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.
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.
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.
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.
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.
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.
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 :
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?
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.