Week 7

Question 1

Partitioning variance

Answer 1

SS between: variance between conditions

SS within: made up of SS subjects and SS error

SS subjects: variance within individuals
SS error: variance that we can’t explain

F ratio: difference between SS between and SS error

Question 2

SS error

Answer 2

variance that we can’t explain

SS within - SS subject

Question 3

Mean squares

Answer 3

Calculated to eliminate the bias associated with the number of scores used to calculate 𝑆𝑆

Question 4

Sphericity

Answer 4

• Sphericity falls under the banner of what is referred to as compound symmetry
• Compound symmetry occurs when both the variances across conditions are equal, and when the covariances between pairs of conditions are equal
• Compound symmetry assumes that the variation within experimental conditions is fairly similar and that no 2 conditions are any more dependent or related than any other 2
• Compound symmetry itself is not a condition of the one-way repeated measures ANOVA
• Whereas, sphericity (which is a less restrictive form of compound symmetry) is a necessary condition

Question 5

Assumptions for one-way, repeated measures ANOVA

Answer 5

• The accuracy of the F-test used in the one-way ANOVA depends on the assumption that scores in different conditions are independent
• Repeated-measures designs violate this assumption
• > This means that the conventional F-test will be inaccurate and biased
• In repeated measures designs, we use a different assumption:
• > Sphericity assumes that the relationship between pairs of experimental conditions is similar, or, that the level of dependence between experimental conditions is roughly equal

Question 6

Testing sphericity in SPSS

Answer 6

• SPSS tests the severity of departures from sphericity using Mauchly’s test
• Tests that the variances of the differences between conditions are equal
• > If test statistic is significant then the assumption has been violated
• > If test statistic is not significant then the assumption has NOT been violated

Question 7

Mauchly’s test

Answer 7

• Mauchly’s test is affected by sample size
• In very big samples, then only small deviations from sphericity can produce a significant test statistic
• In very small samples, then sometimes even quite large deviations from sphericity can produce a non-significant test statistic

Question 8

Violation of sphericity

Answer 8

When the assumption of sphericity has been violated then there is a significant loss in the power of the F-test and inaccuracies in the F-ratio that is produced in the output
If data violate the sphericity assumption there are 3 alternatives
- Greenhouse-Geisser Correction
- Huynh-Feldt Correction
- Bonferroni Correction

Question 9

Greenhouse-Geisser Correction

Answer 9

• Varies between 1/k – 1 and 1 (where k is the number of repeated-measures conditions)
• The closer the correction is to 1, the more homogeneous the variances of differences and the closer the data are to being spherical
• This correction can be over conservative

Question 10

Huynh-Feldt Correction

Answer 10

• Is a less conservative correction than the Greenhouse-Geisser correction
• But it can overestimate sphericity

Question 11

Bonferroni Correction

Answer 11

Divide alpha level by the number of comparisons