Lecture 14 Flashcards
Purpose of a two-factor ANOVA?
Tests for differences in a response variable among all the levels of two different factors at the same time
What is the purpose of adding a second factor?
It will explain more of the total variation in the response variable therefore decreases the unexplained variation
How are the factors labeled?
One factors = Factor A with “a” levels and the other is factor B with “b” levels
What is a cell
The combination of a level of factor A with a level of factor B
What is a two-factor ANOVA with replications?
There are multiple data points per cell, it s a balanced design
How does a two-factor ANOVA constitute as a multiple-sample test?
The samples are the cells which are at least four in a data set (2 factor A x 2 factor B = 4 cells)
How many and what are the null hypotheses in a two-factor ANOVA with replications?
H01: no effect of factor A
H02: no effect of factor B
H03: no A x B interaction
What is unique about hypothesis testing in two-factor ANOVAs with replications?
Do not need to write out alternative hypostheses, just the nulls
What is interaction in the factors?
Implies that the effects of one of the factors depends on the level of the other factor
What are the Sources of variation in two-factor ANOVA with replications?
Total, Error, and Cells. Cells is divided into 3 (A, B, and AxB)
In two-factor ANOVA with replications, what is the total variation?
All the variation in the entire data set
In two-factor ANOVA with replications, what is the Cells Variation?
The among cells variation, additive
In two-factor ANOVA with replications, what is the Error variation?
The within cell variation that is unexplained
In two-factor ANOVA with replications, what is the Factor A variation?
The variations among factor A
In two-factor ANOVA with replications, what is the Factor B variation?
The variations among factor B
In two-factor ANOVA with replications, what is the A x B interaction variation?
How the levels of one factor vary in combination with another level
In two-factor ANOVA with replications, how is the Cell variations addiditive?
Factor A + Factor B + Interaction
Why is it hard to make a definitive conclusion about each of the factors, even if they have significant results as well?
Each factor is doing different things in different combinations with each other that they would not be doing on their own
What is the advantage of conducting a three-factor ANOVA?
Decreases the unexplained variation (error) due to testing more factors
What is a disadvantage of conducting a three-factor ANOVA?
The amount of null hypotheses increases exponentially
