One-way ANOVAs (W3-4) ✅

Question 1

What is Post hoc test and when to use it?

Answer 1

• Post hoc = Secondary analyses used to assess which IV level mean pairs differ -> basically t-tests with corrections for multiple comparisons
• Only used when the F-value is significant AND IV has >2 levels
• Choice of corrections, vary in their risk of Type I and Type
  II errors
  -> Bonferroni (high type II error)
  -> LSD (high type I error)
  -> Tukey (HSD) (high type II but more reasonable)

Question 2

What is meant by partial h2? Compare it to Cohen’s d?

Answer 2

Partial h2: how much variance in the DV is explained by the manipulation of the IV overall
-> on a scale from 0 to 1 (proportion)

Cohen’s d: the difference between pairs of IV level means, expressed in SD units
-> can take any value (real number)

Question 3

What is the F-ratio?

Answer 3

Essentially t-ratio for ANOVA

Formula:
F = var between IVs/var within IVs
-> model variance / residual variance

If homogeneity assumption is violated (significant Levene’s test result) -> report Welch’s F test

Question 4

What are the names and definitions of variance between IVs and variance within IVs in ANOVA?

Answer 4

Model Sum of Squares (SSM):
sum of squared differences between IV level means and grand mean

Residual Sum of Squares (SSR): sum of squared differences between individual values and corresponding IV level mean

SSM/dfM = MSM
SSR/dfR = MSR
=> F = MSM/MSR

Question 5

What are the advantages of repeated measure design?

Answer 5

• Recruitment: needs fewer participants to gain the same number of measurements
• Error variance (within IV levels) is reduced
• More power with the same number of participants
  –> Easier to find significant difference (avoid Type II error)
  –> Resulting F/t value is larger

Question 6

What is the main disadvantage of repeated measure designs and how to reduce it?

Answer 6

• Main: Order effects
  – Practise effects
  – Fatigue effects
  – Sensitisation
  – Carry-over effects
• Solution: Counterbalancing
• Alternatives where counterbalancing not possible
  – Practice: extensive pre-study practise
  – Fatigue: short experiments
  – Sensitisation: intervals between exposure to IV levels
  – Carry-over effects: include a control group

Question 7

How to calculate df for one-way independent & repeated measure ANOVAs?

Answer 7

1. Independent:
   * Between IVs: dfM = k-1
   * Within IVs: dfR = n - k
2. Repeated measure
   * Between IVs: dfM = k -1
   * Within IVs: dfR = dfM x (n - 1)

Question 8

When to use each type of post-hoc analysis?

Answer 8

1. When assumptions of equal variance is not met -> Tukey’s HSD and Bonferroni
2. Number of Comparisons:
   -> Bonferroni (large)
   -> Tukey’s HSD (moderate)
   -> LSD (small)
3. If needed strict control for Type I Error -> Bonferroni or Tukey’s HSD.
4. General rule:
   - Bonferroni for RM ANOVA
   - Tukey for Independent ANOVA