Information Technology Reference
In-Depth Information
The Mauchly test was
significant. We therefore cannot
assume that we have met the
sphericity assumption. As a
result, we need to evaluate the
F
ratio using one of the procedures
accounting for a sphericity
violation.We will use the
Greenhouse-Geisser correction.
Mauchly's Test of Sphericity
b
Measure: MEASURE_1
Epsilon
a
Approx.
Chi-Square
Greenhous
e-Geisser
Sig.
Huynh-Feldt
Within Subjects Effect
prepost
Mauchly's W
Lower-bound
df
.036
17.995
9
.043
.488
.674
.250
Tests the null hypothesis that the error covariance matrix of the orthonormalized transformed dependent variables is
proportional to an identity matrix.
May be used to adjust the degrees of freedom for the averaged tests of significance. Corrected tests are displayed in
the Tests of Within-Subjects Effects table.
a.
b.
Design: Intercept
Within Subjects Design: prepost
Figure 10.12
Mauchly's test of sphericity.
10.12.2 EVALUATING SPHERICITY
Figure 10.12 presents the results of
Mauchly's Test of Sphericity
(this
is automatically performed by
GLM Repeated Measures
). John William
Mauchly was a physicist who, together with John Eckert, built the first
general-purpose electronic digital computer, named ENIAC, in 1946. He
published the sphericity test in 1940. Mauchly's test simultaneously eval-
uates two assumptions: (a) that the levels of the within-subjects variable
have equal variances (i.e., that there is homogeneity of variance); and (b)
that the pairs of levels of the within-subjects variable are correlated to the
same extent (the null hypothesis states that the correlations between the
levels do not differ from each other).
It is worth noting that because of this latter evaluation, it is necessary
to have more than two levels of the within-subjects variable in order for a
Mauchly test to be meaningfully interpreted. That is, the test must compare
at least one correlation (e.g., the correlation of Level 1 and Level 2) with
another correlation (e.g., the correlation of Level 1 with Level 3). If there
are only two levels of the within-subjects variable, there would be only
one correlation without another to which we could compare it.
With three or more levels of the within-subjects variable, there are
more than two correlations, and so Mauchly's sphericity test becomes
enabled. For example, if we had three levels, then we could compare the
correlations of Levels 1 and 2, Levels 2 and 3, and Levels 1 and 3. The null
hypothesis here is that the correlations are of comparable magnitude. If
the Mauchly test is significant, indicating that the assumption of sphericity
