Scatter Diagram

Definitions/Purpose:  Scatter diagrams are used to study possible relationships between two variables.  Although these diagrams cannot prove that one variable causes the other, they do indicate the existence of a relationship, as well as the strength of that relationship.  The scatter diagram can display what happens to one variable when another variable is changed.  The diagram can be used to test a theory that the two variables are related.  It is important to remember that correlation does not necessarily mean causality.  Useful in Measure and Analyze phase.

Instructions:  A scatter diagram is composed of a horizontal axis containing the measured values of one variable and a vertical axis representing the measurements of the other variable.  An example scatter diagram Excel template that has been used for staffing effectiveness is provided for your data entry.

Key terms:

• Variable - a quality characteristic that can be measured and expressed as a number on some continuous scale of measurement.
• Relationship - Relationships between variables exist when one variable depends on the other and changing one variable will effect the other.
• Data Sheet - contains the measurements that were collected for plotting the diagram.
• Correlation - an analysis method used to decide whether there is a statistically significant relationship between two variables.
• Regression - an analysis method used to identify the exact nature of the relationship between two variables.

Interpretation:

The type of relationship that exits is indicated by the shape or slope of the scatter diagram.  Remember to avoid thinking this is a cause/effect relationship; correlation does not necessarily mean causality.  The most common shapes are:

• Positive correlation: as the amount of variable x increases, the variable y also increases. If x is controlled, we have a chance of controlling y. 
• Possible positive correlation- if x increases, y will increase somewhat, but y seems to be caused by something other than x.
• No correlation- the diagram is random without apparent correlation between the two variables.
• Possible negative correlation- an increase in x will cause y to decrease somewhat, but y seems to have causes other than x.
• Negative correlation -an increase in x will cause a decrease in y. If y is controlled, we have a good chance of controlling x.