Error Term for
Post-hoc Tests in GLM, GRM, and ANOVA
Post-hoc
comparisons tests are available on the GLM, GRM, and ANOVA More Results dialog
boxes - Post-hoc tab.
Error
term. Use the options in the
Error term group box to select an error term (estimate of the error
variance sigma) for the post-hoc
comparisons for the effect specified in the Effect
drop-down box on the GLM, GRM, and ANOVA More Results - Post-hoc
tab. For effects including between factors only, you can choose the Between error option button or a user-defined
value (select the MS, df option
button); for effects including within-subject
(repeated measures) factors, you can also choose the Within
error option button (i.e., the error term for the respective effect
involving the repeated measures factor) or an estimate based on the pooled
between and within error term (select the Between;
within; pooled option button). This latter estimate of sigma
is computed using the suggestions by Winer, Brown, and Michels (1991,
pp. 526-531), and Milliken and Johnson (1992, pp. 322-350); note that
the results based on this estimate are biased, and the amount of the bias
will depend (1) on the degrees of freedom for the between error (the fewer,
the less bias), and (2) on the magnitude of the ratio of the between error
to the within error (the closer this ratio is to 1, the smaller the bias).
See Winer, Brown, and Michels (1991, pp. 526) for additional details.
Between error. Select the Between error option button to use
for the estimate of the error variance the mean square error for the between
group portion of the current effect; for example, if the current effect
is A*B*R, where R is a within-subjects (repeated measures) factor, then
the Between error option will
take the mean squares error (mean squares residual) for the between-only
effects (e.g., the A*B interaction)
as the error term for the post-hoc
comparisons. In designs and for effects involving between factors only,
and without random
effects in the design, this would be the appropriate error term.
Within error. Select the Within
error option button to use for the estimate of the error variance
the mean squares error for the current effect (which involves at least
one within-subject
(repeated measures) factor; hence, STATISTICA
will use the error term for the current within effect). This error term
would be appropriate for effects that involve within-subjects (repeated
measures) factors only (and no between effects). Note that this option
is only available if the current effect involves within-subjects (repeated
measures) factors.
Between; within; pooled. Select
the Between; within; pooled option
button to use for the estimate of the error different error terms, depending
on the nature of the comparisons for the respective pair of means:
For comparisons of means at different levels of the
within (repeated measures) factors, and at the same levels of the between-group
factors, Statistica uses the respective Within
error;
For comparisons of means at different levels of the
between and within (repeated measures) factors or at the same level of
the within factor, Statistica uses
the pooled mean squares error for the current (within) effect and the
between portion of the current effect. For example, if the current effect
is A*B*R, where A and B are between factors, and R is a within factor,
then this option would pool for the error term (1) the mean squares residual
for the between design, and (2) the mean squares error for the current
effect (which involves the repeated measures factor R). Note that this
procedure yields a biased estimate of sigma,
and the results thus obtained should be interpreted with caution (see
the first paragraph in this topic above; for details see also the discussion
in Winer, Brown, and Michels, 1991, pp. 526-531; Milliken and Johnson
(1992, pp. 322-350).
Note that this option is only available if the current effect involves
within-subjects (repeated measures) factors and between factors.
MS, df. Select the MS, df option button to specify a user-defined
estimate of the error mean squares and respective degrees of freedom.
This option is particularly useful in custom designs involving random
effects and other designs where the error terms are estimated from other
effects in the design (e.g., cross-over designs with carry-over effects;
see, for example, Milliken and Johnson, 1992).
Specifically, the standard error of the difference
of the mean will be computed using the formula:
where MS
is the user-defined value and ni
and nj
are the sample sizes for the two groups that are being compared. The user-defined
degrees of freedom will be used in the subsequent test of significance.