Final Answer:
Yes The test statistic of 0.543 for Mauchly indicates a violation of sphericity in the analysis.
Thus option a is correct.
Step-by-step explanation:
The Mauchly's test is used to assess sphericity in repeated measures ANOVA, determining if the variances of the differences between all possible pairs of within-subject conditions are equal. When the test statistic associated with Mauchly is less than 1, it indicates a violation of sphericity. In this case, with a test statistic of 0.543, sphericity has been violated.
The Mauchly's test statistic compares the observed variance of the differences between conditions to what would be expected if the variances were equal. If the value is significantly less than 1 (perfect sphericity), it signifies a departure from the assumption of sphericity. A lower value suggests that the variance of the differences between conditions is not consistent across all conditions, violating the assumption required for valid interpretation of repeated measures ANOVA results.
A value of 0.543 indicates a departure from the assumption of sphericity, suggesting that the differences in variances between conditions are not equal. Consequently, adjustments such as Greenhouse-Geisser or Huynh-Feldt correction need to be applied to account for this violation, ensuring the validity of the statistical analysis and avoiding erroneous interpretations due to violated assumptions in the data.
Thus option a is correct.