#### ASQ — Seven Basic Quality Tools: The Scatter Diagram (5)

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This fifth article introduces the scatter diagram, also known as the scatter plot diagram or X-Y graph, a tool that pairs numerical data, with one variable on each axis to look for a relationship between them. If the variables are correlated, the points will fall along a line or curve. The better the correlation, the tighter the points will hug the line.

This series of articles presents the 7 Basic Quality Tools for Process Improvement used in the field. These are defined as instruments or techniques to support and improve the activities of quality management and improvement. ASQ has made available to the members and the public a huge amount of information on the "quality" body of knowledge (BOK). It is only meant to be a starting point, but oh so useful.

When to Use a scatter diagram:
• When you have paired numerical data.
• When your dependent variable may have multiple values for each value of your independent variable.
• When trying to determine whether the two variables are related, such as:
• Trying to identify potential root causes of problems;
• After brainstorming causes and effects using a fishbone diagram to determine objectively whether a particular cause and effect are related;
• To determine if two effects that appear to be related both occur with the same cause;
• To test for autocorrelation before constructing a control chart.

Create a scatter diagram:
Read the complete article on preparing a scatter diagram, pullout your computer, flip charts or whiteboard and markers and start collecting data and prepare graphs. ASQ also supplies a 90 data point working template her: scatter diagram template.

 In this example, the ZZ-400 manufacturing team suspects a relationship between product purity (percent purity) and the amount of iron (measured in parts per million or ppm). Purity and iron are plotted against each other in a scatter plot, as shown in the figure below. There were 24 data points collected. The centre lines are drawn so that 12 points are on each side for percent purity and ppm iron. To test for a relationship, they calculate: A = upper left corner points + lower right points = 9 + 9 = 18. B = upper right points + left lower points = 3 + 3 = 6 Q = the smaller of A and B = the smaller of 18 and 6 = 6 N = A + B = 18 + 6 = 24 Then they look for the limit for N on the trend test chart. For N = 24, the limit is 6. Q is equal to the limit. Therefore, the trend could be random, and no relationship is shown.

Scatter diagram considerations

• Even if the scatter diagram shows a relationship, do not assume that one variable caused the other. Both may be influenced by a third variable.
• When the data are plotted, the more the diagram resembles a straight line, the stronger the relationship.
• If a line is not clear, statistics (N and Q) determine whether there is reasonable certainty that a relationship exists. If the statistics say that no relationship exists, the pattern could have occurred by random chance.
• If the scatter diagram shows no relationship between the variables, consider whether the data might be stratified.
• If the diagram shows no relationship, consider whether the independent (x-axis) variable has been varied widely. Sometimes a relationship is not apparent because the data do not cover a wide enough range.

§ This News post was adapted by J.P. Amiel, ASQ Senior, CQA ret., Web committee Chair, from content at ASQ's Quality Resources pages, which are excerpted and adapted from The Quality Toolbox, Second Edition, ASQ Quality Press.

ASQ References:

Here is a list of the articles in this series:

 Article Title ASQ — Seven Basic Quality Tools: The SeriesASQ — Basic (And Not So Basic) Quality Tools Resources ASQ — Seven Basic Quality Tools: The Check Sheet And The Histogram (1)ASQ — Seven Basic Quality Tools: The Pareto Chart (2)ASQ — Seven Basic Quality Tools: The Control Chart (3)ASQ — Seven Basic Quality Tools: The Fish Bone Diagram (4)ASQ — Seven Basic Quality Tools: The Scatter Diagram (5)ASQ — Seven Basic Quality Tools: Stratification (6)
News Montreal Section 10/21/2022 4:49pm CDT