In a two-factor ANOVA analysis, the sum of squares due to both factors, the interaction sum of squares and the within sum of squares must add up to the total sum of squares.

Question

Quizplus · Accepted Answer

This is a fundamental principle of ANOVA analysis, known as the partitioning of variance or the law of total variance. The total sum of squares represents the total variation in the data, which is decomposed into separate components attributed to the factors, their interaction, and the error term. Therefore, the sum of squares due to both factors, the interaction sum of squares and the within sum of squares must account for all the sources of variation in the data. This is a fundamental property of ANOVA, where the total variation in the data is partitioned into these three sources of variation. Therefore, the sum of squares due to both factors, the interaction sum of squares and the within sum of squares must add up to the total sum of squares.

In a Two-Factor ANOVA Analysis, the Sum of Squares Due