# Partitioning of variability in ANOVA

This applet illustrates the partitioning of variability into explained and unexplained variability, in the context of ANOVA.
The top plot shows data from three groups ([color=#c51414]group 1[/color], [color=#0a971e]group 2[/color], [color=#1551b5]group 3[/color]). A dotplot of the combined data is shown on the left, and the grand mean $\bar{\bar{y}}$ is shown as the horizontal line.[br][br]Click and drag the coloured arrows to change the group means. Adjust the within-groups variability by dragging the slider. Click '[b]Generate new samples[/b]' to produce a new set of data.[br][br]Click '[color=#6600cc][b]Show explained variability[/b][/color]' and '[color=#ff6600][b]Show unexplained variability[/b][/color]' to visualise the partitioning of variability into explained and unexplained components.[br][br]The middle plot shows a separate-means model for the data. This accounts for the [color=#6600cc]explained[/color] (between-groups) variability.[br][br]The bottom plot shows the [color=#d69210]unexplained [/color] (residual) variability within groups.[br][br]The corresponding parts of the overall variability, shown in the bar to the left, are coloured.