And the end of this section, you will be able to answer the following questions:
1.
What are quantitative methods?
2.
What are the ingredients of quantitative
methods?
3.
How do you go about research design?
Recently, as a researcher you may come across number of
studies whose data analyzed by different software packages such as SPSS. With
the use of sophisticated software packages such as SPSS, it is easy to deal
with the computation side of things and it is possible to come up with numerous
tables and charts almost instantly once your data is installed. However, it is
very important that the underlying principles of statistical analysis are
understood if sense is to be made of the results spewed out by such a package
in terms of your research.
I begin with an overview of quantitative methods.
In simple terms, we can think of two approaches to investigations
in educational research: qualitative and quantitative. In the former we use
words to describe the outcomes and in the latter we use numbers.
Quantitative research methods: They were
originally developed in the natural sciences to study natural phenomena. However
examples of quantitative methods now well accepted in the social sciences and
education includes: surveys; laboratory experiments; formal methods such as econometrics:
numerical methods such as mathematical modeling.
Qualitative research methods: They were developed
in the social sciences to enable researchers to study social and cultural
phenomenon. Examples of qualitative methods include: action research (aims to contribute both to the practical concerns
of people in an immediate problematic situation and to the goals of social
science by joint collaboration within a mutually acceptable ethical framework);
case study research (is an empirical inquiry that investigates a contemporary phenomenon within its real-life context);ethnography( the ethnographer immerses
her/himself in the life of people s/he studies and seeks to place the phenomena
studied in its social and cultural context).
Structure of Research
Papers
When conducting an educational research you will be (have
been) encouraged by your supervisor to read appropriate publications. And this
is a good way of identifying the methods of research that seem most used in
your research area. A typical structure for a research paper is summarized in
the table below:
literature
survey |
Other people’s work
|
results
|
Your work
|
methodology
|
Qualitative or quantitative
|
Discussion/
conslusions |
Your discussion/
references to others |
As part of your research you will be looking at certain variables
and endeavoring to show something interesting about how they are distributed
within a certain population. The nature of your research will determine the
variables in which you are interested. A variable needs to be measured for the
purpose of quantitative analysis.
We may collect data concerning many variables, perhaps
through a questionnaire, or choose to measure just two or several variables by
observation or testing. The variables we are interested in may be dependent or
independent. There will be other features present in the problem that may be
constant or confounding.
Using the data that you have collected then you can:
- Describe variables
in terms of distribution: frequency, central tendency and measures and form of
dispersion. Descriptive statistics include averages, frequencies, cumulative
distributions, percentages, variance and standard deviations, associations and
correlations. Variables can be displayed graphically by tables, bar or pie
charts for instance. This may be all the statistics you need and you can make
deductions from your descriptions.
Perhaps the best way to begin to appreciate the kind of
statistics that you might employ in your own research is to have a look at what
others have done.
Read different papers where the statistics that are used.
While reading findings, you will come across some terms. For instances, standard
deviation tell us about the average and spread of the data. Another one might
be a symbol ‘p’ which represents the probability of a significant difference
between the two groups. This is probably the most difficult concept to grasp
because in some senses it is counter intuitive. The probability of an event
happening range is between 0 and 1. A large probability (i.e. p close to 1)
implies a high likelihood of the event happening. For example if you are told
that there is a 95% chance of winning a game (p = 0.95) then put your money on
winning! On the other hand if there is a 5% chance of you winning (p = 0.05)
it’s probably best not to bet on yourself! So if p is small (close to 0) the event is
less likely to happen than if p is large (close to 1).
One of the first
steps in the design of a piece of quantitative research is proposing your
hypothesis. For example, we might propose the hypothesis that there is no
difference between the American pupils and Turkish pupils views of their
teachers. This is called the null hypothesis. We then need to use the pupil
responses to try to disprove this hypothesis.
To be able to compare quantities we need to define a
statistic whose distribution is known. For instance, in your paper t-statistic
is used as a measure of the difference between the means of the two groups of
pupils.
At the heart of quantitative research methods is some very
sound statistical theory. If you are planning to carry out a research
investigation using quantitative research methods you do not need a thorough
grounding in this theory but you will need an understanding of the statistical
methods. We use statistical software packages to do the arithmetical calculations
so the important skill is not doing the mathematics but is interpreting the
results.
In what follows I have gathered together some of the essential
statistical ideas needed for quantitative research ( It is just a summary).
1.
Variables
a.
numerical measurements: student’s age, size of a
school.
b.
non-numerical measurements: position on a
scale indicating a level of agreement e.g. Likert rating scale
c.
continuous data: measurement that can, in
principle, take any value within a certain range e.g. time, age and weight
d.
categorical data: (or discrete data):
measurements that can take only known discrete values e.g. the number of students
in fourth grade, the number of K 6-8 in a specific school
e.
nominal data: numerical values are assigned to
categories as codes e.g. in coding a questionnaire for computer analysis, the
response ‘male’ might be coded as ‘1’; and ‘female’ as ‘2’.
f.
ordinal
data: numerical values are assigned in accordance with a qualitative scale e.g.
in coding a questionnaire for computer analysis, the responses ‘very good’,
‘good’, ‘poor’ and ‘very poor’ are coded ‘4’, ‘3’, ‘2’ and ‘1’ respectively.
2.
Basic Measures
Mean: is a measure of the central location
or average of a set of numbers, e.g. the mean of 2 7 2 1 8 2 6 9 10 5 1 4 is
4.75
Standard
deviation: is the square root of the variance!!
Variance:
is a measure of dispersion (or spread) of a set of data calculated in
the following way:
Median: is
the center or middle number of a data set, e.g. the median of 2 7 2 1 8 2 6 9
10 5 1 4 is 4.5
Quartiles: divide a distribution of
values into four equal parts. The three corresponding values of the variable
are denoted by Q1, Q2 (equal to the median) and Q3
Range: is a measure of dispersion
equal to the difference between the largest and smallest value.
Testing an hypothesis
There are two basic concepts to grasp before starting out on
testing a hypothesis.
Firstly, the tests
are designed to disprove hypotheses. We never set out to prove anything; our
aim is to show that an idea is untenable as it leads to an unsatisfactorily
small probability.
Secondly, the
hypothesis that we are trying to disprove is always chosen to be the one in
which there is no change. For example there is no difference between the two
population means.
This is referred to as the null hypothesis and is labeled Ho.
The conclusions of a hypothesis test lead either to acceptance of the null hypothesis
or its rejection in favor of the alternative hypothesis H1.
Hypothesis testing: a hypothesis test or significance test
is a rule that decides on the acceptance or rejection of the null hypothesis
based on the results of a random sample of the population under consideration.
Statistical tests
t tests: In
hypothesis testing, the t test is used to test for differences between means
when small samples are involved. (n £ 30 say). For larger samples use the z
test.
The t test can test
i) if a sample
has been drawn from a Normal population with known mean and variance. (Single
sample)
ii) if two
unknown population means are identical given two independent random samples.
(Two unpaired samples)
iii) if two
paired random samples come from the same Normal population. (Two paired samples
(paired differences))
Further Information:
http://www.utdanacenter.org/downloads/products/researchib.pdf
http://www.cod.edu/library/libweb/Blewett/How_to_Read_A_Research_Study_Article.doc
http://www.socialresearchmethods.net/kb/
http://www.statsoft.com/textbook/
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