Final answer:
The "proportion of variance accounted for" in an experiment refers to the coefficient of determination (r²), which indicates how much of the variability in the dependent variable can be explained by the model. It involves comparing variances within and between sample groups via an ANOVA test, leading to the calculation of the F Ratio.
Step-by-step explanation:
In an experiment, the "proportion of variance accounted for" is also called the coefficient of determination, represented as r². This statistic is crucial in determining how well your model explains the variability of the dependent variable. To calculate this, you need two estimations of variance: the variance between samples, which includes factors such as treatment effects or explained variation, and the variance within samples, which accounts for error or unexplained variation.
The calculation involves comparing these variations through an Analysis of Variance (ANOVA), which can output an F Ratio. This ratio assesses the significance of the model by comparing the variance between groups to the variance within groups, and it follows an F Distribution with specified degrees of freedom. When r² is expressed as a percentage, it indicates the percentage of the total variation in the dependent variable that your independent variable explains. Conversely, 1 - r² represents the unexplained variation, which consists of the sum of squares of these differences or the residual variation.