an introduction

1. QUANTITATIVE DATA ANALYSIS
Let us commence our look at data analysis by looking at a
hypothetical research study.
Remember that there are different ways of approaching a
research question and how we put together our research
question will determine the type of methodology, data
collection method, statistics, analysis and presentation
that we will use to approach our research problem.
Example of research question
 Are females more likely to be nurses than males?
 Is the proportion of males who are nurses the same
as the proportion of females?
 Is there a relationship between gender and becoming
a nurse?
In the example in the box above, you can see that there
are three different ways of approaching the research
problem, which is concerned with the relationship between
males and females in nursing.
Another research problem with variables

2. In another research problem - the relationship between
gender and smoking, there are 2
categorical variables(gender & smoker), with two or more
categories in each, for example:
Gender (male/female)
Smoker (yes/no)
You are looking for whether or not there is any
significance in the results
Reflection
Before we proceed, you may want to briefly refresh your
knowledge and understanding of some basics, namely:
 hypothesis
 randomised controlled double-blind trial
 variables
 descriptive statistical analysis
 inferential statistical analysis
To recap on statistics, read chapter 9 of the
accompanying book, and/or click on the hyperlink below:
statistics are fun
Now to return to statistical analysis

3. Alpha level (p level)
In statistical analysis we are looking to see if there is any
significance in the results. The acceptance or rejection of
a hypothesis is based upon a level of significance – the
alpha () level
This is usually set at the 5% (0.05)  level, followed in
popularity by the 1% (0.01)  level
We usually designate these as p, i.e. p =0.05 or p = 0.01
So, what do we mean by levels of significance that the 'p'
value can give us?
Statistical tests
There are many tests that we can use to analyse our data,
and which particular one we use to analyse our data
depends upon what we are looking for, and what data we
collected (and how we collected it).
Below are just a few of the more common ones that you
may come across in research papers.
Mann-Whitney U-test
This test is used to test for differences between 2
independent groups on a continuous measure, e.g. do

4. males and females differ in terms of their levels of self-
esteem.
This test requires two variables (e.g. male/female gender)
and one continuous variable (e.g. self-esteem).
It actually compares medians.
It converts the scores on the continuous variable
to ranks, across the two groups.
It then evaluates whether the medians for the two groups
differ significantly.
Spearman rank correlation test
This test is used to demonstrate the relationship between
two ranked variables
Frequently used to compare judgements by a group of
judges on two objects, or the scores of a group of
subjects on two measures.
This is a coefficient correlation based on ranks.
It shows the association between two variables (X and Y),
which are not normally distributed.

5. Don’t worry about the details – just remember that it is an
acceptable method for parametric data when there are
less than 30 but more than 9 paired variables.
Kruskal-Wallis test
This test is used to compare the means among more than
two samples, when either the data are ordinal or the
distribution is not normal.
If there are only two groups then it is the equivalent of the
Mann-Whitney U-test, so you may as well use that test.
This test would normally be used when you wanted to
determine the significance of difference among three or
more groups.
Below is a very brief look at other common tests - for more
information on statistical tests, read chapter 9 of the
accompanying book.
Other Common Statistical Tests/Procedures

6. t-test
The t-test assesses whether the means of two groups
are statisticallydifferent from each other. This analysis is appropriate
whenever you want to compare the means of two groups.
Pearson Correlation
We use the Pearson's correlation in order to find a correlation
between at least two continuous variables. The value for such a
correlation lies between 0.00 (no correlation) and 1.00 (perfect
correlation).
ANOVA (Analysis of Variance)
ANOVA is one of a number of tests (ANCOVA - analysis of
covariance - and MANOVA - multivariate analysis of variance) that
are used to describe/compare the relationship among a number of
groups.

7. Chi-square test
There are two different types of chi-square tests - but both involve
categorical data (Pallant 2001).
One type of chi-square test compares the frequency count of what is
expected in theory against what is actually observed.
The second type of chi-square test is known as a chi-square test
with two variables or the chi-square test for independence.
Wilcoxon signed-rank test
This is the most common nonparametric test for the two-sampled
repeated measures design of research study, and is also known as
the Wilcoxon matched-pairs test.
This has just been a very brief look at some of the more
common statistical tests for the analysis of data obtained
from quantitative research - more details are given in
chapter 9 of the accompanying book. There are, of course,
many others, and any good statistics book will have details
of them.
Selecting your statistical test

8. When it comes to the selection of the appropriate test for
your research in order to determine the p-value, you need
to base the selection of four major factors, namely:
 The level of data (nominal, ordinal, ratio, or interval).
 The number of groups/samples in your research study
(one, two, or more).
 Were the data collected from independent
groups/samples or from related groups? Remember
that independent groups are two or more separated
groups of participants, whilst related groups are often
the same group, but at a different time in the study,
e.g. pre- and post-testing, or even a different
environment.
 The characteristics of the data (i.e. the distribution of
the data).
Now all these statistical tests may look very complicated,
but if ever you are involved in quantitative research and
have to do statistical analysis, don't worry because help is
at hand.
There is a computer package for statistical analysis known
as SPSS
SPSS stands for:
Statistical Package for Social Sciences

9. SPSS is one of a number of computer packages that can
do just about any calculation that you want, using any
statistical test.
Before we finish this section, we just need to remind you
to be careful when you are looking at research that uses
statistics.
Limitations of research study/data/statistical tests
Always look for these – the researchers should reflect on
their study and discuss anything that did not make it
perfect, for example:
 size of sample
 tests used
 initial question
It is easy to tie yourself up into knots when either doing
statistics as part of your research, or when reading
research papers, so remember two things:
1. Keep things simple
2. Statistics by themselves are meaningless, it is the
analysis and
discussion of statistics which makes them meaningful
and brings
them to life.
Finally

10. The time has come for you to decide which statistical test
you will be using for your own quantitative research. As we
keep mentioning, if all this is new to you, do not hesitate to
seek the advice of an experienced quantitative researcher
and/or a statistician - at as early a stage as possible.
TO DO
Click on to the icon below for the example of a
quantitative research study proposal:

When you are satisfied that you have the correct
statistical test(s), and you can justify it/them, then write
them into your research proposal.