| Summary: | 碩士 === 國立臺灣大學 === 農藝學系 === 85 === This thesis focuses on the analysis of repeated measurement
data of two occasions only. In some biomedical research, the
first measurement is referred as initial distribution and the
interests of investigation is the distribution of the second
measurement. This thesis will discuss only thiskind of data.
For the contingency tables resulted from repeated measured data,
the statistical analysis usually try to model the marginal
distributions of the first measurement and second measurement.
If the goodness of fit is good enough then the model can be used
to describe the data and comparisonscan be made between
treatment groups or between occasions. Usually the similarity
of the initial distributions of several treatment groups can
bemade possible by good randomization scheme. One question is
raised by the author: When the initial distributions of several
treatment groups are quite different, will the statistical
analysis end by wrong conclusions? The author assumes the
treatment effects are all equivalent and use various
hypothetical data sets with different initial distributions to
study the raises dquestion. The result shows that the ordinary
analysis of marginal distributions is quite robust in the sense
of type I error. Only inthe data sets with extremely different
initial distributions, wrong conclusion is reached, that is,
treatment effects are declared statistically significant. An
unusual way of analyzing this kind of data which was proposed by
Agresti (1990) is also investigated by the author. Instead of
modeling the marginal distributions, Agresti suggested an
alternative by modeling the conditional distributions. Namely,
the conditional distributions of the second occasion given
thedistribution of thefirst occasion. This kind ofanalysis is
free of the influence ofinitial distributions. Contrast to
this,marginal distributions inthe second occasion are averages
of conditional distributions weighted by the initial
distributions. This thesis reveals that detailed analysis can
be made by this kind of analysis which can notbe reachedby the
analysis of marginal distributions. Thus, the conclusion
of this thesis is: An analysis of marginal distributions may be
run as a preliminary analysis, since it is quite robust forthe
situation of different initial distributions. Then for
obtaining amore detailed analysis, we can run an analysis by
modeling the conditional distributions.
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