The Mauchly test for sphericity has been found to be a poor test of the sphericity assumption.

Name: The Mauchly test for sphericity has been found to be a poor test of the sphericity assumption.
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The Mauchly test has been shown to have low power and can lead to incorrect conclusions about sphericity, making it a poor test for the sphericity assumption in many cases. Alternative tests such as the Greenhouse-Geisser or Huynh-Feldt corrections are often recommended instead.

The Mauchly Test for Sphericity Has Been Found to Be