Why is anova robust

Blanca, M. Skewness and kurtosis in real data samples. Methodology, 9, 78— Box, G. Non-normality and tests on variances. Biometrika, 40, — Some theorems on quadratic forms applied in the study of analysis of variance problem. Effect of inequality of variance in one-way classification. The Annals of Mathematical Statistics, 25, — Bradley, J. British Journal of Mathematical and Statistical Psychology, 31, — Brown, M. The small sample behaviour of some statistics which test the equality of several means.

Technomectrics, 16, — Brunner, E. Box-type approximations in nonparametric factorial designs. Journal of the American Statistical Association, 92, — Bryk, A. Heterogeneity of variance in experimental studies: A challenge to conventional interpretations. Psychological Bulletin, , — Robust analysis of variance. Journal of Applied Statistics, 24, — Burton, A. The design of simulation studies in medical statistics. Statistics in Medicine, 25, — Article PubMed Google Scholar.

Chen, S. Single-stage analysis of variance under heteroscedasticity. Communications in Statistics — Simulation and Computation, 27, — Clinch, J. Parametric alternatives to the analysis of variance. Journal of Educational Statistics, 7, — Cochran, W. The distribution of the largest of a set of estimated variances as a fraction of their total. Annals of Human Genetics, 11, 47— Google Scholar. Conover, W. A comparative study of test for homogeneity of variances, with applications to the outer continental shelf bidding data.

Technometrics, 23, — Cribbie, R. Effect of non-normality on test statistics for one-way independent group designs. British Journal of Mathematical and Statistical Psychology, 65, 56— Tests for treatment group equality when data are nonnormal and heteroscedastic.

Journal of Modern Applied Statistical Methods, 6, — David, F. The effect of non-normality on the power function of the F -test in the analysis of variance. Biometrika, 38, 43— Dean, A. Design and analysis of experiments.

New York: Springer-Verlag. Book Google Scholar. Erceg-Hurn, D. Modern robust statistical methods: An easy way to maximize the accuracy and power of your research. American Psychologist, 63, — Fan, W. Robust means modeling: An alternative for hypothesis testing of independent means under variance heterogeneity and nonnormality. Journal of Educational and Behavioral Statistics, 37, — Gamage, J. Communications in Statistics—Simulation and Computation, 27, — Glass, G. Consequences of failure to meet assumptions underlying the fixed effects analyses of variance and covariance.

Review of Educational Research, 42, — Statistical Methods in Education and Psychology. Englewood Cliffs: Prentice-Hall. Golinski, C. The expanding role of quantitative methodologists in advancing psychology. Canadian Psychology, 50, 83— Grissom, R. Heterogeneity of variance in clinical data. Journal of Consulting and Clinical Psychology, 68, — Review of assumptions and problems in the appropriate conceptualization of effect size.

Psychological Methods, 6, — Hartley, H. The use of range in analysis of variance. Biometrika, 37, — Harwell, M. Journal of Educational and Behavioral Statistics, 17, — Hays, W. Statistics 3rd ed. Horsnell, G. The effect of unequal group variances on the F -test for the homogeneity of group means. Hsu, P. Statistical Research Memoirs, 2, 1— James, G. The comparison of several groups of observations when the ratios of the population variances are unknown.

Biometrika, 38, — Kang, Y. Reexamining the impact of nonnormality in two-group comparison procedures. The Journal of Experimental Education, 83, — Keppel, G. New York: W. Design and analysis: A researcher's handbook 4th ed. Englewood Cliffs: Prentice Hall.

Keselman, H. A comparison of recent approaches to the analysis of repeated measurements. British Journal of Mathematical and Statistical Psychology, 52, 63— Review of Educational Research , 68 , — Kieffer, K. The Journal of Experimental Education, 69, — Kirk, R. Experimental design. Procedures for the behavioral sciences 4th ed. Thousand Oaks: Sage Publications. Kohr, R. Robustness of the analysis of variance, the Welch procedure and a Box procedure to heterogeneous variances.

The Journal of Experimental Education, 43, 61— Kowalchuk, R. The analysis of repeated measurements with mixed-model adjusted F tests. Educational and Psychological Measurement, 64, — Krishnamoorthy, K. Kruskal, W. Use of ranks in one-criterion variance analysis. Journal of the American Statistical Association, 47, — Lee, S. Communications in Statistics—Simulation and Computation, 32, — Levene, H.

Robust tests for equality of variance. Hotelling Eds. Palo Alto: Stanford University Press. Li, X. Comparison of several means: A fiducial based approach. Computational Statistics and Data Analysis, 55, — Lindquist, E. Design and analysis of experiments in psychology and education. Boston: Houghton Mifflin. Lix, L. To trim or not to trim: Tests of mean equality under heteroscedasticity and nonnormality.

Educational and Psychological Measurement, 58, — Consequences of assumption violations revisited: A quantitative review of alternatives to the one-way analysis of variance F test. Review of Educational Research, 66, — Maxwell, S. Designing experiments and analyzing data: A model comparison perspective. Belmont: Wadsworth. Designing experiments and analyzing data: A model comparison perspective 2nd ed. Mahwah: Lawrence Erlbaum Associates. Mendes, M. Evaluation of four tests when normality and homogeneity of variance assumptions are violated.

Journal of Applied Sciences, 4, 38— Micceri, T. The unicorn, the normal curve, and other improbable creatures. Mickelson, W. A Monte Carlo simulation of the robust rank-order test under various population symmetry conditions. Journal of Modern Applied Statistical Methods, 12, 21— Moder, K. Austrian Journal of Statistics, 36, — Psychological Test and Assessment Modeling, 52, — Montgomery, D.

Design and analysis of experiments 3rd ed. New York: Wiley. Norton, D. An empirical investigation of the effects of nonnormality and heterogeneity upon the F-test of analysis of variance. Unpublished doctoral dissertation, University of Iowa, Iowa City. Parra-Frutos, I. Controlling the Type I error rate by using the nonparametric bootstrap when comparing means.

British Journal of Mathematical and Statistical Psychology, 67, — Patrick, J. Robey, R. Type I error and the number of iterations in Monte Carlo studies of robustness.

British Journal of Mathematical and Statistical Psychology, 45, — Rogan, J. An investigation via a coefficient of variation. American Educational Research Journal, 14, — Assumption violations and rates of Type I error for the Tukey multiple comparison test: A review and empirical investigation via a coefficient of variance variation.

Lets go through the options as above:. You should not report the result as "significant difference", but instead report it as "statistically significant difference".

This is because your decision as to whether the result is significant or not should not be based solely on your statistical test. Therefore, to indicate to readers that this "significance" is a statistical one, include this is your sentence.

What happens if my data fail these assumptions? This means that it tolerates violations to its normality assumption rather well.

Ask Question. Asked 9 years, 7 months ago. Active 9 years, 7 months ago. Viewed 17k times. If I use non-parametric tests, do I need to correct for multiple testing that impacts type 1 error? Improve this question. Sheila Sheila 2 2 gold badges 2 2 silver badges 3 3 bronze badges. Only the latter is of any concern. Add a comment. Active Oldest Votes. Improve this answer. Community Bot 1. William A. Josephson William A. Josephson 21 1 1 bronze badge.

Sign up or log in Sign up using Google. Sign up using Facebook. Sign up using Email and Password. Post as a guest Name.