epsHF

The Huynh-Feldt epsilon its a correction of the Greenhouse-Geisser epsilon.This due that the Greenhouse-Geisser epsilon tends to underestimate epsilon when epsilon is greater than 0.70 (Stevens, 1990). An estimated epsilon = 0.96 may be actually 1. Huynh-Feldt correction is less conservative. The Huynh-Feldt epsilon is calculated from the Greenhouse-Geisser epsilon. As the Greenhouse-Geisser epsilon, Huynh-Feldt epsilon measures how much the sphericity assumption or compound symmetry is violated. The idea of both corrections its analogous to pooled vs. unpooled variance Student's t-test: if we have to estimate more things because variances/covariances are not equal, then we lose some degrees of freedom and P-value increases. These epsilons should be 1.0 if sphericity holds. If not sphericity assumption appears violated. We must to have in mind that the greater the number of repeated measures, the greater the likelihood of violating assumptions of sphericity and normality (Keselman et al, 1996) . Therefore, we nedd to have the most conservative F values. These are obtained by setting epsilon to its lower bound, which represents the maximum violation of these assumptions. When a significant result is obtained, it is assumed to be robust. However, since this test may be overly conservative, Greenhouse and Geisser (1958, 1959) recommend that when the lower-bound epsilon gives a nonsignificant result, it should be followed by an approximate test (based on a sample estimate of epsilon).

Syntax: function epsHF(X)

Inputs:
X - Input matrix can be a data matrix (size n-data x k-treatments)

Output:
x - Huynh-Feldt epsilon value.