Scatter Diagrams
(A Brief Tutorial)

How to Use Tutorial

This tutorial is designed to allow the user to develop and interpret scatter diagrams. Other additional information is presented within the History and Key Terms sections of this tutorial so the user will have a better understanding of scatter diagrams.

The user can venture through the tutorial by clicking on the desired topic in one of the menus, or by using the scroll on the right side of the screen to move through the page.

Several examples are also furnished in this tutorial to enable the user to develop a more clear understanding of the information being presented. When the scatter diagram has been plotted from the data, the user can view several different graphs within the Interpretations sections of the tutorial, read the interpretation of the diagrams pattern, and be able to draw conclusions about the plotted diagram by comparing it to one of the five possible graph patterns.

Overview

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 existance of a relationship, as well as the strength of that relationship.

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.

The purpose of the scatter diagram is to display what happens to one variables when another variable is changed. The diagram is used to test a theory that the two variables are related. The type of relationship that exits is indicated by the slope of the diagram.


|

KEY TERMS | HISTORY | CONSTRUCTION | INTERPRETATIONS | EXAMPLES |

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.


    |     OVERVIEW | HISTORY | CONSTRUCTION | INTERPRETATIONS | EXAMPLES |

    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.


    |     OVERVIEW | KEY TERMS | CONSTRUCTION | INTERPRETATIONS | EXAMPLES |

    Construction of Scatter Diagrams

  • Collect and construct a data sheet of 50 to 100 paired samples of data, that you suspect to be related. Construct your data sheet as follows: 

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

  • Draw the axes of the diagram. The first variable (the independent variable) is usually located on the horizontal axis and its values should increase as you move to the right. The vertical axis usually contains the second variable (the dependent variable) and its values should increase as you move up the axis.



  • Plot the data on the diagram. The resulting scatter diagram may look as follows:

  • Interpret the diagram. See interpretation section of tutorial.

    | OVERVIEW | KEY TERMS | HISTORY | INTERPRETATIONS | EXAMPLES |

    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.



    Key Observations

    *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.

    | OVERVIEW | KEY TERMS | HISTORY | CONSTRUCTION | EXAMPLES |

    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.

    | OVERVIEW | KEY TERMS | HISTORY | CONSTRUCTION | INTERPRETATIONS |