The Module 'Correlations Analysis'

Content

Purpose and short description
The tabular correlations view
The bottom tool bar
The correlations matrix view

Purpose and short description

The data exploration module 'Correlations Analysis' serves to get an overview over the dependencies and correlations between the different data fields within a data source. This is done by creating a table of field-field contingency coefficients.

The tabular correlations view

The main part of the correlations analysis panel displays a table of field-field correlations. In the literature, there are many different definition of measures for correlation, for example the linear correlations coefficient (or Pearson's correlations coefficient) between two nummeric data fields. Linear correlations coefficients have values between -1 (strong negative correlation) and +1 (strong positive correlation).

In Synop Analyzer, we use another measure for correlation which can also be calculated for pairs of textual data fields, or for a numeric and a textual field: the so-called adjusted contingeny coefficient C as it is defined in http://en.wikipedia.org/wiki/Contingency_table. This quantity assumes values between 0 (=no correlation) and 1 (=maximum correlation). The contingency coefficient is stronly related to the bivariate value-value matrix of the two involved fields as it is created in the Synop Analyzer module Bivariate Analysis: if one creates a bivariate value-value matrix for two data fields such that the field with the higher number of different values is traced on the y-axis, then one can derive from this matrix

• a contingency coefficient of 1 if and only of in each matrix row all cells except one are completely empty and all data records fall into one single populated cell. When displayed in the module Bivariate Analysis, the matrix would only show intensively red colored cells with count=0 and one single intensively green colored cell per row.
• a contingency coefficient of 0 if and only if each matrix cell contains exactly the number of data records which one could have expected from calculating the product of the relative appearance frequencies of the column value and the row value. When displayed in the module Bivariate Analysis, such a matrix would have only white matrix cells.

In the following we show an example for a continceny table. The example uses the sample data doc/sample_data/customers.txt and Synop Analyzer's default settings for importing the data.

By right-clicking with the mouse on one of the rows in the contingency table you open a new Bivariate Analysis panel in which the two data fields which appear in the selected table row have been chosen as the x-axis and the y-axis field.

The bottom tool bar

The tool bar at the lower border of the screen provides the following functions:

• :
  This button switches between the table view in the main panel and the alternative matrix view, which will be described in the next section of this chapter.
• Field 1:
  In this pop-up menu you can select the name of a data field from the data source, or you can select an empty string. If a field name has been selected, only contingency coefficients involving that field will be displayed. If no field has been selected, contingencies between all fields can be displayed.
• Lower limit:
  Only contingency coefficients whose value is not below this threshold will be displayed.
• :
  By pressing this button, you can save the currently active data import settings and all settings performed in this module to a persistent XML parameter file. This file can later be opened via Synop Analyzer's main menu (Analysis → Run Correlations Analysis). In this way you can exactly reproduce the current data analysis screen without to be obliged to re-enter all settings and customizations.
• :
  Export the current data exploration results within this module into a spreadsheet in .xlsx format (MS-Excel^© 2007+). The spreadsheet consists of one single worksheet which contains the tabular content of the main part of this module.

The correlations matrix view

In the matrix view, all field-field correlation numbers are shown in a compact matrix representation. The cells' background colors are the more intense the higher the correlation is.

If one chooses a minimum contingency threshold larger than zero in the toolbar, all correlation values smaller than this threshold are removed from the matrix. If a data field has no correlation value above this threshold, the entire row and the entire column representing this field are removed from the matrix. This results in a more compact view which focusses on the highest correlations in the data.