ANOVA Flashcards
What is an ANOVA?
“Analysis of Variance”
- test used to compare the means among more than 2 groups
- a statistical method that separates observed variance data into different components to use for additional tests
What is the omnibus ANOVA?
- Tells us that at least one level of the IV is different from at least one other level, but we don’t know which one.
- Could be 1 difference or a diff. between every condition
What are post hoc tests? When do you use them?
Regular inferential stats (t-tests)
performed after we conclude that the omnibus is significant
→ ie we know there is at least one significant difference between conditions in our data
Describe an ANOVA test start to finish (3 big steps)
- Determine the sampling distribution based on the df
- Calculate the obtained F statistic we found in our study using the formula / ratio
- See where the F-stat falls in the sampling distribution & make a decision
What is the F statistic ratio? (equation & in words)
MS-IV / MS-error
- Variance (IV) / Variance (error)
- Important variability / error
shows us the magnitude of the variability in our experiment that is explained by the IV
What is MS-IV? (Eq & words)
What does it measure?
How does MS-IV relate to F?
SS-IV / df-IV
- Mean of squares for IV
- How much all of the condition means deviate from the grand mean
- When MS-IV is large, F-stat tends to be large
What is MS-error? (Eq & words)
What does it measure?
How does MS-error relate to F?
SS-error / df-error
Mean of squares for error/resid
- measures the variability NOT due to manipulation, natural variability within participants
- when MS-error is small, F-stat tends to be large
What is the term for variance in an ANOVA?
Mean square
What is the grand mean (GM) ?
How is it used?
The mean of ALL data (ie the mean of the condition means)
Used to determine MS-IV
How does increasing / decreasing the numerator and/or the denominator of the F ratio affects one’s ability to reject the null hypothesis?
A larger F ratio makes it more likely to reject the null
So, increasing the numerator and/or decreasing the denominator makes it more likely that you reject the null
what causes increases or decreases in the numerator of the F ratio?
- The numerator is determined by how far away the individual condition distributions are from the Grand Mean
- A smaller numerator means they’re all relatively close to the GM → variation could be due to chance, not the IV
- A large numerator means at least one of them is very far away from the GM → variance IS explained by the IV, would be very unlikely under the null
What is the advantage of a within-groups design over a between-groups design?
- You can decrease the variance in residuals/error which increases your F statistic and makes you more likely to reject the null
- Reduces error variance, increase statistical power
what causes increases or decreases in the denominator of the F ratio?
- You can decrease the denominator in the F ratio if you have a within-groups design (repeated measures ANOVA) because you’re able to decrease a lot of the variance WITHIN each condition.
- This means a greater portion of the variance you see is caused by the IV.
What do the following terms mean (simply):
- One-way & two-way
- Btw-groups
- Repeated measures
- Eta-squared (η2)
- One IV & two IVs
- participants see only one condition
- (same as within-groups), participants see all conditions
- measure of overall effect size of IV on DV, similar to cohens d
What is the source of variance that is explained in a repeated-measures ANOVA that is not accounted for in a between-groups ANOVA?
- MS-Residual / participant variance
- Captures the variability in the DV that is due to differences observed within the same subjects or groups across multiple measurements or conditions
