Wald F statistics
Testing of Fixed Effects with Wald F statistics
The table for testing fixed effects has 4 forms:
Source DF Fic
Source DF Fic Fcn M
Source DF DDFic Fic Pic
Source DF DDFcn Fic Fcn M Pcn
depending on whether conditional F-statistics are reported (requested
) and whether the denominator degrees
of freedom are reported.
is the model term,
is the numerator degrees of freedom ,
DDF is the denominator degrees of freedom for either the incremental
or conditional F statistic,
is the F statistic for the incremental sum of squares,
is the F statistic for the conditional sum of squares,
is an alpha code indicating conditioning level in Fcn
is probability associated with the corresponding F statistic.
Note that the probability is only available when the denominator
degrees of freedom is also present.
ASReml always reports incremental F-statistics ( Fic) for the fixed model terms
(in the DENSE partition) conditional on the order the terms were
nominated in the model.
Users should consult the Theory chapter of the
ASReml User Guide (PDF document)
for details of this table.
The 'conditional maximum' model used as the basis for the conditional F-statistic
is spelt out in the .aov file.
The numerator degrees of freedom for each term is easily determined
as the number of non-singular equations involved in the term.
However, in general, calculation of the denominator degrees of freedom
is not trivial. ASReml will by default attempt the calculation
for small analyses, by one of two methods. In larger analyses,
users can request the calculation be attempted using the
Use !DDF -1 to prevent the calculation.
Sample of Wald F statistics table
Source of Variation NumDF DenDF F-inc Prob
7 mu 1 5.0 245.14 <.001
4 variety 2 10.0 1.49 0.272
2 nitrogen 3 45.0 37.69 <.001
8 variety.nitrogen 6 45.0 0.30 0.932
!FOWN terms to test ; background terms
allows the user to specify the test in the 'conditional' F-statistic column
Wald F statistics table.
It is placed on a separate line immediately before or after the model line.
Multiple !FOWN statements should appear together.
It generates an F-test statistic for each model term in terms to test
which tests its contribution after all after terms in
terms to test
and background terms, conditional
on all terms that appear in the SPARSE equations, and on
not changing the degrees of freedom associated with a term.
It should only include terms which will appear in the ANOVA table.
!FOWN A B C ; mu
!FOWN A.B B.C A.C ; mu A B C
!FOWN A.B.C ; mu A B C A.B B.C A.C
would request the tests
F( A ; mu B C sparse),
F( B ; mu A C sparse),
F( C ; mu A B sparse),
F( A.B ; mu A B C B.C A.C sparse),
F( B.C ; mu A B C A.B A.C sparse),
F( A.C ; mu A B C A.B B.C sparse) and
F( A.B.C ; mu A B C A.B A.C B.C sparse).
This qualifier is provided for advanced users who have a good understanding
of marginality issues in ASReml.
ASReml does not verify the tests requested satisfy marginality
considerations which are normally relevant. Any model terms
in the !FOWN lists which do not appear in the actual model,
are ignored without flagging an error.
Any model terms which are omitted from !FOWN statements
are tested with the usual conditional test. If any model terms
are listed twice, only the first test is performed.
Fcn tests specified in !FOWN statements are given model codes
The !FOWN statements are parsed by the same routine that parses the
model line and so accepts the same model syntax options.
Care should be taken to ensure term names are consistently spelt.
If the !FOWN statements appear before the model line,
model terms that are not previously defined may not be abbreviated (truncated)
in !FOWN statements relative to their form in the model line
because they are defined on their first appearance.
Explanation of the ASReml ANOVA table
Return to start