Far East Journal of Theoretical Statistics
Volume 12, Issue 1, Pages 27 - 37
(January 2004)
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INVESTIGATION OF THE EFFECTS OF TEACHING A COMPREHENSIVE COURSE IN SECTIONS BY DIFFERENT INSTRUCTORS ON THE RATE OF THE SUCCESS OF THE STUDENTS IN BASIC MATHEMATICS EDUCATION
Adnan Mazmanoglu (Turkey)
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Abstract: We
used Analysis of Variance as a solution for
our model which includes qualitative variable.
The course "Comprehensive Algebra and
Analysis" has been distributed to
different semesters such as Algebra I, II, III
and Analysis I, II, III, IV. The variability
of the rate of the success of the students led
us to apply nested Analysis of Variance. Using
Matrix Algebra along with Analysis of Variance
provided us with a lot of facilities. However,
in qualitative variable models there is no one
solution. In normal equations (X¢X)b
= X¢Y
that are obtained from the linear model that
is shown as Y
= Xb
+ e(X¢X)
matrices not having full rank depends on not
having the opposite in classical sense.
Earlier, some solutions were found out by
various limitations or under the obligation of
carrying out suitable conditions. Recently, we
claim that a concept of G-Inverse to
find out the reverse of the matrixes that
don't have full rank. In addition, by using G-Inverse
method we reached the solutions. This method
allowed us to get rid of various limitations
and conditions. The aim of this study is to
show the effects of the usage of the nested
variance Analysis on the rate of the success
of the students (regardless of their
proficiency level) by the help of computer
programming languages. Nested Analysis of
Variance has been applied on randomly selected
students and the factors of unsuccess have
been found. As a result, by changing the
positions and lectures of the instructors,
more effective and efficient conditions in the
fields of basic mathematics education were
provided in our institution. |
Keywords and phrases: the analysis of variance, linear models, models not of full rank, the 2-way nested classification. |
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