ANOVA Flashcards
F statistic equation
F = between groups variance estimate / within groups variance estimate
F statistic equation: what does the numerator measure?
- Between groups variance estimate: how much do groups vary from each other?
- Independent variable “effect”
- NOTHING ABOUT INDIVIDUALS
F statistic equation: what does the denominator measure?
- Within groups variance estimate: how do individual people vary within each group?
- Random fluctuations “error”
- Sswithin
How else can the F equation be written?
Effect / error
* Numerator: IV, “effect”
* Denominator: DV, “error”
4 basic components of the F equation
- Deviation score
- Within groups variance
- Grand mean
- Between groups variance
Deviation score
4 basic components of the F equation
subtract individual score FROM THE WITHIN GROUP MEAN
F statistic equation: how does the numerator measure?
4 basic components of the F equation
- 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
Grand mean
4 basic components of the F equation
Taking the average of EACH GROUP’S average deviation from the mean
Between groups variance
4 basic components of the F equation
- 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
Which (numerator vs denominator) will catch if a group is slightly different?
The betweeng groups variance (numerator), as this would affect that group’s deviation from the overall mean
Why are F tests called “analysis of variance”?
they are used to compare the variation (variance) between different groups of data, and the variation within each group
Why is the F distribution positively skewed?
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.
What is a post-hoc test for?
- to pinpoint which specific groups or variables are significantly different from each other
- EX: TUKEY
When is a Tukey post-hoc test significant/passed?
- 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
HOW DO WE REPORT THE NULL/ALTERNATIVE HYPOTHESES FOR ANOVA?
- H0: U1 = U2 = U3…
- “there’s a difference somewhere among the means”
- In this case, WE NEED A POST HOC
What happens if we have NO variance that’s due to condition, F = 1?
- 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
