The Scatter Diagram

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Not all sets of data pairs will exhibit a strong positive correlation, even if an increase in the x-value somehow results generally in an increase in the y-value.  An example of this 'weak' type of positive correlation is shown in the scatter diagram of Figure 2b, which is said to exhibit just a 'possible positive correlation.'  This scatter diagram still shows a perceivable diagonal line going in the upper right direction, but the points are more spread apart than in a scatter diagram with strong positive correlation.

Figure 2.  Scatter Diagrams showing positive correlation (a, left) and

just a possible positive correlation (b, right)

If the scatter diagram formed also shows a perceivable diagonal line, but the line is going in a direction opposite that of positive correlation (i.e., from the upper left to the lower right corner) as shown in Figure 3a, then the data pairs are exhibiting negative correlation. This means that y decreases as x increases. Again, the negative correlation is strong if the line formed by the data points is narrow and very defined.

If the negative correlation is not strong, resulting in data points that are not closely packed together, then there is just a 'possible negative correlation.'  An example of a scatter diagram for such type of correlation is shown in Figure 3b.

Figure 3.  Scatter Diagrams showing negative correlation (a, left) and

just a possible negative correlation (b, right)

Of course, more complex types of correlation may also be identified using a scatter diagram.  Once a type of correlation is established,  the engineer may choose to proceed with a further and more in-depth investigation of the correlation using other analysis tools.

Determining the exact nature of correlation between variables can lead to benefits.  These include:  1) better understanding of cause-effect relationships; 2) reduction of data gathering requirements; 3) establishment of more effective process controls; 4) easier development of check and balance schemes; etc.  To realize these benefits, however, the engineer has to use other analytical tools to complement the scatter diagram, since the latter is only used as a quick visual check for possible correlation before a more in-depth study is undertaken.

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