Tool #5 - The Scatter Diagram

The Scatter Diagram is another Quality Tool that can be used to show the relationship between "paired data", and can provide more useful information about a production process. What is meant by "paired data"? The term "cause-and-effect" relationship between two kinds of data may also refer to a relationship between one cause and another, or between one cause and several others. For example, you could consider the relationship between an ingredient and the product hardness; between the cutting speed of a blade and the variations observed in length of parts; or the relationship between the illumination levels on the production floor and the mistakes made in quality inspection of product produced.

To illustrate this relationship, below are a few examples of scatter diagrams indicating the relationships between paired data. We will discuss how to interpret these charts, and then we will learn how to make one with paper and pencil.

Strong paired Correlation      Moderate Paired Correlation      No Paired Correlation

      Strong Correlation           Moderate Correlation             No Correlation


In the above examples, you can see that the dots, which are actually data points, have various relationships. The Strong correlation indicates that there is a close relationship between the data that is paired together. In the middle diagram, you see a slightly different pattern indicating that there is, in some cases, a relationship and in other cases there is no relationship. The last diagram on the right indicates that there is no correlation, or no relationship at all between the paired data.

In the first diagram on the left, you would be able to determine that you have a strong relationship and thus one measurement has a strong relationship to the other; therefore, you would be able to prove that one item affects the other closely.

In the last diagram on the right, you would be able to determine that there is absolutely no relationship between the two items, and you need to review the "Cause-and-Effect" Diagram or "brain-storming" session to try and find another item that your primary item measured, might have a relationship to.

The middle diagram is the one that is going to cause you some grief. This particular diagram is more difficult to interpret, and actually requires a more detailed investigation into which data points correlate, and which data points have absolutely no comparison. Then, you need to try and determine why certain ones reveal a relationship and others do not.


How To Make A Scatter Diagram

The Basic Scatter Diagram Layout

Once again, it is best if you have graph paper to make your diagram with. However, I am going to show you how to do this with a spreadsheet form, and at the bottom of this lesson, there is a blank spreadsheet that you can use for the production floor.

On gridline or graph paper:

  • STEP #1 - Draw an "L" form just like you did for the pareto diagram (see the below figure). Make your scale units at even multiples, such as 10, 20, etc. so as to have an even scale system.



  • Figure 5

  • STEP #2 - On the Horizontal axis (Known as the "X" axis, from Left to Right) you place the Independent or "cause" variable.


  • STEP #3 - On the Vertical axis (Known as the "Y" axis, from Bottom to Top) you place the Dependent or "effect" variable.


  • STEP #4 - Plot your data points at the intersection of your data plots of the X and Y values. For Example = X = 5, Y = 2. Go right 5 spaces, and then go up 2 spaces to plot the point.

Linear Relationship: does the Data "Line Up"?

Linearity has Four Parameters:

  1. Correlation - Measures how well the data line up. The more the data resembles a straight line, the higher the correlation to each other.
  2. Slope - Measures the steepness of the data. The steeper the data slope, assuming the correlation is good, the greater the importance of the relationship. A change in the "X" variable will have a larger impact on the "Y" variable, and you will begin to see a pattern that represents the Moderate Correlation diagram above.
  3. Direction - The "X" variable can have a positive or a negative impact on the "Y" variable. As one factor goes up, the other goes down. In a positive correlation, both factors will move in the same direction. In the graph examples below, you can see that the positive correlation moves from the lower left, toward the upward right. The negative correlation moves from the lower right, toward the upward left.
  4. Y Intercept - where a line drawn through the data crosses the "Y" axis. For a positive correlation, it represents the minimum "Y" value; for a negative correlation it presents the maximum "Y" value.

Positive Correlation
You can see that the data pattern moving from the bottom left upward to the top right indicate a positive correlation between the data. This is an upward sloping data grouping.
Negative Correlation
Conversely, here the data pattern moving from the top left downward to the bottom right indicate a negative correlation between the data, and hence a downward sloping data grouping.

Test Your Learning - Class Exercise

Class Example

On the Scatter Chart AT THIS LINK, you are going to plot the data from the table above. This sample data is taken from a manufacturing process. There were thought to be two related factors that affected the outcome of the product. That was the conveyor speed in centimeters per second, and the cut length of the product. The problem is that there was a fairly large inconsistency in cut lengths of the rubber tubing produced. The quest is to try and determine if there is a relationship between the production conveyor speed and the resulting cut lengths.

You will now plot the data from the above data sheet on to the manual scatter diagram, and then add up the totals. You will see a correlation in that as the conveyor speed increases, the length of the cut piece increases as a rule; however, you will also notice that it is not the only probable cause. The dispersion of the cut lengths for the same conveyor speed is due to other causes, which would need to be reconsidered. The point being, then, is while there is partial relationship, there is still more to discover, and more brain storm activity is required.

There is another Scatter Diagram method to be considered further, whereas you would test the correlation between two kinds of data using 4 Quadrants, and calculate the difference per quadrant. This, however, is a more complicated method and often is used with Design of Experiments. We will not consider this method within this lesson context.

CHECK YOUR WORK

Hopefully, you actually did spend the time plotting the Scatter Diagram on the attached chart. The best way to understand it, is to actually create one yourself. You Learn Best by Doing it Yourself!!

Your column totals and row totals, along with your finished Scatter Diagram, should resemble the final product I have prepared for you. CLICK HERE to check your finished work against the actual chart.


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