Lecture 10: ANOVA

Question 1

what does ANOVA stand for

Answer 1

Analysis of variance

Question 2

What is an F-distribution

Answer 2

A continuous probability distribution, most frequently used as a null distribution of the test statistic in analysis of variance

Question 3

What makes ANOVA different from independent t-test

Answer 3

ANOVA allows for more than two groups, independent t-test only compares two groups

Question 4

What is a grand mean

Answer 4

The best guess of 1 value that summarizes the data

Question 5

What is the total sum of squares (SS)

Answer 5

All distances from a data point to the grand mean added together

Question 6

What happens to the total sum of squares and accuracy when you add a parameter

Answer 6

The SS goes down and your accuracy gets better

Question 7

What are the 4 assumptions of a one-way independent ANOVA

Answer 7

1. Continuous variable
2. Random sample
3. Normally distributed (test with Shapiro-Wilk test or Q-Q plots)
4. Equal variance within groups (test with Levene’s test)

Question 8

What is the formula for the F-ratio

Answer 8

MSmodel/MSerror

Question 9

What does the F-ratio quantify

Answer 9

How much better your model is at predicting the data than the null is

Question 10

What is an implication considering the mean squares of model and mean squares of error when the F-ratio is 1

Answer 10

They are the same

Question 11

What happens to the mean squares of model/error when the F-ratio increases

Answer 11

If the F-ratio is 5 then the mean of squares of model is 5 times the mean of squares of error

Question 12

T/F: F can not be smaller than 0

Answer 12

True

Question 13

Why can F not be smaller than 0

Answer 13

Because MSmodel and MSerror are always positive

Question 14

T/F: F-test is always two sided

Answer 14

True

Question 15

What are contrasts

Answer 15

They are planned comparisons between groups

Question 16

What is important when using contrasts and what are 2 positive things about them

Answer 16

The values you assign to them always have to add up to 0

1. They have higher precision
2. They have higher power

Question 17

How can the total sum of squares be divided

Answer 17

Model sum of squares and error sum of squares

Question 18

What is another word for model sum of squares? And error sum of squares?

Answer 18

Model accuracy/model error

Question 19

What does it mean for the model prediction if observed difference between groups is 0

Answer 19

It means that the model is not better at predicting than the grand mean, because the groups means are the same which means they are the same as the grand mean

Question 20

What is the error sum of squares

Answer 20

The distances from the data points in one group to the mean of that group, and the distances from the data points in the other group to the mean of that group (if more groups, same procedure)

Question 21

What is the model sum of squares

Answer 21

It is the distance between the grand mean and the group means = how much less error their is when predicting with the group means

Question 22

What two things does the F-distribution depend on

Answer 22

1. Sample size; DFerror=N-k
2. Number of groups; DFmodel=k-1