael E. O'Neill
Summary. This article develops a weighted least squares version of Levene's test of homogeneity of variance for a general design, available both for univariate and multivariate situations. When the design is balanced, the univariate and two common multivariate test statistics turn out to be proportional to the corresponding ordinary least squares test statistics obtained from an analysis of variance of the absolute values of the standardized mean-based residuals from the original analysis of the data. The constant of proportionality is simply a design-dependent multiplier (which does not necessarily tend to unity). Explicit results are presented for randomized block and Latin square designs and are illustrated for factorial treatment designs and split-plot experiments. The distribution of the univariate test statistic is close to a standard F -distribution, although it can be slightly underdispersed. For a complex design, the test assesses homogeneity of variance across blocks, treatments, or treatment factors and offers an objective interpretation of residual plots. [source]