# Scatter Diagrams(A Brief Tutorial)

## How to Use Tutorial

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.

## 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

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

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 |