Welcome to Sigma Statistics and Research Limited. We are based in Wellington, New Zealand. We provide on-line instruction, face-to-face training and
development of code and software in the R language (the R statistics language and environment for scientific and statistical computing and graphics). Our workshops and courses are suitable for people who are new to R and for managers, data analysts, researchers and students who wish to explore advanced topics in R. We can tailor a workshop or course to suit your needs.

Instruction can be done on-line, using VCN software (or similar) for sharing computer screens. They can also be conducted face-to-face for groups of learners at any suitable venue (your own offices, for example).

We also provide coding and software development in R, statistical modelling, data analysis and policy research. One speciality is in the provision of software for Item Response Theory (IRT), especially for the analysis of national examinations. We can design software for analysing the results distributions of national examinations very efficiently, providing results distributions across demographic subgroups of interest, Principal Components Analysis, Factor Analysis and factor loadings, item discriminations and item difficulty estimates for the available grades, item correlations, item-total correlations, and investigations of differential item functioning. However, we develop R-based software for any application, including applications useful within the biomedical sciences (including epidemiology) and social sciences research.

Sigma Statistics and Research Limited was established with the intention of focusing exclusively on instruction and software development using R, and Sigma now provides effective learning for people of varying backgrounds in statistics and research.  

Our workshops and courses cover the main statistical functions in R, including the following: using R as a calculator, basic R syntax and commands, reading and writing data files, sub-setting data, sorting and ordering data, merging arrays, creating factors and making summary tables from factors, the Normal Distribution (including p-values and associated probabilities, percentiles, quantiles, correlation, tests for normality and confidence intervals), the Poisson distribution, the Binomial distribution, Ordinary Least Squares regression, multivariable regression, logistic regression (for count data, proportions and binary outcomes), t-tests, Analysis of Variance and Multivariable Analysis of Variance, Analysis of Covariance, Factor Analysis and Principal Components Analysis, power tests and sample size estimation, Chi-square tests for categorical variables, writing functions in R, writing software (scripts) in R, control structures (e.g. loops), dealing with dates, introductory Monte Carlo parameter estimation, introductory bootstrapping, set membership, and graphical methods (including scatterplots, bar charts, pie charts, histograms, box plots and dot charts). Our courses also include examples of practical data analysis of large data sets.


My name is David Lillis. I am the Director of Sigma Statistics and Research Limited, a company that specialises in both training and software development in the R statistics and computing environment. I am very experienced in using R for statistical modelling and for analysing complex data sets, and I have developed tutorials for people who are new to R and for statisticians and researchers who wish to explore specific topics through R. I have also published articles on R that you can find on this web-site (see: OUR WORK).

I hold a B.Sc(Hons) and M.Sc in Physics and Mathematics and a Ph.D that involved extensive statistical modelling. In addition I am a trained teacher and I hold a Diploma of Education. For many years I have worked as a statistician in various sectors (including education, agriculture and forestry and have participated in the collection of statistics for climate change policy). Much of my experience in recent years has focussed on the development of R code for the analysis of questionnaires, tests and examinations. In addition, I have a particular interest in biostatistics and epidemiology.
I am experienced in SPSS and am familiar with SAS. However, my main strength lies in data analysis and programming in R, and in teaching R. I have experience in many aspects of statistical modelling, including Item Response Theory and Rasch modelling, and other contemporary statistical methods. 


What is R all about?
The R statistics language and environment for scientific and statistical computing and graphics is a genuine New Zealand success story. While at the University of Auckland during the early 1990s, Ross Ihaka and Robert Gentleman developed the initial version of R, primarily for use as a teaching tool. R is open source software which you can download from the Comprehensive R Network (CRAN) website (see:
http://cran.r-project.org/), and combines a powerful programming language, a comprehensive range of statistical functions, and outstanding graphics.

R implements a dialect of the S language that was developed around 1975 at AT&T Bell Laboratories. Since mid-1997, further development of R has been overseen by a core team (currently about 20 people), drawn from many different institutions worldwide.

If you need a statistics and graphics environment that includes a programming language, R could be just what you are looking for. It’s true that the learning curve is longer than for spread sheet-based packages but, once mastered, R enables you to develop your own very powerful analytic tools. That’s where we at Sigma can assist you.

The main issue for those new to R is the time required to master the syntax, but we at Sigma can help you attain that mastery. R uses command line input that those with limited previous exposure to programming may find intimidating. However, the reward for mastery of R is access to a large and rapidly growing range of abilities that extends widely over many different areas of scientific, statistical, business and other applications. The CRAN task views web pages give some indication of the range of abilities currently available (see: http://cran.r-project.org/web/views/).

In recent years several well-known commercial packages, such as SPSS and SAS, have become very popular around the world. However, for many statisticians and researchers, R is the environment of choice because of its powerful programming language; the wide range of abilities that are available from its contributed packages; the integration of those abilities with powerful and wide-ranging graphics; data input abilities (including the ability to input and process a wide range of specialist data formats such as Excel files and text files, various spatial data formats, Network Common Data Form formats for climate and mapping applications); and powerful data manipulation and analytic abilities.

R and Graphics
Quite simply, the quality and range of graphics available through R is superb and, in my view, superior to those of any other system I have encountered. Of course, you must write the necessary code but, once you have attained this skill, you have the capability to develop wonderful visualisations. Of course, R’s graphics capability provides a comprehensive range of colours and hues (see:

Here is an example of what you can achieve with R. Of course, you may never need to produce a plot quite like this one, but you can see the wonderful graphics capability of R.


R as an Investment for the Future. For many scientists and data analysts, mastery of R is an investment for the future, particularly for those who are beginning their careers. The technology for handling scientific computation is advancing very quickly, and is a major impetus for scientific advance. Some level of skill in R (or an equivalent such as Matlab or Python) has become, for many applications, essential for taking advantage of these developments. Spatial analysis, where R provides access to abilities that are spread across many different computer programs, is a good example.

For my own work as a statistician and data analyst, I have found the abilities discussed here particularly relevant, though others will have different requirements. You may be considering R as a tool for your own data analysis. If so, in contacting Sigma, you have come to the right people.