ANOVA

Question 1

F statistic equation

Answer 1

F = between groups variance estimate / within groups variance estimate

Question 2

F statistic equation: what does the numerator measure?

Answer 2

• Between groups variance estimate: how much do groups vary from each other?
• Independent variable “effect”
• NOTHING ABOUT INDIVIDUALS

Question 3

F statistic equation: what does the denominator measure?

Answer 3

• Within groups variance estimate: how do individual people vary within each group?
• Random fluctuations “error”
• Sswithin

Question 4

How else can the F equation be written?

Answer 4

Effect / error
* Numerator: IV, “effect”
* Denominator: DV, “error”

Question 5

4 basic components of the F equation

Answer 5

1. Deviation score
2. Within groups variance
3. Grand mean
4. Between groups variance

Question 6

Deviation score

4 basic components of the F equation

Answer 6

subtract individual score FROM THE WITHIN GROUP MEAN

Question 7

F statistic equation: how does the numerator measure?

4 basic components of the F equation

Answer 7

• Basically takes the average of each deviation score PER GROUP
• Then, add up all of the group average deviation scores
• Just capturing how much variability is there IN EACH GROUP
• SSbetween

Question 8

Grand mean

4 basic components of the F equation

Answer 8

Taking the average of EACH GROUP’S average deviation from the mean

Question 9

Between groups variance

4 basic components of the F equation

Answer 9

• EACH group mean - grand mean
• Then, take the average deviation of the mean
• FOCUS ON THE GROUP MEAN, AND HOW FAR AWAY IT IS FROM THE GRAND MEAN

Question 10

Which (numerator vs denominator) will catch if a group is slightly different?

Answer 10

The betweeng groups variance (numerator), as this would affect that group’s deviation from the overall mean

Question 11

Why are F tests called “analysis of variance”?

Answer 11

they are used to compare the variation (variance) between different groups of data, and the variation within each group

Question 12

Why is the F distribution positively skewed?

Answer 12

The ratio of two chi squares, each divided by their degrees of freedom, is an F. Again, since these cannot be negative, it is right skewed.

Question 13

What is a post-hoc test for?

Answer 13

• to pinpoint which specific groups or variables are significantly different from each other
• EX: TUKEY

Question 14

When is a Tukey post-hoc test significant/passed?

Answer 14

• When the value is greater or equal to the p value, no statistically significant difference
• If less, it DOES NOT pass, and there is a statistically significant difference

Question 15

HOW DO WE REPORT THE NULL/ALTERNATIVE HYPOTHESES FOR ANOVA?

Answer 15

• H0: U1 = U2 = U3…
• “there’s a difference somewhere among the means”
• In this case, WE NEED A POST HOC

Question 16

What happens if we have NO variance that’s due to condition, F = 1?

Answer 16

• Basically if you don’t have any variance that’s due to condition, it would be 0. This leaves the equation as error variance divided by error variance, meaning = 1.
• F = 0 + error variance / error variance