Scatter Diagram
A scatter diagram shows the relationship between two variables (for
example: speed and gas consumption, hours worked and production output).
It provides an easy way to analyze data.
When should we use a scatter diagram?
We can use a scatter diagram when we want to:
- examine how strong a relationship is between two variables (e.g.,
the relationship between advertising costs and sales, years of experience
and employee performance, etc.);
- confirm “hunches” about a direct cause-and-effect relationship
between types of variables; and
- determine the type of relationship (positive, negative, etc.).
Scatter diagrams are easy to use, and the results are easy to understand.
This tool can be adapted for use in many types of situations.
How do we construct a scatter diagram?
The scatter diagram consists of four major steps:
- Collect data
- Draw the horizontal and vertical axes
- Plot the data on the diagram
- Interpret the scatter diagram
The example that follows illustrates how the scatter diagram is used
to interpret data.
| The training department was beginning to feel
the heat. The training manager recently implemented a number of
quality-related courses. Now she was asked to prove that they were
working. He called a department meeting to discuss the dilemma.
A training specialist thought the scatter diagram would be a good
way to visualize the positive impact of the quality-related training.
After all, their department trained people to use the scatter diagram.
Could they use it just as effectively? |
Step 1: Collect Data
Collect 25 to 50 (no more than 100) data points for each variable you
are studying. Create a summary check sheet showing the specific data
for each variable (i.e., the things being compared).
| A group of training specialists volunteered to
research…a cross section of 50 training participants to determine
how many hours of class they had attended, and how many successful
process improvement efforts they had contributed. After researching
50 participants, they created a table containing 50 data points
relating quality training hours and successful process improvements.
(Viewgraph
1) |
Step 2: Draw the horizontal and vertical axes
To draw your scatter diagram, follow these steps:
- Draw the horizontal (X), and the vertical (Y) axes.
- Name the axes.
Note: It is common for the “cause”
variable (i.e., the event that triggers or causes something else to
happen) to be on the horizontal axis and the “effect”
variable (i.e., what happens in response to the cause variable) on
the vertical axis.
- Add scales to the axes.
| The training specialists noted that the scatter
diagram…begins like any line graph. They drew the horizontal
and vertical axes. After scanning the table, they observed the
numbers did not go over 12, so 12 became the highest value on
each axis. They labeled the horizontal (X) axis with the cause
variable—training hours, and the vertical (Y) axis with
the effect variable—successful process improvements. (Viewgraph
2) |
Step 3: Plot the data on the diagram
For each data point, find the intersections of the variables on the
scatter diagram and then plot each point. If you have two or more identical
data points, circle the points as many times as possible.
| Plotting the data went faster than they thought
it would. “This is easy,” they said to their selves.
“All we have to do is find the intersection of the number
of training hours and the number of successful process improvement
tasks for each participant, and then plot the point.” For
repeated intersections, they change the color to red as many times
as was appropriate (Viewgraph
3) |
Step 4: Interpret the scatter diagram
When you interpret the scatter diagram, it is important to remember
that only possible causal relationships are shown, not actual causal
relationships. More advanced statistical tests are necessary if you
want to determine the exact degree of the relationship.
| The training specialists presented the scatter
diagram…at the next department meeting. The training manager
was pleased to see that there appeared to be a clear positive causal
relationship between training hours and successful process improvements
(i.e., the more training hours utilized, the higher the amount of
successful process improvements). Having tangible data in hand,
she now felt assured that the new quality training was a real success.
She asked the training specialist to keep the diagram updated so
that they could see the changes in the effectiveness of the quality
training. |
The following are samples of possible data patterns, and what those
patterns mean.
Positive Relationship: An increase in Y is caused
by an increase in X. If we control X, we generally control Y (Viewgraph
4).
Possible Positive Relationship: An increase in X seems
to increase Y, but Y has other possible causes (Viewgraph
5).
No Relationship: There is no visible relationship
between X and Y (Viewgraph
6).
Possible Negative Relationship: A decrease in Y appears
to be caused by an increase in X (Viewgraph
7).
Negative Relationship: An increase in Y is generally
caused by a decrease in X (Viewgraph
8).
Follow-up: Decide on the next steps
As with any of the improvement tools, success depends on what you
do with the information you have gathered and analyzed. Some additional
steps to consider after your initial interpretation of the scatter diagram
may be:
- continue to collect data to verify your interpretation;
- make changes based on the scatter diagram;
- identify other cause variables; and
- identify other effect variables.
| After the success of the first scatter diagram,
the training specialists volunteered to create similar diagrams
for other training programs the department offered. The rest of
the department decided to try to improve the quality training further
by analyzing the course evaluations and identifying areas for improvement.
|
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