Abstract
Analysis of variance (ANOVA) is a statistical procedure for summarizing a classical linear model – a decomposition of sum of squares into a component for each source of variation in the model – along with an associated test (the F-test) of the hypothesis that any given source of variation in the model is zero. More generally, the variance decomposition in ANOVA can be extended to obtain inference for the variances of batches of parameters (sources of variation) in multilevel regressions. ANOVA is a useful addition to regression in that it structures inferences about batches of parameters.
This is a preview of subscription content, log in via an institution to check access.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Bibliography
Aldous, D. 1981. Representations for partially exchangeable arrays of random variables. Journal of Multivariate Analysis: 581–598.
Besag, J., and D. Higdon. 1999. Bayesian analysis of agricultural field experiments (with discussion). Journal of the Royal Statistical Society B: 691–746.
Cochran, W., and G. Cox. 1957. Experimental designs. 2nd ed. New York: Wiley.
Cornfield, J., and J. Tukey. 1956. Average values of mean squares in factorials. Annals of Mathematical Statistics: 907–949.
Eisenhart, C. 1947. The assumptions underlying the analysis of variance. Biometrics 3: 1–21.
Fisher, R.A. 1925. Statistical methods for research workers. Edinburgh: Oliver and Boyd.
Gawron, V., B. Berman, R. Dismukes, and J. Peer. 2003. New airline pilots may not receive sufficient training to cope with airplane upsets. Flight Safety Digest (July–August): 19–32.
Gelman, A. 2005. Analysis of variance: Why it is more important than ever (with discussion). Annals of Statistics 33: 1–53.
Gelman, A., and J. Hill. 2006. Data analysis using regression and multilevel/ hierarchical models. New York: Cambridge University Press.
Gelman, A., C. Pasarica, and R. Dodhia. 2002. Let’s practice what we preach: Using graphs instead of tables. American Statistician 56: 121–130.
Goldberger, A. 1964. Econometric theory. New York: Wiley.
Goldstein, H. 1995. Multilevel statistical models. 2nd ed. London: Edward Arnold.
Green, B., and J. Tukey. 1960. Complex analyses of variance: General problems. Psychometrika 25: 127–152.
Hodges, J., Y. Cui, D. Sargent, and B. Carlin. 2005. Smoothed ANOVA. Technical report: Department of Biostatistics, University of Minnesota.
Kirk, R. 1995. Experimental design: Procedures for the behavioral sciences. 3rd ed. Pacific Grove: Brooks/Cole.
Kreft, I., and J. De Leeuw. 1998. Introducing multilevel modeling. London: Sage.
LaMotte, L. 1983. Fixed-, random-, and mixed-effects models. In Encyclopedia of statistical sciences, ed. S. Kotz, N. Johnson, and C. Read. New York: Wiley.
McCullagh, P. 2005. Discussion of Gelman (2005). Annals of Statistics 33: 33–38.
Nelder, J. 1977. A reformulation of linear models (with discussion). Journal of the Royal Statistical Society A 140: 48–76.
Nelder, J. 1994. The statistics of linear models: Back to basics. Statistics and Computing 4: 221–234.
Plackett, R. 1960. Models in the analysis of variance (with discussion). Journal of the Royal Statistical Society B 22: 195–217.
Searle, S., G. Casella, and C. McCulloch. 1992. Variance components. New York: Wiley.
Snedecor, G., and W. Cochran. 1989. Statistical methods. 8th ed. Ames: Iowa State University Press.
Snijders, T., and R. Bosker. 1999. Multilevel analysis. London: Sage.
Yates, F. 1967. A fresh look at the basic principles of the design and analysis of experiments. Proceedings of the Fifth Berkeley Symposium on Mathematical Statistics and Probability 4: 777–790.
Author information
Authors and Affiliations
Editor information
Copyright information
© 2018 Macmillan Publishers Ltd.
About this entry
Cite this entry
Gelman, A. (2018). Variance, Analysis Of. In: The New Palgrave Dictionary of Economics. Palgrave Macmillan, London. https://doi.org/10.1057/978-1-349-95189-5_2402
Download citation
DOI: https://doi.org/10.1057/978-1-349-95189-5_2402
Published:
Publisher Name: Palgrave Macmillan, London
Print ISBN: 978-1-349-95188-8
Online ISBN: 978-1-349-95189-5
eBook Packages: Economics and FinanceReference Module Humanities and Social SciencesReference Module Business, Economics and Social Sciences