Variationsanalys

Variationsanalys, commonly known in English as analysis of variance (ANOVA), is a family of statistical models and procedures used to analyze differences among group means and to partition observed variance into components attributable to different sources. The core idea is to compare the amount of variation explained by the factors under study with the residual variation due to random error.

Originated by Ronald A. Fisher in the 1920s to analyze agricultural experiments, ANOVA has since become a standard tool in experimental design. It encompasses several forms, including one-way ANOVA (single factor), two-way ANOVA (two factors), repeated-measures ANOVA, and multivariate variants such as MANOVA and ANCOVA.

Key assumptions include independence of observations, normal distribution of residuals within groups, and homogeneity of variances (equal variances across groups). The typical output is an ANOVA table with sums of squares, degrees of freedom, mean squares, an F-statistic, and a p-value. A significant F indicates that not all group means are equal, prompting post hoc tests (e.g., Tukey, Bonferroni) to identify which groups differ.

Applications span experimental sciences, psychology, medicine, agriculture, and manufacturing, where researchers seek to understand the influence of one or more factors on a quantitative outcome. Limitations arise when assumptions are violated or when sample sizes are small; ANOVA is sensitive to non-normality and unequal variances.

Alternatives include nonparametric tests such as the Kruskal-Wallis test for one-way designs, Welch's ANOVA for unequal variances, and permutation-based approaches. Modern practice often relies on software tools (R, Python's statsmodels, SPSS, SAS) to fit models, check assumptions, and perform post hoc comparisons.