Much less emphasis on common statistical tests e.g. hypothesis testing … more emphasis on approaches to working with and analysing experimental data
Will cover some useful concepts and principles over the next hour
Encourage some discussion
Session in a couple of weeks will be a chance to have a go yourself
Exploratory data analysis
Exploratory data analysis
“Far better an approximate answer to the right question, which is often vague, than an exact answer to the wrong question, which can always be made precise.” — John Tukey
Exploratory data analysis (EDA) is an important approach that has developed over many years
It is important to undertake when trying to understand almost any data
The broad goal is understanding your data and its characteristics
No set rules as such, but there are common types of analysis that are undertaken
Some aims of EDA
Get a ‘feel’ for your data. At this stage it is useful to check whether the data look to be reasonable based on experience and a theoretical understanding
EDA is useful to help generate questions about data.
These questions can be addressed by visualising, transforming, and modelling data.
Often, EDA will help to refine questions and/or generate new questions…
To some extent, a move away from hypothesis testing to considering the data to help develop hypotheses
Tools for EDA
Over the past 20 years R has become the leading software for conducting statistical analysis — or more generally data analysis.1
In our examples class next week we will use R and an Integrated Development Environment (aka a nice ‘front-end’!) called RStudio. The examples given here are based on using R and RStudio.
Some of the advantages of this approach include:
R is fantastically capable software and goes far beyond ‘just’ statistics;
very good for data exploration and data visualisation;
great for making your work reproducible and sharing it (we’ll come back to that);
these skills are highly valuable in academia, industry and almost any discipline that involves data.
Questions about your data
There are no rules about how EDA should be approached. However, a good place to start is understanding two broad issues:
What type of variation occurs within variables?
What type of covariation occurs between variables?
To answer these questions there are a large number of approaches that can be used that cover:
Numerical-type statistics (understanding numbers of measurements, their ranges, means etc.)
There are also a wide number of very useful ways to plot data to explore these characteristics
No silver bullet and having different ‘views’ / perspectives on data is very useful
Some example data to explore
We will use some air pollution data as a way of exploring some of the techniques for EDA. In the practical session use can be made of this data set … or maybe you have your own?
date ws wd nox no2 o3 pm10 so2 co pm25 month year
1 1998-01-01 00:00:00 0.60 280 285 39 1 29 4.7225 3.3725 NA Jan 1998
2 1998-01-01 01:00:00 2.16 230 NA NA NA 37 NA NA NA Jan 1998
3 1998-01-01 02:00:00 2.76 190 NA NA 3 34 6.8300 9.6025 NA Jan 1998
4 1998-01-01 03:00:00 2.16 170 493 52 3 35 7.6625 10.2175 NA Jan 1998
5 1998-01-01 04:00:00 2.40 180 468 78 2 34 8.0700 8.9125 NA Jan 1998
6 1998-01-01 05:00:00 3.00 190 264 42 0 16 5.5050 3.0525 NA Jan 1998
Some example data to explore
Using the R function summary is very useful in a wide range of circumstances:
A box that stretches from the 25th percentile of the distribution to the 75th percentile (the interquartile range (IQR). In horizontal line displays the median value.
The points show individual observations that fall more than 1.5 times the IQR from either edge of the box. These points are unusual so are plotted individually.
A line (or whisker) that extends from each end of the box and goes to the farthest non-outlier point in the distribution.
Box and whisker plots
Recent developments in R make it possible to produce plots that are interactive. This can be great when exploring data and can be easy to do.
Being able to reproduce scientific experiments and verifying their outcomes is a basic tenet of science.
For simplicity we can think of two main applications:
For ‘real’ experiments this could mean that someone not involved with the experiment being able to follow all the steps necessary to reproduce the outcomes
following a clear method
confirming the same outcomes
For data analysis results are replicable if independent researchers can recreate findings by following the procedures originally used to gather the data and run the computer code.
For this course focused on data, a good working definition is:
The data and code used to make a finding are available and they are sufficient for an independent researcher to recreate the finding
Importance of reproducible research
So why bother thinking about and adopting reproducible research practices? There are many reasons:
From an individual perspective, being able to recreate one’s own work is important
…and very frustrating if you can’t! It’s too easy to revisit previous work and not be able to replicate it — we have all been there!
Collaboration: it is increasingly important to be able to collaborate with others
Reproducible research is more likely to be useful for other researchers than non-reproducible research — more research impact
It’s becoming more prominent e.g. journals requesting the data and code to reproduce findings … most important for most important work
In general, these approaches lead to improved quality of work whether for research or industry, or anywhere else
Practical aspects when analysing data
All that sounds very worthy, but what does it mean in practice?
Use the source, Luke!
For data analysis, use ‘serious’ tools like R and Python and not Excel. Serious tools use scripts (i.e. source code) to carry out analyses. Why are scripts so useful? Here are some of the reasons:
Scripts are written in plain text and are human readable1
They encourage a separation between the data and the processing and analysis of the data — they help avoid the temptation to manually adjust the data directly as is common in Excel
They can be easily shared — email a small text file!
They can be brought under version control using a system such as git and code hosting and sharing sites such as GitHub
Producing documents
A very common way to work is to carry out analysis in software e.g. Excel, make some plots and paste them into Word. This approach is prone to error and inefficient. For example, it is requires some manual effort to copy and paste and if the data is revised, you need to do it all over again.
Is there a better way?
Recently, it is more common to use methods that mix analysis e.g. in R or Python with ordinary report writing in a single document
The approach is often referred to as dynamic documents
The document (a plain text file!) has ordinary report text and code ‘chunks’ that carry out the analysis such as making a plot
The document is compiled and all the code chucks are automatically run
The output can be a pdf, html or even a Word document
This presentation was produced in exactly this way using R!
Producing documents — R and python
Both R and Python are fantastic for producing reproducible note books (a modern-day lab book), as well as a wide range of other outputs including journal publications, web pages / sites and presentations.
