Correlation Matrix

Introduction

The correlation matrix chart tool is similar to the correlation matrix statistical tool. However, in addition to the values of the correlation (from -1 to 0 to 1), the chart provides a pictorial representation of the magnitude of the correlation.

Inputs

To illustrate the use of the Correlation Matrix tool, we will use a dataset with a number of variables in it that can be related to each other – Voting patterns across Victoria for the 2010 Federal Election. To do this:

  • Select Melbourne GCCSA as your area
  • Select Voting Variables by PB for 2013 Australian federal election as your dataset

Once you have done this, open the Correlation Matrix tool (Tools → Charts→ Correlation Matrix) and enter the parameters as shown in the image below (they are also explained under the image in more detail

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  • Dataset Input: The dataset containing the variables that you would like to run through the Correlation Matrix Tool. Here we select Voting Variables by PB for 2013 Australian federal election
  • Correlation Column Input Variable Name: Check the variables you would like to include in the analysis. In this instance we select % Australian Labor Party,  % Liberal Party,  % National Party,   % Greens,  % Independent, % Family First,  % Katter’s Australian Party, and % Palmer United Party
  • Correlation Use: this determines whether or not you include rows if there are no values. Choose from everything, all.obs, complete.obs, na.or.complete, pairwise.complete obs. In this instance we choose everything
  • Correlation Alternative Hypothesis: we determine whether our hypothesis is two.sided, less, or greater. In this instance we choose the default two.sided
  • Chart Title:  A title for your output graph: Correlation Matrix – Melbourne Primary Vote Variables 2013 Federal Election
  • Greyscale: Determine whether or not you want your graph to be greyscale (checked) or colour (unchecked). In this instance we choose to have a colour graph

Once your tool has run, Click Add and Run to execute the tool

Outputs

Once you have run the tool, click the Display button which appears in the pop-up dialogue box. This should open up a chart tool looking like the one shown below.

On the bottom left of the matrix are the correlation values (r) for each pair-wise correlation (see the Correlation tool for an explanation on how to interpret these values). On the top right of the matrix are pictorial representations of each of the correlation values. Ellipses that are yellow represent positive correlation statistics, green ellipses represent negative correlation statistics. Narrow ellipses represent correlation statistics that are stronger (closer to -1 or 1), while wider ellipses represent correlation statistics that are weaker (closer to 0). We can see that the strongest relationship is a negative one between the percentage of people who voted for the ALP and for people who voted for the Liberal party. The next strongest relationships are also negative, between the percentage of people who voted for the Green party, and for the people who voted either for the Family First Party or the Palmer United Party.

[Click to Enlarge]

[Click to Enlarge]