Module 12

Question 1

What is two factor analysis of variance?

Answer 1

• builds on the single factor ANOVA
• looks at the effect of two categoircal variables, we can look at the effect that each level has on the numerical variable, as well as the interaction between the categorical variables

Question 2

How can two factor anova be visualized?

Answer 2

as a two dimensional grid. one factor shown as columns, one as rows

Question 3

What is the factor?

Answer 3

the categorical variables are called factors, and the different types within each factor are called levels

Question 4

What is a cell?

Answer 4

the intersection of two levels is called a cell. within each cell, there will typically be several sampling units and numericalvariable is measured on each sampling unit

Question 5

What 3 questions does two factor ANOVAs answer?

Answer 5

• main effects A are questions about the differences among the levels of factor A averaging across the levels of factor B. These are comparisons among full columns (or full rows)
• Main effects B are questions about the differences among the levels of factor B averaging across the levels of factor A. these are comparisons among full rows (or full columns)
• interactions are questions about the differences among the levels of one factor within each level of the other factor. these are cell by cell comparisons

Question 6

What is the most valuable part of a two factor ANOVA?

Answer 6

can evaluate whether there is an interaction between the factors

Question 7

What is an interactions?

Answer 7

a deviation from the assumption that the levels of each factor simply add together. this is called additivity

Question 8

what is additivity?

Answer 8

Additivity is when the response to the combination of two levels is simply the sum of the two.

Question 9

What is the best way to visualize interactions?

Answer 9

• interactions plot
• use the same information as a box plot, but present the data in a way that showcases the relationship between the categorical variables

Question 10

How are interaction plots set up?

Answer 10

• the y axis shows the numerical variable in the same way as box plots
• the x axis shows the levels one categorical variable
• lines are used to connect cells across the x-axis according to the levels of the other categorical variable

Question 11

If the categorical variables are additive, how does the interaction plot appear?

Answer 11

the lines on an interaction plot will be parallel

Question 12

if the categorical variables are not additive, how will the interaction plot appear?

Answer 12

the lines of the plot are not parallel

Question 13

what are the fout steps a two factr anova tests follow for the hypothesis test?

Answer 13

• define the null and alternative hypothesis
• establish the null distribution
• conduct the statistical test
• draw scientific conclusions

Question 14

Null and alternative hypothesis for main effects A?

Answer 14

null: the means are the same across all levels of factor A

alternative: the means are different somewhere.

Question 15

Null and alternative hypothesis for main effects B?

Answer 15

null: the means are the same across all levels

alternative: means are different somewhere

Question 16

Null and alternative hypothesis for interaction?

Answer 16

null: the deviation of each cell relative to additivity is zero

alternative: there is a deviation

Question 17

What is the null distribution for each of the three F-tests?

Answer 17

• Main Effects A: the null distribution is the sampling distribution from repeatdely sampling a statistical population where the means are the same across all levels of factor A
• main effects B: the null distribution is the sampling distribution from repeatedly sampling a statistical population where the means are the same across all levels of factor B
• interactions: the null distribution is the sampling distribution from repeatedly sampling a statistical population where the cell means are additive

Question 18

4 Sources of variation for the F-tests in a two factor anova?

Answer 18

1. Group Variation Factor A (MSa): the variation among the means of the levels of factor A.
2. Group Variation Factor B (MSb): the variation among the means of the levels of factor B
3. AB interactions (MSab): the amount of variation attributable to the deviation from additivity
4. Residual Variation (MSe): the variation among sampling units within a cell

Question 19

What are the 3 F-tests built arround different ratios of the sources of variation?

Answer 19

1. Main effects a: the F-score is F=MSa/MSe
2. Main effects B: The F-score is F=MSb/MSe
3. Interactions: The F-score is F=MSab/MSe

Question 20

what is the null and alternative hypothesis for all f tests?

Answer 20

null: F</= 1
alternative: F>1

Question 21

How are the scientific conclusions for two factor anova test done?

Answer 21

1. Step 1: Evaluate the interaction

• the scientific conclusions are either: reject the null hypothesis and conclude there is evidence that there is at least one cell that deviates from additivity, or fail to reject it
• if the conclusion is to reject the null hypothesis, then the main effects should not be evaluated

2. Step 2: evaluation of main effects
   * if the interaction is not sig, then the factors are considered additive and it is app. to look at the main effects for each
   * reject the null hypothesis and conclude there is evidence that the means of at least two levels are different in the factor
   * fail to reject the null hypothesis and conclude there is no evidence that the means among levels are different in the factor