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Thesis Writing: Analyses, Presentation, and Interpretation of Data



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ANALYSES, PRESENTATION, AND INTERPRETATION OF DATA


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Analysis

       Analysis is the process of breaking up the whole study into its constituent parts of
categories according to the specific questions under the statement of the problem. This is to
bring out into focus the essential features of the study. Analysis usually precedes
presentation.

       Example: In the study of the teaching of science in the high schools of Province A,
the whole study may be divided into its constituent parts as follows according to the specific
questions:


1.Educational qualifications of the science teachers
2.Methods and strategies used in the teaching of science
3.Facilities available for the teaching of science
4.Forms of supervisory assistance
5.Differences between the perception of the teachers and those of the
students concerning the teaching of science
6.Problems encountered in the teaching of science
7.Proposed solutions to the problems
8.Implications of the findings


       Each constituent part may still be divided into its essential categories. Example: The
educational qualifications of the teachers may further be subdivided into the following:


1.Degrees earned in pre-service education
2.Majors or specializations
3.Units earned in science
4.Teacher’s examinations and other examinations passed
5.Seminars, conferences, and other special trainings attended for the
teaching of science
6.Books, journals, and other materials in science being read
7.Advanced studies

Number of years in science teaching

Then under degrees earned are

Bachelor of Arts
Bachelor of Science in Education
Master of Arts

       The other constituent parts may also be similarly divided and subdivided. The data
are then grouped under the categories or parts to which they belong.


        Classification of data. Classification is grouping together data with similar
characteristics. Classification is a part of analysis. The bases of classification are the
following:


a.Qualitative (kind). Those having the same quality or are of the same
kind are grouped together. The grouping element in the examples
given under analysis is qualitative. See examples under analysis.


b.Quantitative. Data are grouped according to their quantity. In age, for
instance, people may be grouped into ages of 10-14, 15-19, 20-24,
25-29, etc.


c.Geographical. Data may be classified according to their location for
instance; the schools in the secondary level in Province A may be
grouped by district, as District 1, District 2, District 3, etc.


d.Chronological. In this, data are classified according to the order of
their occurrence. Example: The enrolments of the high schools of
Province A may be classified according to school years, as for,
instance, enrolments during the school years 1985-’86, 1986-’87,
1987-’88.


       Cross-classification. This is further classifying a group of data into subclasses. This is
breaking up or dividing a big class into smaller classes. For instance, a group of students
may be classified as high school students as distinguished from elementary and college
students. Then they are further subdivided into curricular years as first, second, third, and
fourth years. Each curricular year may still be subdivided into male and female.


       Arrangement of data or classes of data. The bases of arrangement of data or groups
of data are the same as those of classification.


a.Qualitative. Data may be arranged alphabetically, or from the biggest
class to the smallest class as from the phylum to specie in classifying
animals or vice versa, or listing the biggest country to the smallest one
or vice versa, or from the most important to the least important, or
vice versa, etc. Ranking of students according to brightness is
qualitative arrangement.

b.Quantitative. This is arranging data according to their numerical
magnitudes, from the greatest to the smallest number or vice versa.
Schools may be arranged according to their population, from the most
populated to the least populated, and so with countries, provinces,
cities, towns, etc.


c.Geographical. Data may be arranged according to their geographical
location or according to direction. Data from the Ilocos region may be
listed from north to south by province as Ilocos Norte, Abra, Ilocos Sur
and La Union.

d.Chronological. This is listing down data that occurred first and last
those that occurred last or vice versa according to the purpose of
presentation. This is especially true in historical research. For instance,
data during the Spanish period should be treated first before the data
during the American Period.


        Classification, cross-classification and arrangement of data are done for purposes of
organizing the thesis report and in presenting them in tabular form. In tables, data are
properly and logically classified, cross-classified, and arranged so that their relationships are
readily seen.


Group-derived Generalizations

       One of the main purposes of analyzing research data is to form inferences,
interpretations, conclusions, and/or generalizations from the collected data. In so doing the
researcher should be guided by the following discussions about group-derived
generalizations.


        The use of the survey, usually called the normative survey, as a method of collecting
data for research implies the study of groups. From the findings are formulated conclusions
in the form of generalizations that pertain to the particular group studied. These conclusions
are called group-derived generalizations designed to represent characteristics of groups and
are to be applied to groups rather than to individual cases one at a time. These are
applicable to all kinds of research, be they social, science or natural science research. There
are several types of these but are discussed under four categories by Good and Scates.
(Good and Scates, pp. 290-298) The key sentences are of this author.


        1.Generally, only proportional predictions can be made. One type of
generalization is that which is expressed in terms of proportion of the cases in a group,
often in the form of probability. When this type is used, we do not have enough information
about individual cases to make predictions for them, but we can nevertheless predict for a
group of future observations. As to individual event, however, we can say nothing;
probability is distinctly a group concept and applies only to groups.

       Quality control in manufacturing is an example. Based on the recognition that
products cannot be turned out as precisely as intended, but that so long as a given
proportion of the cases fall within assigned limits of variation, that is all that is expected. In
the biological field, certain proportions of offspring, inherit certain degrees of characteristics
of parents, but individual predictions cannot be made. In the social field, in insurance
especially, based on demographic and actuarial data, life tables indicate life expectancies of
groups but nothing whatsoever is known about the life expectancy of any particular
individual.

        Here is another example. Suppose in a certain school offering civil engineering, it is a
known fact that all through the years, bout 70% of its graduates with an average of 2.0 or
its equivalent or higher pass the licensing examination for civil engineers. On this basis, we
can predict that about 70% of the graduates of the school with an average of 2.0 or higher
will pass the next licensing examination for civil engineers but we cannot predict with
certainty the passing of a particular graduate even if his average grade is 1.25.


      2.The average can be made to represent the whole group. A second type of
group-derived generalization results from using the average as a representation of the
group of cases and offering it as a typical result. This is ignoring the individuals comprising


the group or the variation existing in the group but the average represents the whole group.
Generally, the mean and the median are used to denote the averages of scale position but
other statistical measures such as the common measures of variation, correlation,
regression lines, etc. are also structurally considered as averages. These are group
functions conveying no sure knowledge about any individual case in the group.


        3.Full frequency distribution reveals characteristics of a group. As a third type
of knowledge growing out of the study of the groups, we have the full-frequency distribution
– the most characteristics device, perhaps of all statistical work. Perhaps, too the most
inferential characteristics of frequency distribution are shape and spread. Frequency
distributions carry the implication of probability. One implication is as follows. Suppose the
heights of a Grade I pupils are taken and then grouped into a class frequency distribution,
using height as the trait or basis of distributions in groups. Then the suppliers of chairs and
tables for the pupils will be able to know the number of chairs and tables to suit the heights
of the pupils.


       Here is another example which enables us to know certain characteristics of a group.
Suppose a test is given to a group of students. Then their scores are grouped into a class
frequency distribution. If the standard deviation, a measure of variability, is computed and
it is unusually large, then we know that the group is heterogeneous. If the standard
deviation is small, the group is more or less homogeneous. If the distribution is graphed and
the curve is bell-shaped, the distribution is normal, that is, there is an equal number of
bright and dull students with the average in the middle. If the curve is skewed to the right,
there are more dull students than bright ones, and if the distribution is skewed to th left
there are more bright students than dull ones.


       4.A group itself generates new qualities, characteristics, properties, or aspects
not present in individual cases. For instance, there are many chairs in a room. The chairs
can be arranged in a variety of ways. However, if there is only one chair, there can be no
arrangement in any order. Hence, order and arrangement are group properties and they
represent relationships within a group, properties which can arise only if there are two or
more cases.


       Other group properties that exist only in groups are cooperation, opposition,
organization, specialization, leadership, teaching, morale, reciprocal sharing of emotions,
etc. which vanish in individual cases.


Two or more categories of generalization may be added at this point.

        1. A generalization can also be made about an individual case. For instance, a
high school graduating student is declared valedictorian of his class. We can generalize that,
that student is the brightest in his class. This is a group-derived generalization because it
cannot be made if there is only one student. Here is another example. A teacher declares
that Juan is the best behaved pupil in her class. This is a group-derived generalization
because this statement cannot be made if there is only one pupil. There are many instances
of this kind.

        2.In certain cases, predictions on individual cases can be made. It has been
mentioned earlier that, generally, only proportional predictions can be made. However, in
correlation and regression studies, one variable can be predicted from another. Take the
case of the civil engineering graduate taking the licensing examination by the use of
regression equations. The accuracy of prediction is high if (1) there is linearity in the
relationship of the two variables if graphed, (2) the distributions in the two variables are
normal or not badly skewed, and (3) the spread or scatter of the two variables is the same
for each column or row in the correlation table. The process involves a complicated
statistical book especially that of Garrett, pp. 122-146 for linear correlation and pp. 151-165
for regression and prediction.



Graphical Presentation of Data

         A graph is a chart representing the quantitative variations or changes of a variable
itself, or quantitative changes of variable in comparison with those of another variable or
variables in pictorial or diagrammatic form.

        The quantitative variations or changes in the data may refer to their qualitative,
geographical, or chronological attributes. For instance, if the number of teachers teaching
science in the high schools of Province A is graphed according to their degrees, the graphing
is qualitative; if their number is graphed according to their assignments in the towns where
the high schools are located, the graphing is geographical; and if their number is graphed
according to school year, the graphing is chronological.

       Purpose of graphing. The purpose of graphing is to present the variations, changes,
and relationships of data in a most attractive, appealing, effective and convincing way.
        Advantages of the graphic method. (Bacani, et al., pp. 54-55) According to Bacani,
et al. the following are the advantages of the graphical method:


1.It attracts attention more effectively than do tables, and, therefore, is
less likely to be overlooked. Readers may skip tables but pause to look
at charts.

2.The use of colors and pictorial diagrams makes a list of figures in
business reports more meaningful. (Also in thesis reports)

3.It gives a comprehensive view of quantitative data. The wandering of a
line exerts a more powerful effect in the reader’s mind than tabulated
data. It shows what is happening and what is likely to take place.

4.Graphs enable the busy executive of a business concern to grasp the
essential facts quickly and without much trouble. Any relation not seen
from the figures themselves is easily discovered from the graph.
Illustrations, including attractive charts and graphs, are now
considered by most businessmen as indispensable accompaniment to
good business reports.

5.Their general usefulness lies in the simplicity they add to the
presentation of numerical data.




       Limitations of graphs. (Bacani, et al., pp. 55) If there are advantages there are also
disadvantages of the graph. Some of these are:

1. Graphs do not show as much information at a time as do tables.
2. Graphs do not show as much information at a time as do tables.
3.Charts require more skill, more time, and more expense to prepare
than tables.


       Construction of individual graphs. Stated herein are the principles to be followed in
the construction of individual graphs.

1.The bar graph. The bar graph is often used for the graphic
presentation of data. It is generally used to make comparison of
simple magnitudes very much more clearly and more distinctly
perceptible to the eye. Each bar is drawn to a height or length equal to
the magnitude it represents as indicated in the scale (Y-axis). The bars
are separated from each other by a space equal to one-half the width
of a bar. However, there are no fixed rules that govern the


construction of graphs and the maker may only be guided by
aesthetic, proportional, and symmetrical considerations and for
convenience.

        Comparison in bar graphs is linear. It is the length of each bar that determines the
size of a magnitude it represents and the relative position of that magnitude in a series of
like and related magnitudes.

a.The single vertical graph. In the single vertical graph, the bars are
constructed vertically and they portray the magnitudes of the
categories into which data have been classified. See figure 3 as an
example of bar graph. Vertical bars are usually used to depict time
series data.

b.Single horizontal bar graph. In this graph, the bars are constructed
horizontally and are used to compare magnitudes of the different
categories into which the data are classified. The horizontal bar graph
is usually used to compare magnitudes of categories.

        Construction of graphs. In constructing graphs, two straight lines are drawn
perpendicular to each other, intersecting at a point called the point of origin and marked 0
(zero).

       The horizontal line is called baseline, coordinate, or X-axis. It represents the
variables involved or the classes’ categories of the variable involved.

       The vertical line is called ordinate or Y-axis. It represents the quantities of the
variables involved or the classes or categories of a variable involved. The Y-axis is divided
into unit distances with each unit distance represents 4,2 unit distances represent 8,3 unit
distances represents 12, etc. This is called the scale.

       The distance measured to any point parallel to the X-axis from the Y-axis is called
the abscissa of the point and the distance of that point parallel to the Y-axis from the X-axis
is the ordinate of the point. The abscissa and the ordinate of a point are called the
coordinates of the point.

Plotting the graph means locating the meeting point of the abscissa and the ordinate.
Essentials of a graph. The essential parts of a graph are the following:
1.Number. Charts or graphs are also numbered for reference purposes.
The general is to write the number as Figure 1, Figure 2, Figure 3, etc.
at the bottom of the graph.

2.Title. The same price principles hold in graphs as in tables. The title is
usually written above the graph.

3.Scale. The scale indicates the length or height unit that represents a
certain amount of the variable which is the subject of the graph. The
scale enables the reader to interpret the significance of a number of
length or height units. Thus, if a length or height unit is equal to 2,
two lengths or height units’ equal 4, 3 length or height units equal to
6, etc. The Y-axis represents the scale.

4.Classification and arrangement. The principles of classification and
arrangement are the same in graphs as in tables.

Implications of the Findings

        It is the general practice of thesis writers to discuss the summary of the implications
of their findings at the end of Chapter 4 or elsewhere in the thesis. From observations, it
appears that as far as research reporting is concerned, an implication consists of at least
five elements, namely:


1. The existence of a condition. This condition is a finding discovered in the
research. The condition may be favorable or unfavorable. If it is favorable, it
is strength of the subject studied. If it is unfavorable, it is a weakness of the
subject. For instance, in the study of the teaching of science in the high
schools of Province A, it is discovered that the majority of the science
teachers are not qualified to teach science. This finding is an unfavorable one
it is a weakness in the teaching of science.

2. The probable cause of the condition. If there is a condition there must be a
cause and there must be a logical relationship between the condition and the
cause, otherwise the cause may not be a valid one. In the example above,
the logical cause of the lack of enough qualified teachers to handle science
subjects is that either the people responsible for recruiting teachers were not
careful enough in the selection of teachers or there are not enough qualified
applicants for the positions of science teachers, or both.

3. The probable effect of the condition. Most likely, there is also a probable
effect of the condition and there must be a logical relationship between the
condition and its probable effect. The logical effect of the lack of enough
qualified teachers to teach science is that, taking all other things equal, the
science teachers in the high schools of Province A are not as effective as when
all the science teachers are fully qualified. It is understandable that a fully
qualified science teacher has more science knowledge and skills to impart to
his students than a non-qualified science teacher. Hence, the students would
suffer adversely.

4. The measure to remedy the unsatisfactory condition or to continue to
strengthen the favorable one. It is a natural reaction to institute a measure to
remedy an unfavorable situation. However, if a condition is found to be
favorable one it is also a natural reaction to continue it in operation and to
even further strengthen it. The logical step to take to remedy the unfavorable
situation is, if it is impractical to ease out the unqualified science teachers, to
enjoin or require them to improve their qualification by taking evening or
summer studies in science, by attending more science seminars, or by
increasing their readings in science especially those being published in science
journals, magazines, and other publications.

5. The entity or area involved or affected. In the example cited above, it is the
teaching of science in the high schools of Province A that is affected. Hence,
the topic for discussion must be entitled “Implications of the Findings to the
Teaching of Science.” Some researchers use the title “Implications to
Education” which is too broad and vague. The area directly affected by the
unfavorable or favorable conditions discovered in the study should be cited
more specifically.


Written by:

Prof. Erwin M. Globio, MSIT
Thesis/Dissertation Adviser/Consultant
Mobile: 0939-374-1359 | 09323956678


Thesis and Dissertation Consultancy


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