ANOVA

Question 1

Why use ANOVA?

Answer 1

• Reduce type 1 error with repeated t-tests (p-value gets inflated)
• When comparing more than two groups

Question 2

What is ANOVA?

Answer 2

Analysis of Variance
- test mean differences across multiple groups on a given variable
- Between group variance
- Within group variance

Question 3

Variance

Answer 3

• 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

Question 4

What are reasons for between-group variances?

Answer 4

The mean can differ because;
- Individual differences (past experiences, history)
- Experimental error (misunderstanding verbal response)
- Systematic reason (different conditions to each group)

Question 5

What are reasons for within-group variance?

Answer 5

• Individual differences
• Experimental error

Question 6

What is F?

Answer 6

• 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

Question 7

One-way ANOVA

Answer 7

• 3 conditions or more
• 1 given variable

Question 8

One-way ANOVA - Tables

Answer 8

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

Question 9

What do you need to do if homogeneity of variance is violated in one-way ANOVA?

Answer 9

• Brown-Forsythe test
  or
• Welch’s F test

Question 10

Post-hoc tests

Answer 10

Where is the difference between which groups?
- Planned contrasts
When you have a specific hypothesis
- Post-hoc test
When you dont

Question 11

One-way ANOVA - APA style

Answer 11

• 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)

Question 12

Factorial ANOVA

Answer 12

• 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

Question 13

Factorial ANOVA - Tables

Answer 13

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)

Question 14

In factorial ANOVAs, how can we see where the difference is?

Answer 14

• Look at descriptive data, mean levels between the groups
• Between c and b students - effect 1
• Between female and males - effect 2

Question 15

Factorial ANOVA - APA style

Answer 15

• 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

Question 16

Repeated measure ANOVA

Answer 16

• Participants are followed over time
  OR
• Attend all conditions in an experiment
• One given variable
• Do people change over time in mean level

Question 17

Repeated measure ANOVA - Tables output

Answer 17

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?

Question 18

What is assumption of sphericity?

Answer 18

it assumes that the variances of the differences between conditions are the same for all pairs of conditions.
- Within group variance

Question 19

What do we do when assumption of sphericity isnt met?*

Answer 19

• 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