DECISION MAKING 7 Strategies for Better Group Decision-Making by Torben Emmerling and Duncan Rooders SEPTEMBER 22, 2020 HBR STAFF/CHARLES DELUVIO/UNSPLASH When you have a tough business problem to solve, you likely bring it to a group. After all, more minds are better than one, right? Not necessarily. Larger pools of knowledge are by no means a guarantee of better outcomes. Because of an over-reliance on hierarchy, an instinct to prevent dissent, and a desire to preserve harmony, many groups fall into groupthink. Misconceived expert opinions can quickly distort a group decision. Individual biases can easily spread across the group and lead to outcomes far outside individual preferences. And most of these processes occur subconsciously. 2COPYRIGHT © 2020 HARVARD BUSINESS SCHOOL PUBLISHING CORPORATION. ALL RIGHTS RESERVED. http://williamwolff.org/wp-content/uploads/2016/01/griffin-groupthink-challenger.pdf This doesn’t mean that groups shouldn’t make decisions together, but you do need to create the right process for doing so. Based on behavioral and decision science research and years of application experience, we have identified seven simple strategies for more effective group decision making: Keep the group small when you need to make an important decision. Large groups are much more likely to make biased decisions. For example, research shows that groups with seven or more members are more susceptible to confirmation bias. The larger the group, the greater the tendency for its members to research and evaluate information in a way that is consistent with pre-existing information and beliefs. By keeping the group to between three and five people, a size that people naturally gravitate toward when interacting, you can reduce these negative effects while still benefitting from multiple perspectives. Choose a heterogenous group over a homogenous one (most of the time). Various studies have found that groups consisting of individuals with homogeneous opinions and beliefs have a greater tendency toward biased decision making. Teams that have potentially opposing points of view can more effectively counter biases. However, context matters. When trying to complete complex tasks that require diverse skills and perspectives, such as conducting research and designing processes, heterogeneous groups may substantially outperform homogeneous ones. But in repetitive tasks, requiring convergent thinking in structured environments, such as adhering to safety procedures in flying or healthcare, homogenous groups often do better. As a leader, you need first to understand the nature of the decision you’re asking the group to make before you assemble a suitable team. Appoint a strategic dissenter (or even two). One way to counter undesirable groupthink tendencies in teams is to appoint a “devil’s advocate.” This person is tasked with acting as a counterforce to the group’s consensus. Research shows that empowering at least one person with the right to ...

1. DECISION MAKING
7 Strategies for Better
Group Decision-Making
by Torben Emmerling and Duncan Rooders
SEPTEMBER 22, 2020
HBR STAFF/CHARLES DELUVIO/UNSPLASH
When you have a tough business problem to solve, you likely
bring it to a group. After all, more
minds are better than one, right? Not necessarily. Larger pools
of knowledge are by no means a
guarantee of better outcomes. Because of an over-reliance on
hierarchy, an instinct to prevent
dissent, and a desire to preserve harmony, many groups fall i nto
groupthink.
Misconceived expert opinions can quickly distort a group
decision. Individual biases can easily
spread across the group and lead to outcomes far outside
individual preferences. And most of these
processes occur subconsciously.
2COPYRIGHT © 2020 HARVARD BUSINESS SCHOOL
PUBLISHING CORPORATION. ALL RIGHTS RESERVED.
http://williamwolff.org/wp-content/uploads/2016/01/griffin-
groupthink-challenger.pdf
This doesn’t mean that groups shouldn’t make decisions

2. together, but you do need to create the right
process for doing so. Based on behavioral and decision science
research and years of application
experience, we have identified seven simple strategies for more
effective group decision making:
Keep the group small when you need to make an important
decision. Large groups are much more
likely to make biased decisions. For example, research shows
that groups with seven or more
members are more susceptible to confirmation bias. The larger
the group, the greater the tendency
for its members to research and evaluate information in a way
that is consistent with pre-existing
information and beliefs. By keeping the group to between three
and five people, a size that people
naturally gravitate toward when interacting, you can reduce
these negative effects while still
benefitting from multiple perspectives.
Choose a heterogenous group over a homogenous one (most of
the time). Various studies have
found that groups consisting of individuals with homogeneous
opinions and beliefs have a greater
tendency toward biased decision making. Teams that have
potentially opposing points of view can
more effectively counter biases. However, context matters.
When trying to complete complex tasks
that require diverse skills and perspectives, such as conducting
research and designing processes,
heterogeneous groups may substantially outperform
homogeneous ones. But in repetitive tasks,
requiring convergent thinking in structured environments, such
as adhering to safety procedures in
flying or healthcare, homogenous groups often do better. As a
leader, you need first to understand

3. the nature of the decision you’re asking the group to make
before you assemble a suitable team.
Appoint a strategic dissenter (or even two). One way to counter
undesirable groupthink tendencies
in teams is to appoint a “devil’s advocate.” This person is
tasked with acting as a counterforce to the
group’s consensus. Research shows that empowering at least
one person with the right to challenge
the team’s decision making process can lead to significant
improvements in decision quality and
outcomes. For larger groups with seven or more members,
appoint at least two devil’s advocates to
be sure that a sole strategic dissenter isn’t isolated by the rest
of the group as a disruptive
troublemaker.
Collect opinions independently. The collective knowledge of a
group is only an advantage if it’s used
properly. To get the most out of your team’s diverse
capabilities, we recommend gathering opinions
individually before people share their thoughts within the wider
group. You can ask team members
to record their ideas independently and anonymously in a shared
document, for example. Then ask
the group to assess the proposed ideas, again independently and
anonymously, without assigning
any of the suggestions to particular team members. By
following such an iterative process teams can
counter biases and resist groupthink. This process also makes
sure that perceived seniority, alleged
expertise, or hidden agendas don’t play a role in what the group
decides to do.
Provide a safe space to speak up. If you want people to share
opinions and engage in constructive

4. dissent, they need to feel they can speak up without fear of
retribution. Actively encourage reflection
on and discussion of divergent opinions, doubts, and
experiences in a respectful manner. There are
3COPYRIGHT © 2020 HARVARD BUSINESS SCHOOL
PUBLISHING CORPORATION. ALL RIGHTS RESERVED.
https://psycnet.apa.org/record/1996-98366-008
https://psycnet.apa.org/record/2000-08135-004
https://psycnet.apa.org/record/1996-98365-006
https://hbr.org/2008/11/when-teams-cant-decide
https://journals.aom.org/doi/abs/10.5465/255859
https://store.hbr.org/product/wiser-getting-beyond-groupthink-
to-make-groups-smarter/2299
https://store.hbr.org/product/wiser-getting-beyond-groupthink-
to-make-groups-smarter/2299
https://store.hbr.org/product/the-fearless-organization/ROT389
three basic elements required to create a safe space and harness
a group’s diversity most effectively.
First, focus feedback on the decision or discussed strategy, not
on the individual. Second, express
comments as a suggestion, not as a mandate. Third, express
feedback in a way that shows you
empathize with and appreciate the individuals working toward
your joint goal.
Don’t over-rely on experts. Experts can help groups make more
informed decisions. However, blind
trust in expert opinions can make a group susceptible to biases
and distort the outcome. Research
demonstrates that making them part of the decision-making can
sway the team to adapt their
opinions to those of the expert or make overconfident

5. judgments. Therefore, invite experts to
provide their opinion on a clearly defined topic, and position
them as informed outsiders in relation
to the group.
Share collective responsibility. Finally, the outcome of a
decision may be influenced by elements as
simple as the choice of the group’s messenger. We often
observe one single individual being
responsible for selecting suitable group members, organizing
the agenda, and communicating the
results. When this is the case, individual biases can easily
influence the decision of an entire team.
Research shows that such negative tendencies can be effectively
counteracted if different roles are
assigned to different group members, based on their expertise.
Moreover, all members should feel
accountable for the group’s decision making process and its
final outcome. One way to do that is to
ask the team to sign a joint responsibility statement at the
outset, leading to a more balanced
distribution of power and a more open exchange of ideas.
Of course, following these steps doesn’t guarantee a great
decision. However, the better the quality
of the decision-making process and the interaction between the
group members, the greater your
chances of reaching a successful outcome.
Torben Emmerling is the founder and managing partner of
Affective Advisory. He is the author of the D.R.I.V.E.®
framework for behavioral insights in strategy, a seasoned
lecturer in behavioral science and applied consumer
psychology and an accomplished trainer and keynote speaker.

6. Duncan Rooders is the CEO of a Single Family Office and a
strategic advisor to Affective Advisory. He is a former B747
pilot, a graduate of Harvard Business School’s Owner/President
Management program, and a consultant to several
international organizations in strategic and financial decision
making.
4COPYRIGHT © 2020 HARVARD BUSINESS SCHOOL
PUBLISHING CORPORATION. ALL RIGHTS RESERVED.
https://hbr.org/2008/09/how-pixar-fosters-collective-creativity
https://onlinelibrary.wiley.com/doi/abs/10.1002/bdm.637
https://onlinelibrary.wiley.com/doi/abs/10.1002/bdm.637
https://journals.sagepub.com/doi/abs/10.1177/104649640831598
3
https://hbr.org/2014/12/making-dumb-groups-smarter
https://hbr.org/1993/03/the-discipline-of-teams-2
https://hbr.org/1993/03/the-discipline-of-teams-2
https://affective-advisory.com/
https://affective-advisory.com/
Copyright 2020 Harvard Business Publishing. All Rights
Reserved. Additional restrictions
may apply including the use of this content as assigned course
material. Please consult your
institution's librarian about any restrictions that might apply
under the license with your
institution. For more information and teaching resources from
Harvard Business Publishing
including Harvard Business School Cases, eLearning products,
and business simulations
please visit hbsp.harvard.edu.

7. EDU730: Research
Practices and Methods
Page 1 EDU730: Research Practices and Methods
Week 9:
Quantitative Data Analysis
Topic goals
ng of Quantitative Analysis
research.
analysis
Task – Forum
question that can address two or more variables, using
quantitative terms, defining the variables you will use.

8. Discuss which statistical test you would use to answer
your research question and explain the rationale behind
your choice.
EDU730: Research
Practices and Methods
Page 2 EDU730: Research Practices and Methods
QUANTITATIVE DATA ANALYSIS
1. Introduction
The main purpose to analyze data is to gain useful and valuable
information. Data
analysis is useful to describe data, compare and find
relationships or differences
between variables, etc. The researcher uses techniques to
convert the data to

9. numerical forms.
1.1. Prepare your data
As a researcher you have to be sure that your data are correct
e.g. respondents
answered all of the questions, check your transcriptions, etc.
You have to identify
your missing data and then you have to convert them into a
numerical form e.g.
red=1, yellow=2, green=3, etc.
1.2. Scales of measurements
Before analyzing quantitative data, researchers must identify
the level of
measurement associated with the quantitative data. The type of
data that you have
to use on a set of data depends on the scale of measurement of
your data. The
scales of measurements are nominal, ordinal, interval and ratio.
Nominal data
Data has no logical order and can be classified into non-

10. numerical or named
categories. It is basic classification data. The values we give are
just to replace the
name and they cannot be order. Ex. Male, female, district A,
district b
Example: Male or Female
There is no order associated with male or female
EDU730: Research
Practices and Methods
Page 3 EDU730: Research Practices and Methods
Ordinal data
Data has a logical order, but the differences between values are
not constant.
These data are usually used for questions that are referred to
ratings of quality or
agreements like good, fair, bad, or strongly agree, agree,
disagree, strongly

11. disagree.
Example: 1st , 2nd, 3rd
Example: T-shirt size (small, medium, large)
Interval data:
Data is continuous and has a logical order, data has
standardized differences
between values, but no natural zero .
Example: Fahrenheit degrees
* Remember that ratios are meaningless for interval data. You
cannot say, for
example, that one day is twice as hot as another day.
Ratio data
Data is continuous, ordered, has standardized differences
between values, and a
natural zero
Example: height, weight, age, length
Having an absolute zero allows you to meaningful argue that

12. one measure is twice
as long as another.
For example – 10 km is twice as long as 5 km
Remember that there are several ways of approaching a research
question and how
the researcher puts together a research question will determine
the type of
methodology, data collection method, statistics, analysis and
presentation that will
be used to approach the research problem.
For each type of data you have to use different analysi s
techniques. When using a
quantitative methodology, you are normally testing a theory
through the testing of
a hypothesis.
EDU730: Research
Practices and Methods

13. Page 4 EDU730: Research Practices and Methods
1.3. Hypothesis/Null hypothesis:
A hypothesis is a logical assumption, a reasonable guess, or a
suggested answer to
a research problem.
A null hypothesis states that minor differences between the
variables can occur
because of chance errors, and are therefore not signifi cant.
*Chance error is defined as the difference between the predicted
value of a
variable (by the statistical model in question) and the actual
value of the variable.
In statistical hypothesis testing, a type I error is the incorrect
rejection of a true null
hypothesis (a "false positive"), while a type II error is
incorrectly retaining a false
null hypothesis (a "false negative"). Simply, a type I error is
detecting an effect (e.g.
a relationship between two variables) that is not present, w hile a
type II error is

14. failing to detect an effect that is present.
1.4. Randomised, controlled and double-blind trial
Randomised - chosen by random.
Controlled - there is a control group as well as an experimental
group.
Double-blind - neither the subjects nor the researchers know
who is in which
group.
Variables:
An experiment has three characteristics:
1. A manipulated independent variable (often denoted by x,
whose variation does
not depend on that of another).
2. Control of other variables i.e. dependent variables (a variable
often denoted
by y, whose value depends on that of another.
3. The observed effect of the independent variable on the
dependent variables.

15. EDU730: Research
Practices and Methods
Page 5 EDU730: Research Practices and Methods
1.5. Validity, reliability and generalizability
Validity: refers to whether the researcher measures what he/she
wants to
measure. The three types of validity are:
Content validity – refers to whether or not the content of the
variables is right to
measure the concept.
Criterion validity – refers to the collection of information on
these other measures
that can determine this.
Construct validity - refers to the design of your instrument so
that it contains
several factors, rather than just one.
(Muijs, 2010)

16. Reliability: “refers to the extent to which test scores are free of
measurement
error” (Muijs, 2010, pg.82). The two types of reliability are:
Repeated measures or test-retest reliability - refers to the
instrument that you use
if it can be trusted to give similar result if used later on time
with the same
respondents.
Internal consistency - refers to whether all the items are
measuring the same
construct.
Generalizability: it is about the generalization of your findings
from your sample to
the population.
EDU730: Research
Practices and Methods

17. Page 6 EDU730: Research Practices and Methods
2. Descriptive statistics
Descriptive statistics are summarizing data. These are used to
describe variables
and the basic features of the data that have been collected in a
study. They provide
simple summaries about the sample and measures of central
tendency (e.g. mean,
median, standard deviation etc.). Together with simple graphics
analysis, they form
the basis of virtually every quantitative analysis of data.
It should be noted that with descriptive statistics no conclusions
can be extended
beyond the immediate group from which the data was gathered.
Some popular summary statistics for interval variables
Mean: is the arithmetic average of the values, calculated by
adding all the values
and divided by the total number of values.

18. Median: the data point that is in the middle of "low" and "high"
values , after put in
numerical order
Mode: The most common occurring score in a data set
Range: It is the difference between the highest score and the
lowest score.
Standard deviation: “The standard deviation exists for all
interval variables. It is the
average distance of each value away from the sample mean. The
larger the
standard deviation, the farther away the values are from the
mean; the smaller the
standard deviation the closer, the values are to the mean” (Patel,
2009, pg.5).
Minimum and Maximum value: the smallest and largest score in
data set
Frequency: The number of times a certain value appears
Quartiles: same thing as median for 1/4 intervals

19. EDU730: Research
Practices and Methods
Page 7 EDU730: Research Practices and Methods
(Adapted from Patel, 2009, pg. 6)
3. Data distribution
Before beginning the statistical tests, it is necessary to check
the distribution of
your data. The main types of distribution are normal and non-
normal.

20. Example
Case no Grades
1 90
2 67
3 85
4 90
5 100
6 58
7 90
Total 490
Mean: 70
Median: 90
Mode: 90
Minimum value: 100
Maximum value: 58
EDU730: Research
Practices and Methods

21. Page 8 EDU730: Research Practices and Methods
3.1. The Normal distribution
When the data tends to be around a central value with no bias
left or right, it gets
close to a "Normal Distribution":
The graph of the normal distribution depends on two factors i.e.
the mean (M) and
the standard deviation (SD). The basics characteristics of a
normal curve are: a) a
bell shape curve, b) It is perfectly symmetrical, c) Mode,
median, and mean lie in
the middle of the curve (50% of the values lie to the left of the
mean, and 50% lie to
the right) d) Approximately 95% of the values are found two
standard deviations
away from the mean (in both directions) (Patel, 2009). The
location of the center of
the graph is determined by the mean of the distribution, and the
height and width

22. of the graph is determined by the standard deviation. When the
standard deviation
is large, the curve is short and wide; when the standard
deviation is small, the curve
is tall and narrow. Normal distribution graphs look like a
symmetric, bell-shaped
curve, as shown above. When measuring things like people's
height, weight, salary,
opinions or votes, the graph of the results is very often a normal
curve.(Langley
Perrie, 2014)
https://www.google.com.cy/search?espv=2&biw=1600 &bih=794
&tbm=bks&q=inauthor:%22Chris+Langley%22&sa=X&ved=0ah
UKEwi4vvv62P3RAhUhIMAKHcwwDHQQ9AgIKzAD
https://www.google.com.cy/search?espv=2&biw=1600&bih=794
&tbm=bks&q=inauthor:%22Yvonne+Perrie%22&sa=X&ved=0a
hUKEwi4vvv62P3RAhUhIMAKHcwwDHQQ9AgILDAD

23. EDU730: Research
Practices and Methods
Page 9 EDU730: Research Practices and Methods
3.2. Non-Normal Distributions:
There are several ways in which a distribution can be non-
normal.
4. Statistical Analysis
Statistical tests are used to make inferences about data, and can
tell us if our
observation is real. There is a wide range of statistical tests and
the decision of
which of them you are going to test it depends on your research
design. If your data
is normally distributed you have to choose a parametric test
otherwise you have to
choose non-parametric tests.
4.1. Parametric and Nonparametric Tests

24. A parametric statistical test makes assumptions about the
parameters (defining
properties) of the population distribution(s) from which one's
data are drawn,
whereas a non-parametric test makes no such assumptions.
Nonparametric tests
are also called distribution-free tests because they do not
assume that your data
follow a specific distribution (Frost, 2015).
EDU730: Research
Practices and Methods
Page 10 EDU730: Research Practices and Methods
Parametric tests (means) Nonparametric tests (medians)
1-sample t test 1-sample Sign, 1-sample Wilcoxon
2-sample t test Mann-Whitney test
One-Way ANOVA Kruskal-Wallis, Mood’s median test
Factorial DOE with one factor and one

25. blocking variable
Friedman test
It is argued that nonparametric tests should be used when the
data do not meet
the assumptions of the parametric test, particularly the
assumption about normally
distributed data. However, there are additional considerations
when deciding
whether a parametric or nonparametric test should be used.
4.2. Reasons to Use Parametric Tests
Reason 1: Parametric tests can perform well with skewed and
non-normal
distributions
Parametric tests can perform well with continuous data that are
not normally
distributed if the sample size guidelines demonstrated in the
table below are
satisfied.

26. EDU730: Research
Practices and Methods
Page 11 EDU730: Research Practices and Methods
Parametric analyses Sample size guidelines for non-normal data
1-sample t test Greater than 20
2-sample t test Each group should be greater than 15
One- -9 groups, each group should
be
greater than 15.
-12 groups, each group should be
greater than 20.
Note: These guidelines are based on simulation studies
conducted by statisticians at
Minitab.
Reason 2: Parametric tests can perform well when the spread of

27. each group
is different
While nonparametric tests do not assume that your data are
normally distributed,
they do have other assumptions that can be hard to satisfy. For
example, when
using nonparametric tests that compare groups, a common
assumption is that the
data for all groups have the same spread (dispersion). If the
groups have a different
spread, then the results from nonparametric tests might be
invalid.
Reason 3: Statistical power
Parametric tests usually have more statistical power compared
to nonparametric
tests. Hence, they are more likely to detect a significant effect
when one truly
exists.

28. http://support.minitab.com/en-us/minitab/17/topic-library/basic-
statistics-and-graphs/power-and-sample-size/what-is-power/
EDU730: Research
Practices and Methods
Page 12 EDU730: Research Practices and Methods
4.3. Reasons to Use Nonparametric Tests
Reason 1: Your area of study is better represented by the
median
The fact that a parametric test can be performed with no normal
data does not
imply that the mean is the best measure of the central tendency
for your data. For
example, the center of a skewed distribution (e.g. income), can
be better measured
by the median where 50% are above the median and 50% are
below. However, if
you add a few billionaires to a sample, the mathematical mean

29. increases greatly,
although the income for the typical person does not change.
When the distribution is skewed enough, the mean is strongly
influenced by
changes far out in the distribution’s tail, whereas the median
continues to more
closely represent the center of the distribution.
Reason 2: You have a very small sample size
If the data are not normally distributable and do not meet the
sample size
guidelines for the parametric tests, then a nonparametric test
should be used. In
addition, when you have a very small sample, it might be
difficult to ascertain the
distribution of your data as the distribution tests will lack
sufficient power to
provide meaningful results.
http://support.minitab.com/en-us/minitab/17/topic-library/basic-
statistics-and-graphs/summary-statistics/measures-of-central-
tendency/

30. EDU730: Research
Practices and Methods
Page 13 EDU730: Research Practices and Methods
Reason 3: You have ordinal data, ranked data, or outliers that
you cannot
remove
Typical parametric tests can only assess continuous data and the
results can be
seriously affected by outliers. Conversely, some nonparametric
tests can handle
ordinal data, ranked data, without being significantly affected
by outliers.
4.4. Statistical tests
One-tailed test: A test of a statistical hypothesis, where the
region of rejection is on
only one side of the sampling distribution is called a one-tailed
test. For example,
suppose the null hypothesis states that the mean is less than or

31. equal to 10. The
alternative hypothesis would be that the mean is greater than 10.
Two-tailed test: When using a two-tailed test, regardless of the
direction of the
relationship you hypothesize, you are testing for the possibility
of the relationship
in both directions. For example, we may wish to compare the
mean of a sample to a
given value x using a t-test. Our null hypothesis is that the
mean is equal to x.
Alpha level (p value): In statistical analysis the researcher
examines whether there
is any significance in the results. This is equal to the probability
of obtaining the
observed difference, or one more extreme, if the null hypothesis
is true.
The acceptance or rejection of a hypothesis is based upon a
level of significance –
the alpha (a) level
This is typically set at the 5% (0.05) a level, followed in
popularity by the 1% (0.01) a

32. level
These are usually designated 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?
EDU730: Research
Practices and Methods
Page 14 EDU730: Research Practices and Methods
The p value is concerned with confidence levels. This states the
threshold at which
you are prepared to accept the possibility of a Type I Error –
otherwise known as a
false positive – rejecting a null hypothesis that is actually true.
The question that significance levels answer is 'How confident
can the researcher
be that the results have not arisen by chance?'
Note: The confidence levels are expressed as a percentage.

33. So if we had a result of:
p =1.00, then there would be a 100% possibility that the results
occurred by chance.
p = 0.50, then there would be a 50% possibility that the results
occurred by chance.
p = 0.05, then we are 95% certain that the results did not arise
by chance
p = 0.01, then we are 99% certain that the results did not arise
by chance.
Clearly, we want our results to be as accurate as possible, so we
set our significance
levels as low as possible - usually at 5% (p = 0.05), or better
still, at 1% (p = 0.01)
Anything above these figures, are considered as not accurate
enough. In other
words, the results are not significant.
Now, you may be thinking that if an effect could not have arisen
by chance 90 times
out of 100 (p = 0.1), then that is pretty significant.
However, what we are determining with our levels of
significance, is 'statistical

34. significance', hence we are much more strict with that, so we
would usually not
accept values greater than p = 0.05.
So when looking at the statistics in a research paper, it is
important to check the 'p'
values to find out whether the results are statistically significant
or not.
(Burns & Grove, 2005)
EDU730: Research
Practices and Methods
Page 15 EDU730: Research Practices and Methods
p-value Outcome of test Statement
greater than 0.05 Fail to reject H0 No evidence to reject H0

35. between 0.01 and 0.05 Reject H0 (Accept H1) Some evidence to
reject H0
(therefore accept H1)
between 0.001 and 0.01 Reject H0 (Accept H1) Strong evidence
to reject H0
(therefore accept H1)
less than 0.001 Reject H0 (Accept H1) Very strong evidence to
reject
H0 (therefore accept H1)
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
association between a number of groups. ANOVA is used to
determine whether the
difference in means (averages) for two groups is statistically
significant.
T-test
The t-test is used to assess whether the means of two groups
differ statistically
from each other.

36. Mann-Whitney U-test
The Mann-Whitney U-test test is used to test for differences
between two
independent groups on a continuous measure, e.g. do males and
females differ in
terms of their levels of anxiety.
This test requires two variables (e.g. male/female gender) and
one continuous
variable (e.g. anxiety level). Basically, the Mann-Whitney U-
test converts the scores
on the continuous variable to ranks, across the two groups and
calculates and
compares the medians of the two groups. It then evaluates
whether the medians
for the two groups differ significantly.
EDU730: Research
Practices and Methods

37. Page 16 EDU730: Research Practices and Methods
Wilcoxon signed-rank test
The Wilcoxon signed-rank test (also known as Wilcoxon
matched-pairs test) is the
most common nonparametric test for the two-sampled repeated
measures design
of research study.
Kruskal-Wallis test
The Kruskal-Wallis test is used to compare the means amongst
more than two
samples, when either the data are ordinal or the distribution is
not normal. When
there are only two groups, then it is the equivalent of the Mann-
Whitney U-test.
This test is typically used to determine the significance of
difference among three or
more groups.
Correlations

38. These tests are used to justify the nature of the relationship
between two
variables, and this relation statistically, is referred to as a linear
trend. This
relationship between variables usually presented on scatter
plots. A correlation
does not explain causation and it does not mean that one
variable is the cause of
the other.
This and other possibilities are listed below:
Variable 1 Action Variable 2 Action Type of Correlation
Math Score ↑ Science Score ↑ Positive; as Math Score
improves,
Science Score improves
Math Score ↓ Science Score ↓ Positive; as Math Score declines,
Science Score declines
Math Score ↑ Science Score ↓ Negative; as Math Score
improves,
Science Score declines

39. Math Score ↓ Science Score ↑ Negative; as Math Score declines,
Science Score improves
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The following graphs show the same relationships:
Perfect Positive Correlation
Pearson's correlation
It is used to test the correlation between at least two continuous
variables. The
value for Pearson's correlation lies between 0.00 (no
correlation) and 1.00 (perfect
correlation).
Spearman rank correlation test

40. The Spearman rank correlation test is used to demonstrate the
association
between two ranked variables (X and Y), which are not
normally distributed. It is
frequently used to compare the scores of a group of subjects on
two measures (i.e.
a coefficient correlation based on ranks).
Chi-square test
There are two different types of chi-square tests - but both
involve categorical data.
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.
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41. Practices and Methods
Page 18 EDU730: Research Practices and Methods
Regression
It is an extension of correlation and is used to define whether
one variable is a
predictor of another variable. Regression is used to determine
how strong the
relationship is between your intervention and your outcome
variables
Table for common statistical tests
Type of test Use Parametric/ Non-parametric
Correlation These test justifies the nature of the relationship
between two
variables
Pearson's correlation Tests for the strength of the association
between two continuous variables
Parametric

42. Spearman rank
correlation test
Tests for the strength of the association
between two ordinal, ranked variables (X
and Y).
Non-parametric
Chi-square test Tests for the strength of the association
between two categorical variables
Non-parametric
Comparison of
Means:
Look for the difference between the means of variables
Paired T-test Tests for difference between two related
variables
Parametric
Independent T-test Tests for difference between two
independent variables
Parametric

43. ANOVA Test if the difference in means (averages)
for two groups is statistically significant. It
is used to describe/compare the
association between a number of groups.
Parametric
Regression
Assess if change in one variable predicts change in another
variable
Simple regression Tests how change in the predictor variable
Parametric
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predicts the level of change in the
outcome variable
Multiple regression Tests how change in the combination of

44. two or more predictor variables predict
the level of change in the outcome
variable
Parametric
Non-parametric
Mann-Whitney U-test Test for differences between two
independent groups on a continuous
measure
Non-parametric
Wilcoxon rank-sum
test
Tests for difference between two
independent variables - takes into account
magnitude and direction of difference
Non-parametric
Wilcoxon signed-rank
test
tests for difference between two-sampled

45. repeated measures - takes into account
magnitude and direction of difference
Non-parametric
Kruskal-Wallis test Tests the means among more than two
samples,
if two related variables are different –
ignores magnitude of change, only takes
into account direction.
Non-parametric
5. Power of the study
There is increasing criticism about the lack of statistical power
of published
research in sports and exercise science and psychology.
Statistical power is defined
as the probability of rejecting the null hypothesis; that is, the
probability that the
study will lead to significant results. If the null hypothesis is
false but not rejected, a
type 2 error occurs. Cohen suggested that a power of 0.80 is
satisfactory when an

46. alpha is set at 0.05—that is, the risk of type 1 error (i.e.
rejection of the null
hypothesis when it is true) is 0.05. This means that the risk of a
type 2 error is 0.20.
The magnitude of the relation or treatment effect (known as the
effect size) is a
factor that must receive a lot of attention when considering the
statistical power of
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a study. When calculated in advance, this can be used as an
indicator of the degree
to which the researcher believes the null hypothesis to be false.
Each statistical test
has an effect size index that ranges from zero upwards and is
scale free. For
instance, the effect size index for a correlation test is r; where
no conversion is
required. For assessing the difference between two sample
means, Cohen's d ,

47. Hedges g, or Glass's Δ can be used. These divide the difference
between two means
by a standard deviation. Formulae are available for converting
other statistical test
results (e.g. t test, one way analysis of variance, and χ2
results—into effect size
indexes (see Rosenthal, 1991).
Effect sizes are typically described as small, medium, and large.
Effect sizes of
correlations that equal to 0.1, 0.3, and 0.5 and effect sizes of
Cohen's that equal
0.2, 0.5, and 0.8 equate to small, medium, and large effect sizes
respectively. It is
important to note that the power of a study is linked to the
sample size i.e. the
smaller the expected effect size, the larger the sample size
required to have
sufficient power to detect that effect size.
For example, a study that assesses the effects of habitual
physical activity on body
fat in children might have a medium effect size (e.g. see
Rowlands et al., 1999). In

48. this study, there was a moderate correlation between habitual
physical activity and
body fat, with a medium effect size. A large effect size may be
anticipated in a study
that assesses the effects of a very low energy diet on body fat in
overweight women
(e.g. see Eston et al, 1995). In Eston et al’s study, a significant
reduction in total
body intake resulted in a substantial decrease in total body mass
and the
percentage of body fat.
The effect size should be estimated during the design stage of a
study, as this will
allow the researcher to determine the size required to give
adequate power for a
given alpha (i.e. p value). Therefore, the study can be designed
to ensure that there
is sufficient power to detect the effect of interest, that is
minimising the possibility
of a type 2 error.
Table 3.

49. Small, medium and large effect sizes as defined by Cohen
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When empirical data are available, they can be used to assess
the effect size for a
study. However, for some research questions it is difficult to
find enough
information (e.g. there is limited empirical information on the
topic or insufficient
detail provided in the results of the relevant studies) to estimate
the expected
effect size. In order to compare effect sizes of studies that differ
in sample size, it is
recommended that, in addition to reporting the test statistic and
p value, the
appropriate effect size index is also reported.
6. Data presentation

50. A set of data on its own is very hard to interpret. There is a lot
of information
contained in the data, but it is hard to see. Eye-balling your data
using graphs and
exploratory data analysis is necessary for understanding
important features of the
data, detecting outliers, and data which has been recorded
incorrectly. Outliers are
extreme observations which are inconsistent with the rest of the
data. The
presence of outliers can significantly distort some of the more
formal statistical
techniques, and hence there is a high need for preliminary
detection and correction
or accommodation of such observations, before further analysis
takes place.
Usually, a straight line fits the data well. However, the outlier
“pulls” the line in the
direction of the outlier, as demonstrated in the lower graph in
Figure 2. When the
line is dragged towards the outlier, the rest of the points then
fall farther from the
line that they would otherwise fall on or close to. In this case

51. the “fit” is reduced;
thus, the correlation is weaker. Outliers typically occur from an
error including a
mismarked answer paper, a mistake in entering a score in a
database, a subject who
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misunderstood the directions etc. The researcher should always
seek to understand
the cause of an outlying score. If the cause is not legitimate, the
researcher should
eliminate the outlying score from the analysis to avoid distorts
in the analysis.
Figure 1. A demonstration of how outliers can identified using
graphs

52. EDU730: Research
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Figure 2. The two graphs above demonstrate Data where no
outliers are observed
(top graph) and Data where an Outlier is observed (bottom
graph).
6.1. Charts for quantitative data
There are different types of charts that can be used to present
quantitative data.
Dot plots are one of the simplest ways of displaying all the
data. Each dot
represents an individual and is plotted along a vertical axis.
Data for several groups
can be plotted alongside each other for comparison (Freeman&
Julious, 2005).

53. Scatter plots: it is a type of diagram that typically presents the
values of tow
variables. The data are displayed as a collection of points. Each
point position
depends of the horizontal and vertical axis.
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7. Quantitative Software for Data Analysis
Quantitative studies often result in large numerical data sets
that would be difficult
to analyse without the help of computer software packages.
Programs such as
EXCEL are available to most researchers and are relatively
straight-forward. These
programs can be very useful for descriptive statistics and less
complicated analyses.
However, sometimes the data require more sophisticated
software. There are a

54. number of excellent statistical software packages including:
SPSS – The Statistical Package for Social Science (SPSS) is one
of the most popular
software in social science research. SPSS is comprehensive and
compatible with
almost any type of data and can be used to run both descriptive
statistics and other
more complicated analyses, as well as to generate reports,
graphs, plots and trend
lines based on data analyses.
STATA – This is an interactive program that can be used for
both simple and
complex analyses. It can also generate charts, graphs and plots
of data and results.
This program seems a bit more complicated than other programs
as it uses four
different windows including the command window, the review
window, the result
window and the variable window.
SAS – The Statistical Analysis System (SAS) is another very
good statistical software

55. package that can be useful with very large data sets. It has
additional capabilities
that make it very popular in the business world because it can
address issues such
as business forecasting, quality improvement, planning, and so
forth. However,
some knowledge of programming language is necessary to use
the software,
making it a less appealing option for some researchers.
R programming – R is an open source programming language
and software
environment for statistical computing and graphics that is
supported by the R
Foundation for Statistical Computing. The R language is
commonly used
among statisticians and data miners for developing statistical
software and data
analysis.
(Blaikie, 2003)
https://en.wikipedia.org/wiki/Open_source
https://en.wikipedia.org/wiki/Programming_language
https://en.wikipedia.org/wiki/Statistical_computing

56. https://en.wikipedia.org/wiki/Statistician
https://en.wikipedia.org/wiki/Data_mining
https://en.wikipedia.org/wiki/Statistical_software
https://en.wikipedia.org/wiki/Data_analysis
https://en.wikipedia.org/wiki/Data_analysis
EDU730: Research
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8. Statistical Symbols:
α: significance level (type I error).
b or b0: y intercept.
b1: slope of a line (used in regression).
β: probability of a Type II error.
1-β: statistical power.
BD or BPD: binomial distribution.
CI: confidence interval.
CLT: Central Limit Theorem.
d: difference between paired data.

57. df: degrees of freedom.
DPD: discrete probability distribution.
E = margin of error.
f = frequency (i.e. how often
something happens).
f/n = relative frequency.
HT = hypothesis test.
Ho = null hypothesis.
H1 or Ha: alternative hypothesis.
IQR = interquartile range.
m = slope of a line.
M: median.
n: sample size or number of trials in
a binomial experiment.
σ : standard error of the proportion.
p: p-value, or probability of success in
a binomial experiment, or population
proportion.

58. ρ: correlation coefficient for a
population.
: sample proportion.
P(A): probability of event A.
P(AC) or P(not A): the probability that A
doesn’t ha en.
P(B|A): the probability that event B
occurs, given that event A occurs.
Pk: kth percentile. For example, P90 =
90th percentile.q: probability of failure in
a binomial or geometric distribution.
Q1: first quartile.
Q3: third quartile.
r: correlation coefficient of a sample.
R²: coefficient of determination.
s: standard deviation of a sample.
s.d or SD: standard deviation.
SEM: standard error of the mean.

59. SEP: standard error of the proportion.
http://www.statisticshowto.com/what-is-an-alpha-level/
http://www.statisticshowto.com/type-i-and-type-ii-errors-
definition-examples/
http://cs.selu.edu/~rbyrd/math/intercept/
http://www.statisticshowto.com/regression/
http://www.statisticshowto.com/type-i-and-type-ii-errors-
definition-examples/
http://www.statisticshowto.com/statistical-power/
http://www.statisticshowto.com/binomial-distribution-article-
index/
http://www.statisticshowto.com/how-to-find-a-confidence-
interval/
http://www.statisticshowto.com/central-limit-theorem-examples/
http://www.statisticshowto.com/degrees-of-freedom/
http://www.statisticshowto.com/discrete-probability-
distribution/
http://www.statisticshowto.com/how-to-calculate-margin-of-
error/#WhatMofE
http://www.statisticshowto.com/probability-and-
statistics/hypothesis-testing/
http://www.statisticshowto.com/what-is-the-null-hypothesis/
http://www.statisticshowto.com/what-is-an-alternate-hypothesis/
http://www.statisticshowto.com/probability-and-
statistics/interquartile-range/
http://www.statisticshowto.com/median
http://www.statisticshowto.com/find-sample-size-statistics/
http://www.statisticshowto.com/how-to-determine-if-something-
is-a-binomial-experiment/
http://www.statisticshowto.com/p-value/
http://www.statisticshowto.com/how-to-determine-if-something-
is-a-binomial-experiment/
http://www.statisticshowto.com/population-proportion/
http://www.statisticshowto.com/population-proportion/

60. http://www.statisticshowto.com/how-to-compute-pearsons-
correlation-coefficients/
http://www.statisticshowto.com/probability-and-
statistics/probability-main-index/
http://www.statisticshowto.com/percentiles/
http://www.statisticshowto.com/geometric-distribution/
http://www.statisticshowto.com/what-are-quartiles/
http://www.statisticshowto.com/what-are-quartiles/
http://www.statisticshowto.com/how-to-compute-pearsons-
correlation-coefficients/
http://www.statisticshowto.com/what-is-a-coefficient-of-
determination/
http://www.statisticshowto.com/what-is-standard-deviation/
http://www.statisticshowto.com/sample/
http://www.statisticshowto.com/what-is-standard-deviation/
http://www.statisticshowto.com/calculate-standard-error-
sample-mean/
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N: population size.
ND: normal distribution.
σ: standard deviation.
σ : standard error of the mean.
t: t-score.

61. μ mean.
ν: degrees of freedom.
X: a variable.
χ
2
: chi-square.
x: one data value.
: mean of a sample.
z: z-score.
Accessed: http://www.statisticshowto.com/statistics-symbols/
9. Task – Forum
“Research studies suggest that teachers’ attitudes towards the
inclusion
of students with disabilities are influenced by a number of
interrelated
factors. For example, some earlier studies indicate that the
nature of
disability and the associated educational problems presented

62. influence
teachers’ attitudes. These are termed as ‘child-related’
variables. Other
studies suggest demographic and other personality factors which
can be
classified as ‘teacher-related’ factors. Finally, the specific
context is
found to be another influencing factor and can be termed as
‘educational environment-related’ (Avramidis & Norwich,
2002).
Based on this research problem, please provide a research
question that
can address two or more variables. Bear in mind that the
research
question needs to use quantitative terms, defining the variables
you will
use.
Finally, discuss which statistical test you would use to answer
your
research question and explain the rationale behind your choice.
http://www.statisticshowto.com/what-is-a-population/

63. http://www.statisticshowto.com/probability-and-
statistics/normal-distributions/
http://www.statisticshowto.com/what-is-standard-deviation/
http://www.statisticshowto.com/calculate-standard-error-
sample-mean/
http://www.statisticshowto.com/t-score/
http://www.statisticshowto.com/mean
http://www.statisticshowto.com/degrees-of-freedom/
http://www.statisticshowto.com/variable/
http://www.statisticshowto.com/chi-square/
http://www.statisticshowto.com/mean/
http://www.statisticshowto.com/sample/
http://www.statisticshowto.com/z-score-definition/
http://www.statisticshowto.com/statistics-symbols/
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Further Reading and Study
Book
Muijs, D. (2010). Doing quantitative research in education with
SPSS. Sage.
References:

64. Avramidis, E., & Norwich, B. (2002). Teachers' attitudes
towards
integration/inclusion: a review of the literature. European
Journal of Special
Needs Education, 17(2), 129-147.
Blaikie, N. (2003). Analyzing quantitative data: From
description to
explanation. Sage.
Burns N, Grove SK (2005). The Practice of Nursing Research:
Conduct, Critique,
and Utilization (5th Ed.). St. Louis, Elsevier Saunders
Eston, RG, Fu F. Fung L (1995). Validity of conventional
anthropometric
techniques for estimating body composition in Chinese adults.
Br J Sports Med,
29, 52–6.
Freeman, J. V., & Julious, S. A. (2005). The visual display of
quantitative
information. Scope, 14(2), 11-15.

65. EDU730: Research
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Page 28 EDU730: Research Practices and Methods
Frost J. (2015). Choosing Between a Nonparametric Test and a
Parametric Test.
Retrieved from http://blog.minitab.com/blog/adventures-in-
statistics-
2/choosing-between-a-nonparametric-test-and-a-parametric-test
angley , Perrie Y (2014). Maths Skills for Pharmacy:
Unlocking
Pharmaceutical Calculations. Oxford University Press.
Muijs, D. (2010). Doing quantitative research in education with
SPSS. Sage.
Patel, P. (2009, October). Introduction to Quantitative Methods.
In Empirical
Law Seminar.

66. Rosenthal R. (1991.). Meta-analytic procedures for social
research (revised
edition). Newbury Park, CA: Sage,
Rowlands A.V, Eston R.G, Ingledew D.K. (1999). The
relationship between
activity levels, body fat and aerobic fitness in 8–10 year old
children. J Appl
Physiol, 86, 1428–35.
EDU730: Research
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Week 9:
Quantitative Data Analysis
Topic goals

67. research.
analysis
Task – Forum
provide a research
question that can address two or more variables, using
quantitative terms, defining the variables you will use.
Discuss which statistical test you would use to answer
your research question and explain the rationale behind
your choice.
EDU730: Research

68. Practices and Methods
Page 2 EDU730: Research Practices and Methods
QUANTITATIVE DATA ANALYSIS
1. Introduction
The main purpose to analyze data is to gain useful and valuable
information. Data
analysis is useful to describe data, compare and find
relationships or differences
between variables, etc. The researcher uses techniques to
convert the data to
numerical forms.
1.1. Prepare your data
As a researcher you have to be sure that your data are correct
e.g. respondents
answered all of the questions, check your transcriptions, etc.
You have to identify
your missing data and then you have to convert them into a
numerical form e.g.
red=1, yellow=2, green=3, etc.

69. 1.2. Scales of measurements
Before analyzing quantitative data, researchers must identify
the level of
measurement associated with the quantitative data. The type of
data that you have
to use on a set of data depends on the scale of measurement of
your data. The
scales of measurements are nominal, ordinal, interval and ratio.
Nominal data
Data has no logical order and can be classified into non-
numerical or named
categories. It is basic classification data. The values we give are
just to replace the
name and they cannot be order. Ex. Male, female, district A,
district b
Example: Male or Female
There is no order associated with male or female

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Ordinal data
Data has a logical order, but the differences between values are
not constant.
These data are usually used for questions that are referred to
ratings of quality or
agreements like good, fair, bad, or strongly agree, agree,
disagree, strongly
disagree.
Example: 1st , 2nd, 3rd
Example: T-shirt size (small, medium, large)
Interval data:
Data is continuous and has a logical order, data has
standardized differences
between values, but no natural zero .

71. Example: Fahrenheit degrees
* Remember that ratios are meaningless for interval data. You
cannot say, for
example, that one day is twice as hot as another day.
Ratio data
Data is continuous, ordered, has standardized differences
between values, and a
natural zero
Example: height, weight, age, length
Having an absolute zero allows you to meaningful argue that
one measure is twice
as long as another.
For example – 10 km is twice as long as 5 km
Remember that there are several ways of approaching a research
question and how
the researcher puts together a research question will determine
the type of
methodology, data collection method, statistics, analysis and
presentation that will
be used to approach the research problem.

72. For each type of data you have to use different analysis
techniques. When using a
quantitative methodology, you are normally testing a theory
through the testing of
a hypothesis.
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1.3. Hypothesis/Null hypothesis:
A hypothesis is a logical assumption, a reasonable guess, or a
suggested answer to
a research problem.
A null hypothesis states that minor differences between the
variables can occur
because of chance errors, and are therefore not significant.

73. *Chance error is defined as the difference between the predicted
value of a
variable (by the statistical model in question) and the actual
value of the variable.
In statistical hypothesis testing, a type I error is the incorrect
rejection of a true null
hypothesis (a "false positive"), while a type II error is
incorrectly retaining a false
null hypothesis (a "false negative"). Simply, a type I error is
detecting an effect (e.g.
a relationship between two variables) that is not present, while a
type II error is
failing to detect an effect that is present.
1.4. Randomised, controlled and double-blind trial
Randomised - chosen by random.
Controlled - there is a control group as well as an experimental
group.
Double-blind - neither the subjects nor the researchers know
who is in which
group.

74. Variables:
An experiment has three characteristics:
1. A manipulated independent variable (often denoted by x,
whose variation does
not depend on that of another).
2. Control of other variables i.e. dependent variables (a variable
often denoted
by y, whose value depends on that of another.
3. The observed effect of the independent variable on the
dependent variables.
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1.5. Validity, reliability and generalizability
Validity: refers to whether the researcher measures what he/she
wants to

75. measure. The three types of validity are:
Content validity – refers to whether or not the content of the
variables is right to
measure the concept.
Criterion validity – refers to the collection of information on
these other measures
that can determine this.
Construct validity - refers to the design of your instrument so
that it contains
several factors, rather than just one.
(Muijs, 2010)
Reliability: “refers to the extent to which test scores are free of
measurement
error” (Muijs, 2010, pg.82). The two types of reliability are:
Repeated measures or test-retest reliability - refers to the
instrument that you use
if it can be trusted to give similar result if used later on time
with the same
respondents.
Internal consistency - refers to whether all the items are
measuring the same

76. construct.
Generalizability: it is about the generalization of your findings
from your sample to
the population.
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2. Descriptive statistics
Descriptive statistics are summarizing data. These are used to
describe variables
and the basic features of the data that have been collected in a
study. They provide
simple summaries about the sample and measures of central
tendency (e.g. mean,
median, standard deviation etc.). Together with simple graphics

77. analysis, they form
the basis of virtually every quantitative analysis of data.
It should be noted that with descriptive statistics no conclusions
can be extended
beyond the immediate group from which the data was gathered.
Some popular summary statistics for interval variables
Mean: is the arithmetic average of the values, calculated by
adding all the values
and divided by the total number of values.
Median: the data point that is in the middle of "low" and "high"
values , after put in
numerical order
Mode: The most common occurring score in a data set
Range: It is the difference between the highest score and the
lowest score.
Standard deviation: “The standard deviation exists for all
interval variables. It is the

78. average distance of each value away from the sample mean. The
larger the
standard deviation, the farther away the values are from the
mean; the smaller the
standard deviation the closer, the values are to the mean” (Patel,
2009, pg.5).
Minimum and Maximum value: the smallest and largest score in
data set
Frequency: The number of times a certain value appears
Quartiles: same thing as median for 1/4 intervals
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(Adapted from Patel, 2009, pg. 6)

79. 3. Data distribution
Before beginning the statistical tests, it is necessary to check
the distribution of
your data. The main types of distribution are normal and non-
normal.
Example
Case no Grades
1 90
2 67
3 85
4 90
5 100
6 58
7 90

80. Total 490
Mean: 70
Median: 90
Mode: 90
Minimum value: 100
Maximum value: 58
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3.1. The Normal distribution
When the data tends to be around a central value with no bias
left or right, it gets
close to a "Normal Distribution":

81. The graph of the normal distribution depends on two factors i.e.
the mean (M) and
the standard deviation (SD). The basics characteristics of a
normal curve are: a) a
bell shape curve, b) It is perfectly symmetrical, c) Mode,
median, and mean lie in
the middle of the curve (50% of the values lie to the left of the
mean, and 50% lie to
the right) d) Approximately 95% of the values are found two
standard deviations
away from the mean (in both directions) (Patel, 2009). The
location of the center of
the graph is determined by the mean of the distribution, and the
height and width
of the graph is determined by the standard deviation. When the
standard deviation
is large, the curve is short and wide; when the standard
deviation is small, the curve
is tall and narrow. Normal distribution graphs look like a
symmetric, bell-shaped
curve, as shown above. When measuring things like people's
height, weight, salary,
opinions or votes, the graph of the results is very often a normal
curve.(Langley

82. Perrie, 2014)
https://www.google.com.cy/search?espv=2&biw=1600&bih=794
&tbm=bks&q=inauthor:%22Chris+Langley%22&sa=X&ved=0ah
UKEwi4vvv62P3RAhUhIMAKHcwwDHQQ9AgIKzAD
https://www.google.com.cy/search?espv=2&biw=1600&bih=794
&tbm=bks&q=inauthor:%22Yvonne+Perrie%22&sa=X&ved=0a
hUKEwi4vvv62P3RAhUhIMAKHcwwDHQQ9AgILDAD
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3.2. Non-Normal Distributions:
There are several ways in which a distribution can be non-
normal.

83. 4. Statistical Analysis
Statistical tests are used to make inferences about data, and can
tell us if our
observation is real. There is a wide range of statistical tests and
the decision of
which of them you are going to test it depends on your research
design. If your data
is normally distributed you have to choose a parametric test
otherwise you have to
choose non-parametric tests.
4.1. Parametric and Nonparametric Tests
A parametric statistical test makes assumptions about the
parameters (defining
properties) of the population distribution(s) from which one's
data are drawn,
whereas a non-parametric test makes no such assumptions.
Nonparametric tests
are also called distribution-free tests because they do not
assume that your data
follow a specific distribution (Frost, 2015).

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Parametric tests (means) Nonparametric tests (medians)
1-sample t test 1-sample Sign, 1-sample Wilcoxon
2-sample t test Mann-Whitney test
One-Way ANOVA Kruskal-Wallis, Mood’s median test
Factorial DOE with one factor and one
blocking variable
Friedman test
It is argued that nonparametric tests should be used when the
data do not meet
the assumptions of the parametric test, particularly the
assumption about normally
distributed data. However, there are additional considerations
when deciding
whether a parametric or nonparametric test should be used.

85. 4.2. Reasons to Use Parametric Tests
Reason 1: Parametric tests can perform well with skewed and
non-normal
distributions
Parametric tests can perform well with continuous data that are
not normally
distributed if the sample size guidelines demonstrated in the
table below are
satisfied.
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Parametric analyses Sample size guidelines for non-normal data
1-sample t test Greater than 20

86. 2-sample t test Each group should be greater than 15
One- ou have 2-9 groups, each group should
be
greater than 15.
-12 groups, each group should be
greater than 20.
Note: These guidelines are based on simulation studies
conducted by statisticians at
Minitab.
Reason 2: Parametric tests can perform well when the spread of
each group
is different
While nonparametric tests do not assume that your data are
normally distributed,
they do have other assumptions that can be hard to satisfy. For
example, when
using nonparametric tests that compare groups, a common
assumption is that the
data for all groups have the same spread (dispersion). If the
groups have a different

87. spread, then the results from nonparametric tests might be
invalid.
Reason 3: Statistical power
Parametric tests usually have more statistical power compared
to nonparametric
tests. Hence, they are more likely to detect a significant effect
when one truly
exists.
http://support.minitab.com/en-us/minitab/17/topic-library/basic-
statistics-and-graphs/power-and-sample-size/what-is-power/
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4.3. Reasons to Use Nonparametric Tests

88. Reason 1: Your area of study is better represented by the
median
The fact that a parametric test can be performed with no normal
data does not
imply that the mean is the best measure of the central tendency
for your data. For
example, the center of a skewed distribution (e.g. income), can
be better measured
by the median where 50% are above the median and 50% are
below. However, if
you add a few billionaires to a sample, the mathematical mean
increases greatly,
although the income for the typical person does not change.
When the distribution is skewed enough, the mean is strongly
influenced by
changes far out in the distribution’s tail, whereas the median
continues to more
closely represent the center of the distribution.
Reason 2: You have a very small sample size

89. If the data are not normally distributable and do not meet the
sample size
guidelines for the parametric tests, then a nonparametric test
should be used. In
addition, when you have a very small sample, it might be
difficult to ascertain the
distribution of your data as the distribution tests will lack
sufficient power to
provide meaningful results.
http://support.minitab.com/en-us/minitab/17/topic-library/basic-
statistics-and-graphs/summary-statistics/measures-of-central-
tendency/
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Reason 3: You have ordinal data, ranked data, or outliers that
you cannot
remove

90. Typical parametric tests can only assess continuous data and the
results can be
seriously affected by outliers. Conversely, some nonparametric
tests can handle
ordinal data, ranked data, without being significantly affected
by outliers.
4.4. Statistical tests
One-tailed test: A test of a statistical hypothesis, where the
region of rejection is on
only one side of the sampling distribution is called a one-tailed
test. For example,
suppose the null hypothesis states that the mean is less than or
equal to 10. The
alternative hypothesis would be that the mean is greater than 10.
Two-tailed test: When using a two-tailed test, regardless of the
direction of the
relationship you hypothesize, you are testing for the possibility
of the relationship
in both directions. For example, we may wish to compare the
mean of a sample to a
given value x using a t-test. Our null hypothesis is that the
mean is equal to x.

91. Alpha level (p value): In statistical analysis the researcher
examines whether there
is any significance in the results. This is equal to the probability
of obtaining the
observed difference, or one more extreme, if the null hypothesis
is true.
The acceptance or rejection of a hypothesis is based upon a
level of significance –
the alpha (a) level
This is typically set at the 5% (0.05) a level, followed in
popularity by the 1% (0.01) a
level
These are usually designated 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?
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92. Page 14 EDU730: Research Practices and Methods
The p value is concerned with confidence levels. This states the
threshold at which
you are prepared to accept the possibility of a Type I Error –
otherwise known as a
false positive – rejecting a null hypothesis that is actually true.
The question that significance levels answer is 'How confident
can the researcher
be that the results have not arisen by chance?'
Note: The confidence levels are expressed as a percentage.
So if we had a result of:
p =1.00, then there would be a 100% possibility that the results
occurred by chance.
p = 0.50, then there would be a 50% possibility that the results
occurred by chance.
p = 0.05, then we are 95% certain that the results did not arise
by chance
p = 0.01, then we are 99% certain that the results did not arise
by chance.
Clearly, we want our results to be as accurate as possible, so we

93. set our significance
levels as low as possible - usually at 5% (p = 0.05), or better
still, at 1% (p = 0.01)
Anything above these figures, are considered as not accurate
enough. In other
words, the results are not significant.
Now, you may be thinking that if an effect could not have arisen
by chance 90 times
out of 100 (p = 0.1), then that is pretty significant.
However, what we are determining with our levels of
significance, is 'statistical
significance', hence we are much more strict with that, so we
would usually not
accept values greater than p = 0.05.
So when looking at the statistics in a research paper, it is
important to check the 'p'
values to find out whether the results are statistically significant
or not.
(Burns & Grove, 2005)

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p-value Outcome of test Statement
greater than 0.05 Fail to reject H0 No evidence to reject H0
between 0.01 and 0.05 Reject H0 (Accept H1) Some evidence to
reject H0
(therefore accept H1)
between 0.001 and 0.01 Reject H0 (Accept H1) Strong evidence
to reject H0
(therefore accept H1)
less than 0.001 Reject H0 (Accept H1) Very strong evidence to
reject
H0 (therefore accept H1)
ANOVA (Analysis of Variance)

95. 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
association between a number of groups. ANOVA is used to
determine whether the
difference in means (averages) for two groups is statistically
significant.
T-test
The t-test is used to assess whether the means of two groups
differ statistically
from each other.
Mann-Whitney U-test
The Mann-Whitney U-test test is used to test for differences
between two
independent groups on a continuous measure, e.g. do males and
females differ in
terms of their levels of anxiety.
This test requires two variables (e.g. male/female gender) and
one continuous

96. variable (e.g. anxiety level). Basically, the Mann-Whitney U-
test converts the scores
on the continuous variable to ranks, across the two groups and
calculates and
compares the medians of the two groups. It then evaluates
whether the medians
for the two groups differ significantly.
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Wilcoxon signed-rank test
The Wilcoxon signed-rank test (also known as Wilcoxon
matched-pairs test) is the
most common nonparametric test for the two-sampled repeated
measures design
of research study.

97. Kruskal-Wallis test
The Kruskal-Wallis test is used to compare the means amongst
more than two
samples, when either the data are ordinal or the distribution is
not normal. When
there are only two groups, then it is the equivalent of the Mann-
Whitney U-test.
This test is typically used to determine the significance of
difference among three or
more groups.
Correlations
These tests are used to justify the nature of the relationship
between two
variables, and this relation statistically, is referred to as a linear
trend. This
relationship between variables usually presented on scatter
plots. A correlation
does not explain causation and it does not mean that one
variable is the cause of
the other.

98. This and other possibilities are listed below:
Variable 1 Action Variable 2 Action Type of Correlation
Math Score ↑ Science Score ↑ Positive; as Math Score
improves,
Science Score improves
Math Score ↓ Science Score ↓ Positive; as Math Score declines,
Science Score declines
Math Score ↑ Science Score ↓ Negative; as Math Score
improves,
Science Score declines
Math Score ↓ Science Score ↑ Negative; as Math Score declines,
Science Score improves
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99. The following graphs show the same relationships:
Perfect Positive Correlation
Pearson's correlation
It is used to test the correlation between at least two continuous
variables. The
value for Pearson's correlation lies between 0.00 (no
correlation) and 1.00 (perfect
correlation).
Spearman rank correlation test
The Spearman rank correlation test is used to demonstrate the
association
between two ranked variables (X and Y), which are not
normally distributed. It is
frequently used to compare the scores of a group of subjects on
two measures (i.e.
a coefficient correlation based on ranks).
Chi-square test

100. There are two different types of chi-square tests - but both
involve categorical data.
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.
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Regression
It is an extension of correlation and is used to define whether
one variable is a
predictor of another variable. Regression is used to determine
how strong the

101. relationship is between your intervention and your outcome
variables
Table for common statistical tests
Type of test Use Parametric/ Non-parametric
Correlation These test justifies the nature of the relationship
between two
variables
Pearson's correlation Tests for the strength of the association
between two continuous variables
Parametric
Spearman rank
correlation test
Tests for the strength of the association
between two ordinal, ranked variables (X
and Y).
Non-parametric
Chi-square test Tests for the strength of the association
between two categorical variables

102. Non-parametric
Comparison of
Means:
Look for the difference between the means of variables
Paired T-test Tests for difference between two related
variables
Parametric
Independent T-test Tests for difference between two
independent variables
Parametric
ANOVA Test if the difference in means (averages)
for two groups is statistically significant. It
is used to describe/compare the
association between a number of groups.
Parametric
Regression
Assess if change in one variable predicts change in another

103. variable
Simple regression Tests how change in the predictor variable
Parametric
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predicts the level of change in the
outcome variable
Multiple regression Tests how change in the combination of
two or more predictor variables predict
the level of change in the outcome
variable
Parametric
Non-parametric
Mann-Whitney U-test Test for differences between two
independent groups on a continuous
measure

104. Non-parametric
Wilcoxon rank-sum
test
Tests for difference between two
independent variables - takes into account
magnitude and direction of difference
Non-parametric
Wilcoxon signed-rank
test
tests for difference between two-sampled
repeated measures - takes into account
magnitude and direction of difference
Non-parametric
Kruskal-Wallis test Tests the means among more than two
samples,
if two related variables are different –
ignores magnitude of change, only takes
into account direction.

105. Non-parametric
5. Power of the study
There is increasing criticism about the lack of statistical power
of published
research in sports and exercise science and psychology.
Statistical power is defined
as the probability of rejecting the null hypothesis; that is, the
probability that the
study will lead to significant results. If the null hypothesis is
false but not rejected, a
type 2 error occurs. Cohen suggested that a power of 0.80 is
satisfactory when an
alpha is set at 0.05—that is, the risk of type 1 error (i.e.
rejection of the null
hypothesis when it is true) is 0.05. This means that the risk of a
type 2 error is 0.20.
The magnitude of the relation or treatment effect (known as the
effect size) is a
factor that must receive a lot of attention when considering the
statistical power of
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106. Practices and Methods
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a study. When calculated in advance, this can be used as an
indicator of the degree
to which the researcher believes the null hypothesis to be false.
Each statistical test
has an effect size index that ranges from zero upwards and is
scale free. For
instance, the effect size index for a correlation test is r; where
no conversion is
required. For assessing the difference between two sample
means, Cohen's d ,
Hedges g, or Glass's Δ can be used. These divide the difference
between two means
by a standard deviation. Formulae are available for converting
other statistical test
results (e.g. t test, one way analysis of variance, and χ2
results—into effect size
indexes (see Rosenthal, 1991).
Effect sizes are typically described as small, medium, and large.
Effect sizes of

107. correlations that equal to 0.1, 0.3, and 0.5 and effect sizes of
Cohen's that equal
0.2, 0.5, and 0.8 equate to small, medium, and large effect sizes
respectively. It is
important to note that the power of a study is linked to the
sample size i.e. the
smaller the expected effect size, the larger the sample size
required to have
sufficient power to detect that effect size.
For example, a study that assesses the effects of habitual
physical activity on body
fat in children might have a medium effect size (e.g. see
Rowlands et al., 1999). In
this study, there was a moderate correlation between habitual
physical activity and
body fat, with a medium effect size. A large effect size may be
anticipated in a study
that assesses the effects of a very low energy diet on body fat in
overweight women
(e.g. see Eston et al, 1995). In Eston et al’s study, a significant
reduction in total
body intake resulted in a substantial decrease in total body mass
and the

108. percentage of body fat.
The effect size should be estimated during the design stage of a
study, as this will
allow the researcher to determine the size required to give
adequate power for a
given alpha (i.e. p value). Therefore, the study can be designed
to ensure that there
is sufficient power to detect the effect of interest, that is
minimising the possibility
of a type 2 error.
Table 3.
Small, medium and large effect sizes as defined by Cohen
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When empirical data are available, they can be used to assess
the effect size for a

109. study. However, for some research questions it is difficult to
find enough
information (e.g. there is limited empirical information on the
topic or insufficient
detail provided in the results of the relevant studies) to estimate
the expected
effect size. In order to compare effect sizes of studies that differ
in sample size, it is
recommended that, in addition to reporting the test statistic and
p value, the
appropriate effect size index is also reported.
6. Data presentation
A set of data on its own is very hard to interpret. There is a lot
of information
contained in the data, but it is hard to see. Eye-balling your data
using graphs and
exploratory data analysis is necessary for understanding
important features of the
data, detecting outliers, and data which has been recorded
incorrectly. Outliers are
extreme observations which are inconsistent with the rest of the
data. The

110. presence of outliers can significantly distort some of the more
formal statistical
techniques, and hence there is a high need for preliminary
detection and correction
or accommodation of such observations, before further analysis
takes place.
Usually, a straight line fits the data well. However, the outlier
“pulls” the line in the
direction of the outlier, as demonstrated in the lower graph in
Figure 2. When the
line is dragged towards the outlier, the rest of the points then
fall farther from the
line that they would otherwise fall on or close to. In this case
the “fit” is reduced;
thus, the correlation is weaker. Outliers typically occur from an
error including a
mismarked answer paper, a mistake in entering a score in a
database, a subject who
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111. misunderstood the directions etc. The researcher should always
seek to understand
the cause of an outlying score. If the cause is not legitimate, the
researcher should
eliminate the outlying score from the analysis to avoid distorts
in the analysis.
Figure 1. A demonstration of how outliers can identified using
graphs
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Figure 2. The two graphs above demonstrate Data where no
outliers are observed
(top graph) and Data where an Outlier is observed (bottom
graph).

112. 6.1. Charts for quantitative data
There are different types of charts that can be used to present
quantitative data.
Dot plots are one of the simplest ways of displaying all the
data. Each dot
represents an individual and is plotted along a vertical axis.
Data for several groups
can be plotted alongside each other for comparison (Freeman&
Julious, 2005).
Scatter plots: it is a type of diagram that typically presents the
values of tow
variables. The data are displayed as a collection of points. Each
point position
depends of the horizontal and vertical axis.
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113. 7. Quantitative Software for Data Analysis
Quantitative studies often result in large numerical data sets
that would be difficult
to analyse without the help of computer software packages.
Programs such as
EXCEL are available to most researchers and are relatively
straight-forward. These
programs can be very useful for descriptive statistics and less
complicated analyses.
However, sometimes the data require more sophisticated
software. There are a
number of excellent statistical software packages including:
SPSS – The Statistical Package for Social Science (SPSS) is one
of the most popular
software in social science research. SPSS is comprehensive and
compatible with
almost any type of data and can be used to run both descriptive
statistics and other
more complicated analyses, as well as to generate reports,
graphs, plots and trend
lines based on data analyses.

114. STATA – This is an interactive program that can be used for
both simple and
complex analyses. It can also generate charts, graphs and plots
of data and results.
This program seems a bit more complicated than other programs
as it uses four
different windows including the command window, the review
window, the result
window and the variable window.
SAS – The Statistical Analysis System (SAS) is another very
good statistical software
package that can be useful with very large data sets. It has
additional capabilities
that make it very popular in the business world because it can
address issues such
as business forecasting, quality improvement, planning, and so
forth. However,
some knowledge of programming language is necessary to use
the software,
making it a less appealing option for some researchers.
R programming – R is an open source programming language

115. and software
environment for statistical computing and graphics that is
supported by the R
Foundation for Statistical Computing. The R language is
commonly used
among statisticians and data miners for developing statistical
software and data
analysis.
(Blaikie, 2003)
https://en.wikipedia.org/wiki/Open_source
https://en.wikipedia.org/wiki/Programming_language
https://en.wikipedia.org/wiki/Statistical_computing
https://en.wikipedia.org/wiki/Statistician
https://en.wikipedia.org/wiki/Data_mining
https://en.wikipedia.org/wiki/Statistical_software
https://en.wikipedia.org/wiki/Data_analysis
https://en.wikipedia.org/wiki/Data_analysis
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116. 8. Statistical Symbols:
α: significance level (type I error).
b or b0: y intercept.
b1: slope of a line (used in regression).
β: probability of a Type II error.
1-β: statistical power.
BD or BPD: binomial distribution.
CI: confidence interval.
CLT: Central Limit Theorem.
d: difference between paired data.
df: degrees of freedom.
DPD: discrete probability distribution.
E = margin of error.
f = frequency (i.e. how often
something happens).
f/n = relative frequency.
HT = hypothesis test.
Ho = null hypothesis.

117. H1 or Ha: alternative hypothesis.
IQR = interquartile range.
m = slope of a line.
M: median.
n: sample size or number of trials in
a binomial experiment.
σ : standard error of the proportion.
p: p-value, or probability of success in
a binomial experiment, or population
proportion.
ρ: correlation coefficient for a
population.
: sample proportion.
P(A): probability of event A.
P(AC) or P(not A): the probability that A
doesn’t ha en.
P(B|A): the probability that event B
occurs, given that event A occurs.

118. Pk: kth percentile. For example, P90 =
90th percentile.q: probability of failure in
a binomial or geometric distribution.
Q1: first quartile.
Q3: third quartile.
r: correlation coefficient of a sample.
R²: coefficient of determination.
s: standard deviation of a sample.
s.d or SD: standard deviation.
SEM: standard error of the mean.
SEP: standard error of the proportion.
http://www.statisticshowto.com/what-is-an-alpha-level/
http://www.statisticshowto.com/type-i-and-type-ii-errors-
definition-examples/
http://cs.selu.edu/~rbyrd/math/intercept/
http://www.statisticshowto.com/regression/
http://www.statisticshowto.com/type-i-and-type-ii-errors-
definition-examples/
http://www.statisticshowto.com/statistical-power/
http://www.statisticshowto.com/binomial-distribution-article-
index/
http://www.statisticshowto.com/how-to-find-a-confidence-
interval/
http://www.statisticshowto.com/central-limit-theorem-examples/

119. http://www.statisticshowto.com/degrees-of-freedom/
http://www.statisticshowto.com/discrete-probability-
distribution/
http://www.statisticshowto.com/how-to-calculate-margin-of-
error/#WhatMofE
http://www.statisticshowto.com/probability-and-
statistics/hypothesis-testing/
http://www.statisticshowto.com/what-is-the-null-hypothesis/
http://www.statisticshowto.com/what-is-an-alternate-hypothesis/
http://www.statisticshowto.com/probability-and-
statistics/interquartile-range/
http://www.statisticshowto.com/median
http://www.statisticshowto.com/find-sample-size-statistics/
http://www.statisticshowto.com/how-to-determine-if-something-
is-a-binomial-experiment/
http://www.statisticshowto.com/p-value/
http://www.statisticshowto.com/how-to-determine-if-something-
is-a-binomial-experiment/
http://www.statisticshowto.com/population-proportion/
http://www.statisticshowto.com/population-proportion/
http://www.statisticshowto.com/how-to-compute-pearsons-
correlation-coefficients/
http://www.statisticshowto.com/probability-and-
statistics/probability-main-index/
http://www.statisticshowto.com/percentiles/
http://www.statisticshowto.com/geometric-distribution/
http://www.statisticshowto.com/what-are-quartiles/
http://www.statisticshowto.com/what-are-quartiles/
http://www.statisticshowto.com/how-to-compute-pearsons-
correlation-coefficients/
http://www.statisticshowto.com/what-is-a-coefficient-of-
determination/
http://www.statisticshowto.com/what-is-standard-deviation/
http://www.statisticshowto.com/sample/
http://www.statisticshowto.com/what-is-standard-deviation/
http://www.statisticshowto.com/calculate-standard-error-

120. sample-mean/
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N: population size.
ND: normal distribution.
σ: standard deviation.
σ : standard error of the mean.
t: t-score.
μ mean.
ν: degrees of freedom.
X: a variable.
χ
2
: chi-square.
x: one data value.
: mean of a sample.
z: z-score.

121. Accessed: http://www.statisticshowto.com/statistics-symbols/
9. Task – Forum
“Research studies suggest that teachers’ attitudes towards the
inclusion
of students with disabilities are influenced by a number of
interrelated
factors. For example, some earlier studies indicate that the
nature of
disability and the associated educational problems presented
influence
teachers’ attitudes. These are termed as ‘child-related’
variables. Other
studies suggest demographic and other personality factors which
can be
classified as ‘teacher-related’ factors. Finally, the specific
context is
found to be another influencing factor and can be termed as
‘educational environment-related’ (Avramidis & Norwich,
2002).

122. Based on this research problem, please provide a research
question that
can address two or more variables. Bear in mind that the
research
question needs to use quantitative terms, defining the variables
you will
use.
Finally, discuss which statistical test you would use to answer
your
research question and explain the rationale behind your choice.
http://www.statisticshowto.com/what-is-a-population/
http://www.statisticshowto.com/probability-and-
statistics/normal-distributions/
http://www.statisticshowto.com/what-is-standard-deviation/
http://www.statisticshowto.com/calculate-standard-error-
sample-mean/
http://www.statisticshowto.com/t-score/
http://www.statisticshowto.com/mean
http://www.statisticshowto.com/degrees-of-freedom/
http://www.statisticshowto.com/variable/
http://www.statisticshowto.com/chi-square/
http://www.statisticshowto.com/mean/
http://www.statisticshowto.com/sample/
http://www.statisticshowto.com/z-score-definition/
http://www.statisticshowto.com/statistics-symbols/

123. EDU730: Research
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Page 27 EDU730: Research Practices and Methods
Further Reading and Study
Book
Muijs, D. (2010). Doing quantitative research in education with
SPSS. Sage.
References:
Avramidis, E., & Norwich, B. (2002). Teachers' attitudes
towards
integration/inclusion: a review of the literature. European
Journal of Special
Needs Education, 17(2), 129-147.
Blaikie, N. (2003). Analyzing quantitative data: From
description to
explanation. Sage.

124. Burns N, Grove SK (2005). The Practice of Nursing Research:
Conduct, Critique,
and Utilization (5th Ed.). St. Louis, Elsevier Saunders
Eston, RG, Fu F. Fung L (1995). Validity of conventional
anthropometric
techniques for estimating body composition in Chinese adults.
Br J Sports Med,
29, 52–6.
Freeman, J. V., & Julious, S. A. (2005). The visual display of
quantitative
information. Scope, 14(2), 11-15.
EDU730: Research
Practices and Methods
Page 28 EDU730: Research Practices and Methods
Frost J. (2015). Choosing Between a Nonparametric Test and a
Parametric Test.
Retrieved from http://blog.minitab.com/blog/adventures-in-

125. statistics-
2/choosing-between-a-nonparametric-test-and-a-parametric-test
angley , Perrie Y (2014). Maths Skills for Pharmacy:
Unlocking
Pharmaceutical Calculations. Oxford University Press.
Muijs, D. (2010). Doing quantitative research in education with
SPSS. Sage.
Patel, P. (2009, October). Introduction to Quantitative Methods.
In Empirical
Law Seminar.
Rosenthal R. (1991.). Meta-analytic procedures for social
research (revised
edition). Newbury Park, CA: Sage,
Rowlands A.V, Eston R.G, Ingledew D.K. (1999). The
relationship between
activity levels, body fat and aerobic fitness in 8–10 year old
children. J Appl
Physiol, 86, 1428–35.

126. EDU730: Research
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Week 8:
Qualitative data analysis
Topic goals
qualitative data can be analysed and to select the most
appropriate model for a particular piece of research.
analysis, and gain some experience in coding and
developing categories.
data analysis.

127. Task – Forum
analysis phases as presented in this week’s materials in
order to generate ‘codes’ or ‘themes’.
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QUALITATIVE DATA ANALYSIS
1.1 INTRODUCTION TO QUALITATIVE DATA ANALYSIS:
You are probably familiar with the basic differences between
qualitative and
quantitative research methods based on the previous weeks and
the materials

128. provided and the different applications those methods can have
in order to deal
with the research questions posed.
Qualitative research is particularly good at answering the ‘why’,
‘what’ or ‘how’
questions, such as:
learning
disability, as regards their own health needs?”
“Why do students choose to study for the MSc in Research
Methods through
the online programme?
1.2 What do we mean by analysis?
As being explored in previous weeks, Quantitative research
techniques generate a
mass of numbers that need to be summarised, described and
analysed. The data
are explored by using graphs and charts, and by doing cross
tabulations and
calculating means and standard deviations. Further analysis
would build on these
initial findings, seeking patterns and relationships in the data by

129. performing
multiple regression, or an analysis of variance perhaps (Lacey
and Luff, 2007).
So it is with Qualitative data analysis. .
and
procedures whereby we move from the qualitative data that have
been collected into some form of explanation, understanding or
interpretation of the people and situations we are investigating.
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idea is to
examine the meaningful and symbolic context of qualitative
data
(http://onlineqda.hud.ac.uk/Intro_QDA/what_is_qda.php)
s or
observational data

130. and needs to be described and summarised.
relationships
between various themes that have been identified, or to relate
behaviour
or ideas to biographical characteristics of respondents such as
age or
gender.
data, or
interpretation sought of puzzling findings from previous
studies.
advanced analytical
techniques.
1.3 Approaches in Analysis
a) Deductive approach
- Using your research questions to group the data and then look
for
similarities and differences

131. - Used when time and resources are limited
- Used when qualitative research is a smaller component of a
larger
quantitative study
b) Inductive approach
- Used when qualitative research is a major design of the
inquiry
- Using emergent framework to group the data and then look for
relationships
http://onlineqda.hud.ac.uk/Intro_QDA/what_is_qda.php
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listening etc

132. identification
-coding
ion of relationships between categories
-existing
knowledge
if
appropriate
(e.g. quotes from interviews)
Adapted from Pacey and Luff (2009, p. 6-7)
In summary:
There are no ‘quick fix’ techniques in qualitative analysis
(Lacey and Luff, 2007).

133. qualitative data as
there are qualitative researchers doing it!
subjective
exercise is intimately involved in the process, not aloof from it
(Pope and
Mays 2006).
re some theoretical approaches to choose
from and in this
week we will explore a basic one. In addition there are some
common
processes, no matter which approach you take. Analysis of
qualitative data
usually goes through some or all of the following stages (though
the order
may vary):

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1.2 What do you want to get out of your data?
It is not always necessary to go through all the stages above,
but it is suggested
that some of them are necessary in order to go in-depth in your
analysis!
Let’s take an example based on the research question provided
above about the
health needs of the carers:
Research question:
“What are the perceptions of carers living with people with
learning disability, as
regards their own health needs?”

135. that needs to
be provided in order the perceived needs of the carers to be met.
might also be interested to know what kind of services
are needed or
are valued by most of the carers.
depression and
loneliness
In order to explore this, three broad levels of analysis that could
be pursued are
as follows:
particular word or
concept occurs (e.g. loneliness) in a narrative. Such approach is
called
content analysis. It is not purely qualitative since the quali tative
data can
then be categorised quantitatively and will be subjected to
statistical
analysis
would want to go

136. deeper than this. All units of data (eg sentences or paragraphs)
referring to
loneliness could be given a particular code, extracted and
examined in
more detail. Do participants talk of being lonely even when
others are
present? Are there particular times of day or week when they
experience
loneliness? In what terms do they express loneliness? Are those
who speak
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of loneliness are also those who experience depress? Such
questions can
lead to themes which could eventually be developed such as
‘lonely but
never alone’.
further in

137. depth. For example, you may have developed theories when you
have been
analysing the data with regard to depression as being associated
with
perceived loss of a ‘normal’ child/spouse. The disability may be
attributed
to an accident, or to some failure of medical care, without
which the person
cared for would still be ‘normal’. You may be able to test this
emerging
theory against existing theories of loss in the literature, or
against further
analysis of the data. You may even search for ‘deviant cases’
that is data
which seems to contradict your theory, and seek to modify your
theory to
take account of this new finding. This process is sometimes
known as
‘analytic induction’, and is use to build and test emerging
theory.
(Lacey and Luff, 2009, p.8)
In the following sections we will explore two approaches for
qualitative data
analysis: a) grounded theory approach and b) thematic analysis.

138. 1.4 Grounded Theory
(1967). Glaser
and Strauss were concerned to outline an inductive method of
qualitative
research which would allow social theory to be generated
systematically
from data. As such theories should be ‘grounded’ in rigorous
empirical
research, rather than to be produced based in the abstract.
about and
conceptualising data. It is an approach to research as a whole
and as such
can use a range of different methods.
theory
‘emerges’ from the data through a process of rigorous and
structured
analysis.

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1.5 Procedure and the Rules of Grounded Theory approach
1) Data Collection and Analysis are Interrelated Processes. In
grounded theory,
the analysis begins as soon as the first bit of data is collected.
2) Concepts Are the Basic Units of Analysis. A theorist works
with
conceptualizations of data, not the actual data per se. Theories
can't be built with
actual incidents or activities as observed or reported; that is,
from "raw data." The
incidents, events, and happenings are taken as, or analyzed as,
potential
indicators of phenomena, which are thereby given conceptual
labels. If a
respondent says to the researcher, "Each day I spread my
activities over the
morning, resting between shaving and bathing," then the
researcher might label

140. this phenomenon as "pacing." As the researcher encounters
other incidents, and
when after comparison to the first, they appear to resemble the
same
phenomena, then these, too, can be labeled as "pacing." Only by
comparing
incidents and naming like phenomena with the same term can a
theorist
accumulate the basic units for theory. In the grounded theory
approach such
concepts become more numerous and more abstract as the
analysis continues
3. Categories Must Be Developed and Related. Concepts that
pertain to the
same phenomenon may be grouped to form categories. Not all
concepts become
categories. Categories are higher in level and more abstract than
the concepts
they represent. They are generated through the same analytic
process of making
comparisons to highlight similarities and differences that is
used to produce lower
level concepts. Categories are the "cornerstones" of a
developing theory. They

141. provide the means by which a theory can be integrated.
4. Sampling in Grounded Theory Proceeds on Theoretical
Grounds. Sampling
proceeds not in terms of drawing samples of specific groups of
individuals, units
of time, and so on, but in terms of concepts, their properties,
dimensions, and
variations.
5) Analysis Makes Use of Constant Comparisons. As an incident
is noted, it
should be compared against other incidents for similarities and
differences. The
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resulting concepts are labeled as such, and over time, they are
compared and
grouped as previously described.
6) Patterns and Variations Must Be Accounted For. The data