sphericity

Examples of sphericity in the following topics:

• Within-Subjects ANOVA

  • Discuss courses of action that can be taken if sphericity is violated
  • Naturally the assumption of sphericity, like all assumptions, refers to populations not samples.
  • Although ANOVA is robust to most violations of its assumptions, the assumption of sphericity is an exception: Violating the assumption of sphericity leads to a substantial increase in the Type I error rate.
  • Possible violation of sphericity does make a difference in the interpretation of the analysis shown in Table 2.
  • A final method for dealing with violations of sphericity is to use a multivariate approach to within-subjects variables.

• Repeated Measures Design

  • Sphericity: Difference scores computed between two levels of a within-subjects factor must have the same variance for the comparison of any two levels.
  • This test is not recommended for use when there are more than 2 levels of the within-subjects factor because the assumption of sphericity is commonly violated in such cases.
  • Alternative Univariate test: These tests account for violations to the assumption of sphericity, and can be used when the within-subjects factor exceeds 2 levels.
  • Multivariate Test: This test does not assume sphericity, but is also highly conservative.
  • The rANOVA is still highly vulnerable to effects from missing values, imputation, unequivalent time points between subjects, and violations of sphericity.