Random Statistical Knowledge

Question 1

What is the sphericity assumption?

Answer 1

Variability in the context of the sphericity assumption refers to how much scores differ or fluctuate across different conditions within the same participants. Assessing variability helps ensure that the analysis accurately reflects the patterns in the data and maintains the validity of statistical tests.

Question 2

Homogeneity of variance assumption

Answer 2

In simpler terms, the homogeneity of variance assumption states that the variability in the scores of your dependent variable should be roughly the same across different groups or conditions. However, in a repeated measures design, where the same individuals are measured multiple times under different conditions, each person’s scores are likely to be more similar to themselves across conditions than to scores of others. This violates the assumption of independence required for homogeneity of variance. Therefore, this assumption cannot be applied to repeated measures designs.

Question 3

Validity of the F-Test:

Answer 3

Validity of the F-Test:
In repeated measures ANOVA, the F-test compares the variability between group means to the variability within groups. For this test to be valid, it assumes that the variances of the differences between all pairs of conditions (or time points) are equal. This is the sphericity assumption.

Question 4

Assumption of Independence:

Answer 4

Assumption of Independence:
The sphericity assumption is necessary because repeated measures designs involve correlated observations within the same participants. Without sphericity, the assumption of independence underlying the F-test is violated, which can lead to inaccurate results.

Question 5

Correct Interpretation of Results:

Answer 5

Correct Interpretation of Results:
Violations of the sphericity assumption can affect the accuracy of statistical tests and lead to incorrect conclusions. For example, if the assumption is violated, the F-test may be overly conservative (i.e., less likely to detect a true effect) or overly liberal (i.e., more likely to detect an effect that doesn’t actually exist).

Question 6

Avoiding Type I and Type II Errors:

Answer 6

Avoiding Type I and Type II Errors:
Violations of the sphericity assumption can result in inflated or deflated Type I error rates (false positives) and Type II error rates (false negatives). This can lead to invalid conclusions about the significance of relationships between variables.