Bob Luttman, Robert Luttman & Associates
Scatter Diagrams
Shows the relationship between two, or more, variables. Will graphically indicate if any relationship exists between variables and the extent of the relationship.
Construction
Basic Scatter Graphs
On gridline graph paper
- Independent ("cause") variable goes on "X", or horizontal, axis. Left to right.
- Dependent ("effect") variable goes on "Y", or vertical, axis. Bottom to top.
- Plot point at intersection of X and Y values
Example: X=5, Y=2. Go right 5 and up 2 to plot point.
Do's and Don'ts
- Beware of "saturated" points. When more than one data point falls on the same location some computer programs only plot one ("saturated") point.
- Make each axis the same scale ("square grid")
- Graph all the data. The graph should cover the complete range of both variables, even if the collected data may not cover it.
- Keep it simple. Again, the enhancements are great and can add a wealth of information to a graph, but, sometimes making more graphs is just as effective and much more readable.
- Be consistent. If you are comparing multiple graphs scaling must be consistent. In order not to distort slopes and linearity.
Interpretation
Linear Relationships: Does the data "line up"?
Linearity has four parameters:
A. Correlation. Measures how well the data line up. The more the data resembles a straight line, the higher the correlation.
B. Slope. Measures the steepness of the data. The steeper the data, 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.
C. Direction. The "X" variable can have a positive or a negative impact on the "Y" variable.
D. 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 the maximum "Y" value.
Linear Relationships - Correlation
Strong Positive Correlation
Moderately Negative Correlation
NO Correlation
Summary
Scatter diagrams show the relationship between two variables. They also show the strength of the relationship.
