Analysis of variance is a widely used methodology, across various disciplines, to test more than two means. Citing scholarly articles, describe why such methodology is so useful and what kind of data can be analyzed using such methodology.
Analysis of Variance (ANOVA) tries to explain variation based on grouping of observations. This is enormously important in helping to explain the sources of statistical effects.
Why preferable to straight-up F-Test:
Wilcox, R. R. (1995). ANOVA: The practical importance of heteroscedastic methods, using trimmed means versus means, and designing simulation studies. British Journal of Mathematical and Statistical Psychology, 48(1), 99-114.
Rank data:
Brownie, C., & Boos, D. D. (1994). Type I error robustness of ANOVA and ANOVA on ranks when the number of treatments is large. Biometrics, 542-549.
Scenarios based on balance:
Swallow, W. H., & Monahan, J. F. (1984). Monte Carlo comparison of ANOVA, MIVQUE, REML, and ML estimators of variance components. Technometrics, 26(1), 47-57.
Ratio data (continuous data) are generally best suited data types for ANOVA. However for other scale, one may use either transformation or Non-parametric test.
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