Scatter Diagram

Scatter Diagrams (or Plots) are used to visually represent data for further analysis in correlation or regressionThe diagram shows a pair of numerical data, one for each axis (horizontal and vertical with are x-y respectively). 

They explore associations between two variables and the "x" variable (input) is varied systematically and the "y" (output) is measured once the input changes. The intention is to visually examine trends or patterns of the input (x) onto the response in the experiment. 

The chart below would indicate a weak negative linear correlation. From here the Coefficient of Correlation can be determined as well as best fit line to describe the behavior of the data. 

Negative correlation on a Scatter PlotA possible negative correlation but not overly convincing

There are no assumptions of normality or sequence to use a Scatter Plot. Sequential plotting is required for a Time-Series plot (and for SPC). In other words, the data for Scatter Plots does not have to be in sequence or chronological order but this is required for SPC and Time-Series charts. 

It is most useful when there is a lot of data in table and very difficult to tell if there is any type, and to what degree, of correlation. 

As association of variables does not always imply cause. There could be other lurking variables affecting the measured "y" response.

A scatter plot of the blue dots shown below makes it very obvious that there is strong positive linear correlation but it does not provide any value other than a visual indication. 

Scatter Plot, Scatter

A Scatter diagram itself is limited in its use but is rather a starting point for further analysis of correlation and regression.

This is another one of the many visual tools (such as a Box Plot and Pareto Chart)  that a Six Sigma project manager can use to help break down data into more meaningful terms.

Line charts are similar to Scatter Plots but contain lines connecting the data.

Scatter plots can make it easier to find a correlation as most of it is not easy to see a non-linear correlation amongst thousands of lines of data.

The chart above is an example of the value of the plot. Simply looking at a set of x-y data on a sheet would be a challenge to see this relationship. There appears to be a strong non-linear relationship with a few outliers within the range of 0-200 units.

Those outliers are concerning. There are only a few of them so it would be worthwhile understanding what happened in each case. 

7 Basic Quality Tools

A Scatter Plot is considered 1 of 7 Basic Quality Tools for process improvement. The others are:

If you're considering a Six Sigma Certification exam or a PMP certification, memorize and understand the purpose of these 7 tools.


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