When conducting a one-way ANOVA, the differences of what must be approximately equal to meet sphericity?

In the context of a one-way ANOVA, the assumption of sphericity refers specifically to the variances of the differences among the groups being tested. Sphericity is a condition that pertains to the equality of variances of the differences between all possible pairs of groups, which is crucial for the validity of certain statistical tests, particularly when there are more than two levels of a factor.

When conducting a one-way ANOVA, the test studies how different group means are affected by a single independent variable. Although the equality of group means is important for interpreting the results, it is not what is meant by sphericity. Rather, what is essential are the variances of those differences, which need to be approximately equal to avoid inflation of type I error rates and ensure robustness in the results.

In summary, the correct answer focuses on the necessity for similar variances of the differences across groups to maintain the reliability of the ANOVA results, as violations of this assumption can lead to incorrect conclusions about the relationships between the groups being compared.