Data Analysis Australia

# Applied Statistical Analysis

Data can be confusing since it rarely records anything without some form of ambiguity, uncertainty or "error".  Statistics is the theory and practice of most effectively extracting the real information from such data.  It not only extracts this information, but does so with a clear statement on how precise any inferences can be.

The statistical methods that revolutionised science and industry in the twentieth century are continually being developed, especially in computation and large data sets.  Data Analysis Australia brings together these methods to solve clients' problems.  Our depth of statistical knowledge and our mathematical expertise means that we can apply the right set of tools for every problem either familiar or unique.

Data Analysis Australia statisticians employ a range of exploratory and analytical statistical techniques including:

• Experimental design, ensuring information is collected as efficiently as possible;
• Regression modelling, using classical linear models as well as modern extensions such as generalised additive models and structured equation models;
• Multivariate methods such as factor analysis, conjoint analysis and perceptual mapping;
• Cluster analysis and multi-dimensional scaling to understand complex datasets with many variables; and
• Time series and longitudinal methods that can handle data with difficult correlations over time.

Examples of project experience where Data Analysis Australia has used applied statistical analysis are listed below.

### Valuation Procedure for Mineral Samples

A program was developed for the statistical validation of mineral samples used in the gold industry.  Standards are material with known grades of gold -  typically between 1 and 5 grams per tonne - that are used by all mineral laboratories for calibration and quality control.  Data Analysis Australia developed a validation procedure that builds upon the normal procedures of having samples tested by a number of laboratories by blind testing a number of standards at once, to ensure both honesty in results and to measure overall laboratory accuracy.  This used concepts from Experimental design while the analysis needed to use robust methods to remove outliers and identify problems.

### Multiple Factor Analysis of Environmental Data

Studies of water quality and benthic fauna in Cockburn Sound south of Perth were conducted before and after the operation of Perth's first desalination plant to allay fears that the hyper-saline discharge would have negative environmental effects on the Sound.  Data was collected at over 100 points in the Sound and the benthic fauna was classified into over 100 species, some new to science.  Data Analysis Australia conducted that analysis, using tools including krigging and multiple factor analysis.

### Examination of Radar Data on Aircraft

Data Analysis Australia was asked to examine radar data that tracked the flight of an aircraft involved in an incident.  This data had uncertainties since radar systems have limited angular and distance resolution.  The problem of tracking is therefore a statistical one.  Cubic smoothing splines were identified as giving a solution that both made physical sense in limiting acceleration and were flexible enough to handle almost any possible track.