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# A Really Simple Guide to Quantitative Data Analysis

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## Abstract

This purpose of this guide is to help university students, staff and researchers understand the basic principles of analysing the typical kinds of quantitative data they may collect or encounter in the course of their learning, teaching or research. It focuses upon descriptive statistics and statistical testing in the context of undertaking a research project.
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A Really Simple Guide to Quantitative Data Analysis
Why this guide?
This purpose of this guide is to help university students, staff and researchers understand the basic
principles of analysing the typical kinds of quantitative data they may collect or encounter in the
course of their learning, teaching or research.
What is statistics?
Statistics is an academic subject that involves presenting, interpreting and reasoning about
summary quantities derived from data sets. Common statistical quantities are measures of middle
values, such as average (also known as mean), mode and median, and measures of spread, such
as range and standard deviation.
There are five main sub-areas of this academic subject:
Descriptive statistics (also known as exploratory data analysis) this does not involve
any decision making
Data mining a systematic approach to looking for relationships in large data sets that
were not anticipated in advance. A classic example is Google Flu Trends
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data analytics uses data mining in the context of decision making within an organisation.
Time series analysis a systematic approach to analysing time-related events which
depend on previous events (such as pulse rates or share prices).
Statistical testing (also known as inferential statistics) this involves reasoning about
statistical quantities derived from a sample from a population, where it is assumed that the
events are independent, and making decisions with a certain level of confidence.
Probability theory this provides the theory that underpins the reasoning in statistical
analysis and decision making.
Although statistics is a branch of mathematics, much of its reasoning is very different as it is either
qualitative or it involves probability-based decisions rather than exact mathematical proof.
The quantitative research process
This guide focuses on descriptive statistics and statistical testing as these are the common forms
of quantitative data analysis required at the university and research level. It is assumed that data is
being analysed in the context of a research project involving the following stages:
Define your aim and research questions
Carry out a literature review
For primary data research: establish and conceptual framework and use it to design a data
collection instrument to collect your primary data.
For secondary data research: identify a data source and evaluate its validity and reliability
Carry out an exploratory data analysis using descriptive statistics and an informal
interpretation
(Optional: carry out an inferential analysis)
University and research level data analysis
The experience of statistics at university and in research is often very different from the way
statistics is taught at school. School-level statistics education typically involves summary
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See Lazer, D., Kennedy, R., King, G. and Vespignani, A. (2014) The parable of Google Flu: traps in big
data analysis. Science, 343(6176), pp. 1203-1205, available at: http://dx.doi.org/10.1126/science.1248506.
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information about contrived problems with simple clean data and one right way to carry out an
analysis. University and research-level statistics is often applied. This means the data sets tend to
be large, complex and messy, with some data missing and other data of questionable validity.
Rather than there being one right way to analyse such data sets you need to put forward a plan of
analysis that is credible but you should be willing to modify your plan as you go along, depending
upon what you find, if necessary carrying out an alternative analysis. This requires an additional
skill known as heuristics or metacognition, which means being in control of the process.
What is quantitative data?
Essentially, quantitative data is factual information involving numbers and categories.
Categories often refer to choices between options, such as your favourite type of food or your
opinion in a range from strongly disagree to strongly agree. This leader to three fundamental types
of data:
Numerical data (this could be whole numbers or decimals)
Categories with a natural ordering (such as strongly agree, agree, neutral, disagree,
strongly disagree) this is known as ordinal data
Categories without any agreed ordering (such as protein, dairy, carbohydrate, fruit and
vegetables) this is known as nominal data
The best kind of quantitative data in statistical analysis is numerical, followed by ordinal, and lastly
nominal. It is important to know what kind of data you are planning to collect or analyse as this will
A 12 step approach to quantitative data analysis
Most research starts with these. Vague investigations are dangerous as they are unfocused and
may not be undertaken systematically. There is also a greater risk that you will find something that
is just a random event.
Step 2: Collect data consistent with your aim and research questions
Assuming you have started with a research question you need to think about what data you need
to collect in order to investigate this issue. Then there are also the questions: where will you get
this data, how will you approach this process, and how much data should you obtain?
Where is known as your sample this is assumed to come from a larger population
How this is your sampling method is it random or non-random? Most statistical testing
assumes data has been sampled randomly. For a questionnaire you should also consider
how to maximize your response rate in order to reduce bias.
How much essentially, you should collect as much data as possible. It should also be
as good quality as possible. There are rules of thumb about what a minimum acceptable
amount of data is and a formal process known as sample size calculations. However, both
methods suffer from the weakness of not knowing whether there is something that can be
found in the first place.
Step 3: Process your data and create a
This step is often overlooked. Data
with types of collected data in the
columns and instances in the rows rather
than summary statistics derived from raw
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online questionnaire, it is often quite messy and needs tidying up first.
Step 4: Get a feel for your data with a descriptive analysis
Descriptive analysis involves creating
tables, charts and summary statistics from
individual types of collected data (known as
a variable), but it is often more useful to
compare one variable against another. Your
choice of which variables to compare
against each other should be guided by
your aim and research questions. Do not do
this at random and do not report on
everything.
Also, the choice of a table or a chart should
be based on what best explains the
contain too many figures. The shape of the data is often more important that the specific numerical
values in interpreting its meaning.
Step 5: Interpret and report on your analysis informally
Now you can write a narrative to go with your descriptive statistics. This should seek to answer
your research questions by providing an informal interpretation of the meaning of your descriptive
statistics. Do not use both a chart and a table to represent the same thing choose which is best
and always write a narrative to go with it. Be careful not to use inappropriate statistical language,
such as the word “significant” when you have not conducted any statistical testing.
Descriptive analysis finishes here: the remaining steps relate to statistical testing
Step 6: Decide whether to analyse groups of variables in your data set or just individual
variables
Questionnaires, for example, often contain groups of questions on the same thing, known as
scales. This makes the analysis easier and potentially more accurate as you only have to analyse
the values of the scales (which are numeric) rather than the data from individual questions (known
as items) which make up your scales (which are often ordinal).
If you choose to use someone else’s questionnaire and wish to use its scales you first need to
assess the published literature about it to ensure that its scales are valid and reliable (measure
what they are supposed to measure accurately). If you have designed your own questionnaire and
wish to use the scales you have designed you first need to carry out a reliability analysis, but be
prepared to remove about half of the
items you created. There is also an in
between option where you use part of
someone else’s questionnaire or
modify it, but this is beyond the scope
this guide.
There are many myths about reliability
design
There are two main things statistical
tests do: investigate differences
between groups and explore
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relationships between variables (known as an association or a correlation). There is also the
issue of whether the same subjects are being measured several times or whether different subjects
are being measured. Finally, there are two main kinds
of test known as parametric and nonparametric.
Parametric tests are generally more sensitive but they
have assumptions that you first need to check before
you can run them. The chart above shows a decision
tree for choosing simple tests.
Step 8: Generate advanced level descriptive
statistics and check test assumptions
The assumptions of most parametric tests are for the
data to be normally distributed. This can be checked
by producing a histogram with a fitted normal curve.
There are also tests of normality, such as the
Shapiro-Wilk test. Other assumptions are: the
equality of variances for an independent
samples t-test, which can be assessed using a
Levene’s test; and an elliptical distribution
shape of a scatter plot for linear correlation and
regression, which can be assessed qualitatively.
Confidence intervals are a useful advanced descriptive statistic that bridges the gap between
exploring data and a statistical test. These are often displayed on an error bar chart.
Step 9: Understand the null hypothesis statistical testing process
Whilst it is often criticised
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, the null hypothesis statistical testing process provides a clear approach
to making a decision about a comparison of groups or variables. Imagine that you are a judge in a
courtroom and your data is on trial. The assumption that you data is innocent is known as the null
hypothesis. This usually refers to there being no difference between two groups or no relationship
between two variables. Your job is to evaluate to decide whether there is sufficient evidence to
convict your data of having a difference or a relationship beyond reasonable doubt, or to acquit
your data. The beyond reasonable doubt level is usually set at 95% confidence. The evidence
often comes in two forms a statistic value which represents the event that occurred in your
sample and an associated probability value (known as a significance value) that measures how
2
For example, see Häggström, O. (2017) The need for nuance in the null hypothesis significance testing
debate. Educational and Psychological Measurement, 77(4), pp. 616-630, available at:
https://www.ncbi.nlm.nih.gov/pmc/articles/PMC5991794/, and Halsey, L. G. (2019) The reign of the p-value
is over: what alternative analyses could we employ to fill the power vacuum? Biology Letters, 15(5), available
at: http://dx.doi.org/10.1098/rsbl.2019.0174.
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likely or unlikely your event was. If a significance value is less
than 0.05 you reject the null hypothesis. For example, if
value), the probability of this event is about 0.037 but its
signifiance value is 0.115 as it is calculated by summing the
probabilities of events with less heads (i.e. from 0 to 5 heads)
and also the opposite side of the distribution (i.e. from 14 to 20
heads). So getting 6 heads out of 20 coin tosses is not a
significant event and you would conclude that there is
insufficient evidence to decide that your coin is biased.
Step 10: Run and interpret an
appropriate test
Statistical software such as Excel or
SPSS is often used to run statistical tests.
The output from these tests requires
interpretation.
For example, the table on the right is the
output from SPSS for a Chi-squared test
of whether there is an association
between a cause of rioting and the police
force using. The number to
interpret is the Asymptotic
significance (2-sided) of the
Pearson Chi-Square row
(0.172). However, the Exact
Sig. (2-sided) of the Fisher’s
exact test (0.214) can also be
interpreted. As both of these
values is above the 0.05
threshold, we would conclude
that there is insufficient
evidence of an association.
Step 11: Report on your results
Results need to be reported on after they are interpreted. This requires quoting relevant probability
values, comparing them with the significance threshold in order to make a decision about a null
hypothesis and referring this decision back to your research question. It is usually not appropriate
to copy and paste software output into your findings but this can be provided in an appendix. You
may also need to compare your findings with other people’s findings in the literature and discuss
any differences or implications.
Step 12: Be prepared to re-analyse your data using metacognition
As already mentioned, in applied statistics, data sets are complex and messy, and there are many
ways they could be analysed. In view of this, you should consider whether to run additional
analyses to investigate your research questions further. However, be aware that every time you
run a statistical test you are introducing the possibility of a false positive result (known as a Type I
error). If you decide to run several tests, you may wish to increase your confidence threshold, for
example from 95% to 99%, and look for correspondingly lower significance values, for example
less than 0.01 instead of less than 0.05.
© 2020 Dr Peter Samuels, Birmingham City University
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