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