Asked by Lorre Taylor on Jun 09, 2024
Verified
In a two-way factor ANOVA, the sum of squares due to both factors, the interaction sum of squares, and the error sum of squares must add up to the total sum of squares.
Two-way Factor ANOVA
A statistical method used to determine if there are any statistically significant differences between the means of three or more independent groups based on two factors.
Sum of Squares
The sum of the squared deviations of each data point from its mean, a measure used in statistical analysis to quantify variability within a dataset.
- Acquire knowledge on how variance is segmented in ANOVA models.
Verified Answer
MZ
myself ZubairJun 09, 2024
Final Answer :
True
Explanation :
This is a fundamental principle of ANOVA and is true for all types of ANOVA. The total sum of squares represents the variability in the dependent variable that can be attributed to all sources of variation, including the main effects of each factor, the interaction between the factors, and the residual or error variance. The sum of squares due to the main effects and the interaction must add up to the total sum of squares because they represent all possible sources of variability that might explain the variability in the dependent variable. The error sum of squares is a measure of the variability in the dependent variable that cannot be explained by the main effects or the interaction between factors.
Learning Objectives
- Acquire knowledge on how variance is segmented in ANOVA models.
Related questions
In a Two-Way Factor ANOVA, the Total Sum of Squares ...
The Simple Analysis of Variance,or One-Way Analysis of Variance,includes Only ...
When the Amount of Variability Due to Within-Group Differences Is ...
A Researcher Wants to Create an Intervention to Improve the ...
There Are Several Types of ANOVA