  Goodness-of-Fit tests, including Smooth ones, are introduced and applied to
detect non-Gaussianity in Cosmic Microwave Background simulations. We study the
power of three different tests: the Shapiro-Francia test (1972), the
uncategorised smooth test developed by Rayner and Best(1990) and the Neyman's
Smooth Goodness-of-fit test for composite hypotheses (Thomas and Pierce 1979).
The Smooth Goodness-of-Fit tests are designed to be sensitive to the presence
of ``smooth'' deviations from a given distribution. We study the power of these
tests based on the discrimination between Gaussian and non-Gaussian
simulations. Non-Gaussian cases are simulated using the Edgeworth expansion and
assuming pixel-to-pixel independence. Results show these tests behave similarly
and are more powerful than tests directly based on cumulants of order 3, 4, 5
and 6. We have applied these tests to the released MAXIMA data. The applied
tests are built to be powerful against detecting deviations from univariate
Gaussianity. The Cholesky matrix corresponding to signal (based on an assumed
cosmological model) plus noise is used to decorrelate the observations previous
to the analysis. Results indicate that the MAXIMA data are compatible with
Gaussianity.
