What is the difference between ANOVA and ANCOVA? In the context of using only experiment data for ANOVA analysis, ANCOVA offers post hoc statistical control. Is this a valid conclusion and why?
 A: Usually 'post hoc' means making inferences inspired by what you
see in the data. This is always dangerous because even random
data may appear to have interesting patterns. I am not saying
that ANCOVA is never used for 'post hoc' analysis, nor that
some kinds of 'post hoc' analysis are not intended for 'statistical
control'. But without knowing more, and admittedly without
context, I am instantly skeptical
of what may lie behind your statement.
So let me try to describe the actual difference between ANOVA
and ANCOVA. Suppose you are testing five new kinds of keyboards,
each designed to mitigate the kind of repetitive stress injury
that leads to carpal tunnel disease. Subjects are office workers
who have complained of such repetitive stress. Each worker is
evaluated before and after a two-week period of time using
one of the new keyboards and the change in degree of pain
is described numerically for each subject. This is the response
variable for the experiment.
A one-way ANOVA would have five groups, one for each type of
keyboard under test. Suppose we have 15 subjects per group.
Without 'controlling for' other factors as a pre-planned of the experiment, our experiment will likely be a disaster. 
A couple of possible difficulties may be: (1) Some people
have jobs that require more keyboarding that others. (2) Some
people will adapt readily to a change in keyboard and some will
take more than the two-week experimental period to adapt.
One artifact might be that the worst keyboard appears to be
best. Subjects will hate using it and put off heavy keyboarding
until after the experiment is over, so they will appear to show magnificent
decrease in pain from assignment to the horrible keyboard.
If we have advance information about one of these factors, we
might use it as part of the ANOVA design. For example, we might
have type of keyboard as one factor, and whether the job requires
Heavy, Medium, or Light keyboarding as a second factor. Then
we would have a two-factor ANOVA with $5 \times 3$ 'cells' in
the design. If we plan 15 subjects per keyboard type, perhaps
we can obtain subjects so that we have 5 per cell. In this design
subjects would have to promise to do their normal amounts of
keyboarding during the period of the study.
However, it might be difficult to find $5 \times 3 \times 5$
subjects to assign to the 15 cells. And it might be awkward
to get subjects to comply with their promise to do their normal amounts
of keyboarding. Another approach would be to collect information on actual hours $H$ of keyboarding, and treat it as a covariate.
Perhaps also to ask subjects how easily they adapted to the
new keyboard of a scale $A$ of 1 to 10. Then we could treat
$H$ and $A$ as covariates. Many ANCOVA designs and
analytic paths are possible. The design would be certainly be
chosen in advance of collecting data. Ideally, the analytic
paths would also be specified in advance by the protocol for the
experiment. 
In any experiment, it is possible that, upon seeing the data,
additional tests and methods of analysis come to mind. Strictly
speaking, any findings from these 'post hoc' procedures would
not be reported with the same level of assurance as the
analyses from the original design and protocol. They should go
into the 'possible future work' section of the report, and
might be pursued in future studies when they are pre-planned
features of a new project.
Reporting 'ad hoc' results on the same level as pre-designed
ones is the essence of 'irreproducible results' so much in the
news lately.
Acknowledgment: An experiment somewhat like the one I describe
here is reported and analyzed in Chapter 17 of Gary Oehlert's book on the design
of experiments, available here. You can read a very nice
formal description of ANCOVA there.
