Scatter Diagrams

(A Brief Tutorial)

History

Commonly, while a cause-effect diagram has been used to describe the relationship between two variables, the histogram was used to visualize the structure of the data. However, a means of observing the kinds of relationships between variables was needed. Using the theory of linear regression which originated from studies performed by Sir Francis Galton (1822-1911), the scatter diagram was developed so that intuitive and qualitative conclusions could be drawn about the paired data, or variables. The concept of correlation was employed to decide whether a significant relationship existed between the paired data. Furthermore, regression analysis was used to identify the exact nature of the relationship.

The Guide to Quality Control and The Statistical Quality Control Handbook, written by a Japanese quality consultant named Kaoru Ishikawa are useful in providing an understanidng on how to use and interpret a scatter diagram. Ishikawa believed that there was no end to qualithy improvement and in 1985 suggested that seven base tools be used for collection and analysis of qualtiy data. Among the tools was the scatter diagram.

Construction of Scatter Diagrams

	Car		Age(In Years)		Price(In Dollars)
	  1			2			4000
	  2			4			2500
	  3			1			5000
	  4			5			1250
	  :			:			  :
	  :			:			  :
	  :			:			  :
	  :			:			  :
	100			7			1000

Interpretations

The scatter diagram is a useful tool for identifying a potential relationship between two variables. The shape of the scatter diagram presents valuable information about the graph. It shows the type of relationship which may be occurring between the two variables. There are several different patterns (meanings) that scatter diagrams can have. The following describe five of the most common scenerios :

1. The first pattern is positive correlation, that is, as the amount of variable x increases, the variable y also increases. It is tempting to think this is a cause/effect relationship. This is an incorrect thinking pattern, because correlation does not necessarily mean causality. This simple relationship could be caused by something totally different. For instance, the two variables could be related to a third, such as curing time or stamping temperature. Theoretically, if x is controlled, we have a chance of controlling y.
   
   
2. Secondly, we have possible positive correlation, that is, if x increases, y will increase somewhat, but y seems to be caused by something other than x. Designed experiments must be utilized to verify causality.

   
   

   
   
3. We also have the no correlation category. The diagram is so random that there is no apparent correlation between the two variables.

   
   

   
   
4. There is also possible negative correlation, that is, an increase in x will cause a tendency for a decrease in y, but y seems to have causes other than x.

   
   

   
   
5. Finally, we have the negative correlation category. An increase in x will cause a decrease in y. Therefore, if y is controlled, we have a good chance of controlling x.

   
   

*A strong relationship between the two variables is observed when most of the points fall along an imaginary straight line with either a positive or negative slope.

*No relationship between the two variables is observed when the points are randomly scattered about the graph.

Example 1

Situation: The new commissioner of the American Basketball League wants to construct a scatter diagram to find out if there is any relationship between a players weight and her height. How should she go about making her scatter diagram?

1. Collect the data (Remember to use 50-100 paired samples).

   
   

   
   
2. Draw and label your x and y axes.

   
   

   
   

3. Plot the data on the diagram.

   
   

   
   
4. Interpret your chart.

According to this scatter diagram the new commisioner was right. There does seem to be a positive correlation between a player's weight and her height. In other words, the taller a player is the more she tends to weight.

Related Topics

• Regression Analysis
• Cause and Effect Diagram
• Correlation
• Regression Curves

Additional Sources

• Making Quality Happen: Upper Management’s Role (5th edition)
• Sample Design in Business Research
• An Introduction to Applied Probability and Random Processes
• Regression Analysis
• Metrics and Models in Software Quality Engineering