Why use ANOVA?
- Reduce type 1 error with repeated t-tests (p-value gets inflated)
- When comparing more than two groups
What is ANOVA?
Analysis of Variance
- test mean differences across multiple groups on a given variable
- Between group variance
- Within group variance
Variance
- How much the spread is
- Within-group; the spread of individual scores on the given variable, in comparison to the group mean
- Between-group; the spread of the means of a given variable
- F-statistics is calculated using between groups and within groups mean squares estimates
What are reasons for between-group variances?
The mean can differ because;
- Individual differences (past experiences, history)
- Experimental error (misunderstanding verbal response)
- Systematic reason (different conditions to each group)
What are reasons for within-group variance?
- Individual differences
- Experimental error
What is F?
- The variance among sample means divided by variance expected from sampling error
- Is there a systematic reason these two groups differ?
- Individual differences and experimental error takes each other out
One-way ANOVA
- 3 conditions or more
- 1 given variable
One-way ANOVA - Tables
Table 1
- Descriptives; sample size, mean, SD and range of variable
Table 2
- Homogeneity of variance
Table 3
- ANOVA test result
- F-value and Sig
If there is an overall significant difference across groups
What do you need to do if homogeneity of variance is violated in one-way ANOVA?
- Brown-Forsythe test
or - Welch’s F test
Post-hoc tests
Where is the difference between which groups?
- Planned contrasts
When you have a specific hypothesis
- Post-hoc test
When you dont
One-way ANOVA - APA style
- F (degrees of freedom between groups, within groups
- p value
- n2 (eta square) effect size
- t-test results for individual differences (post-hoc/planned contrasts)
Factorial ANOVA
- 2 or more independent variables
Categorical variable - 2 main effects of independent variables on the dependent variable(individually)
- Interaction effect
When the effect of one independent variable on the outcome variable depends on the level of the other independent variable
Factorial ANOVA - Tables
Table 1
- Between-subject factors
Table 2
- Descriptive statistics
Table 3
- Homogeneity of variance
Table 4
- Test of between-subjects Effects
- 5th column bottom three(ME 1, ME2, IE-significant)
In factorial ANOVAs, how can we see where the difference is?
- Look at descriptive data, mean levels between the groups
- Between c and b students - effect 1
- Between female and males - effect 2
Factorial ANOVA - APA style
- Reporting the main effects
F, p and effect size - Describe how the changes were
- Interaction effect
F, p and effect sizes - Describe the interaction effect
Repeated measure ANOVA
- Participants are followed over time
OR - Attend all conditions in an experiment
- One given variable
- Do people change over time in mean level
Repeated measure ANOVA - Tables output
Table 1
- What youve measured
Table 2
- Descriptive statistics
Table 3
-
Table 4
- Mauchly’s Test of Sphericity
Table 5
- Is there a change over time?
- Dont know shape or direction yet
Table 6
- F-sig (first “line”) for shape(linearity)
Table 9
- … Comparisons
- First 3 columns; is the difference from time 1 and time 2 significant?
What is assumption of sphericity?
it assumes that the variances of the differences between conditions are the same for all pairs of conditions.
- Within group variance
What do we do when assumption of sphericity isnt met?*
- Green-house Geisser or Huynh-Feldt
- Mauchly’s W less than .75 - go with greenhouse
- Means that the scores between each condition is significantly different from each other
- Changing degrees of freedom
