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A transformation of the sample coefficient of variation ($CV$)
for normal data is shown
to be nearly proportional to a $chi^2$ random variable.
The associated density is applied to inference
on the common $CV$ of $k$ populations,
testing $CV$ homogeneity across populations,
and confidence intervals for the ratio of two $CV$s.
The resulting tests and confidence intervals are shown
via theory and simulation to be valid and powerful.
In other work on the coefficient of variation, a sample of scientific abstracts is used
to characterize the values of the
$CV$ encountered in practice, point estimation for
a common $CV$ in normal populations is studied, and the literature
on testing $CV$ homogeneity in normal populations is reviewed.
There is very little literature on the problem
of conducting inference in models for continuous data conditional on
sufficient statistics for nuisance parameters.
This thesis explores Monte Carlo approaches to conditional $p$-value calculation
in such models, including
Dirichlet data generation, importance sampling, Markov chain Monte Carlo,
and a method related to fiducial inference.
Importance sampling is used to create a conditional test of $CV$ homogeneity in
normal populations using the $chi^2$ approximation mentioned above.
A Markov chain Monte Carlo solution is given to the long-standing
problem of testing the homogeneity of exponential
populations subject to Type I censoring.
Conditional Monte Carlo algorithms are also applied to testing
for an effect of a factor in an experiment with
testing for a dispersion effect in a replicated
experiment with normal data, and testing a null value of a coefficient in exponential
regression with an inverse link; brief consideration is also given to the problem of testing the
homogeneity of $k$ $gamma$ distributions.