Week 12: One-Way Within-Subjects ANOVA

Question 1

• What is a one-way within-subjects ANOVA? What is another name for this method?

Answer 1

Often referred to as a one way repeated measures ANOVA
- one way = 1 IV
An IV consists of levels

Question 2

• What are levels also called in a within-subjects design? Why is it sometimes called “repeated measures”?

Answer 2

Within-subjects - a person participates in ALL of the levels

levels- sometimes called condition for a within-subjects design

It is called “repeated measures” because a person is measured repeatedly on a DV based on the number of levels the same person participates in for an IV

Question 3

• IV and DV: categorical or continuous?

Answer 3

IV = categorical
DV = continuous
*Note = the way you IV and DV is set up on SPSS for a within-subjects design is different from a between-subjects design

-We calculate f-test based on variances, not mean differences like a t-test

Question 4

• What happens to your error variance when you conduct a one-way within-subjects ANOVA?

Answer 4

Error Variance ( variance within groups) or our  noise tends to be smaller because the same participants are taking part in all the levels.
- Participating in all the levels reduces individual differences not associated to the group manipulation

Question 5

• What are the assumptions of a one-way within-subjects ANOVA?

Answer 5

Assumptions =
Normal Distribution - no skewness or kurtosis on DV

Sphericity - the same concept as homogeneity of variance (all levels of an IV must have similar variances for all levels)

*Note - we do not have independent observations as an assumption because we depend on the same participants for all levels

Question 6

• What happens when you violate sphericity?
  According to Mauchly’s test of sphericity, what does it mean when your significance is p GREATER THAN .05 AND P IS LESS THAN .05?
  Why is violating sphericity bad?

Answer 6

What happens when Violating Sphericity:

• Our levels or conditions are NOT similar invariances
• Just like how we use Levene’s Test for homogeneity of variances in t-tests, we use Mauchly’s test for sphericity in within-subjects ANOVA
• p (GREATER) .05 = sphericity is NOT violated
• p (LESS THAN) .05 = sphericity is violated (can’t be the same if it is significantly different)

Why is Violating Sphericity bad?:

• You increase the likelihood of Type I error (seeing a significant difference when there is none)
• Remember, when you significance for Mauchly’s test is significant (p LESS THAN .05 you violate sphericity

Question 7

• How do you correct for sphericity? (Hint: Greenhouse-Geisser and Hyunh-Feldt) What happens to the degrees of freedom?

What is another name for correction estimates?

When do you use Greenhouse-Geisser or Hyunh-Feldt?

Answer 7

Correcting Sphericity:
You can correct for this violation by using Greenhouse Geyser or Huynh- Feldt
- Degrees of freedom are adjusted in an f-test

Corrections Estimate for Sphericity:
Sphericity correction estimates range from 0 to 1
-Lower than 1 indicates more violation of sphericity
- correction estimates = denoted epsilon (E)

When do you use Greenhouse-Geisser or Hyunh-Feldt?
- Greenhouse-Geisser (most often used)
if the correction estimates are LESS THAN .75, use this correction estimate for omnibus test

-Hyunh-Feldt
if correction estimates are GREATER THAN .75, use this correction estimate for omnibus test