RUSHI KAPADIA
2013036
GROUP 6
Also called: scatter plot, X–Y graph
The scatter diagram graphs
pairs of numerical data, with one variable on each axis, to look for a
relationship between them. If the variables are correlated, the points will
fall along a line or curve. The better the correlation, the tighter the points
will hug the line.
The pattern of their intersecting
points can graphically show relationship patterns. Most often a scatter diagram
is used to prove or disprove cause-and-effect relationships. While the diagram
shows relationships, it does not by itself prove that one variable causes the
other. In addition to showing possible cause and effect relationships, a
scatter diagram can show that two variables are from a common cause that is
unknown or that one variable can be used as a surrogate for the other.
When to Use a Scatter
Diagram
·
When you have paired
numerical data.
·
When your dependent
variable may have multiple values for each value of your independent variable.
·
When trying to determine
whether the two variables are related, such as…
o
When trying to identify
potential root causes of problems.
o
After brainstorming causes
and effects using a fishbone diagram, to determine objectively whether a
particular cause and effect are related.
o
When determining whether
two effects that appear to be related both occur with the same cause.
o
When testing for
autocorrelation before constructing a control chart.
Use a scatter diagram to examine
theories about cause-and-effect relationships and to search for root causes of
an identified problem.
Use a scatter diagram to design a
control system to ensure that gains from quality improvement
efforts are maintained.
Scatter Diagram Procedure
1. Collect pairs of data where a relationship is suspected.
2. Draw a graph with the independent variable on the horizontal axis and
the dependent variable on the vertical axis. For each pair of data, put a dot
or a symbol where the x-axis value intersects the y-axis value. (If two dots
fall together, put them side by side, touching, so that you can see both.)
3. Look at the pattern of points to see if a relationship is obvious. If
the data clearly form a line or a curve, you may stop. The variables are
correlated. You may wish to use regression or correlation analysis now.
Otherwise, complete steps 4 through 7.
4. Divide points on the graph into four quadrants. If there are X points on
the graph,
·
Count X/2 points from top
to bottom and draw a horizontal line.
·
Count X/2 points from left
to right and draw a vertical line.
·
If number of points is odd,
draw the line through the middle point.
5. Count the points in each quadrant. Do not count points on a line.
6. Add the diagonally opposite quadrants. Find the smaller sum and the
total of points in all quadrants.
A = points in upper left + points in lower right
B = points in upper right + points in lower left
Q = the smaller of A and B
N = A + B
A = points in upper left + points in lower right
B = points in upper right + points in lower left
Q = the smaller of A and B
N = A + B
7. Look up the limit for N on the trend test table.
·
If Q is less than the
limit, the two variables are related.
·
If Q is greater than or
equal to the limit, the pattern could have occurred from random chance.
Scatter Diagram Example
The ZZ-400 manufacturing
team suspects a relationship between product purity (percent purity) and the
amount of iron (measured in parts per million or ppm). Purity and iron are plotted
against each other as a scatter diagram, as shown in the figure below.
There are 24 data points.
Median lines are drawn so that 12 points fall on each side for both percent
purity and ppm iron.
To test for a relationship,
they calculate:
A = points in upper left + points in lower right = 9 + 9 = 18
B = points in upper right + points in lower left = 3 + 3 = 6
Q = the smaller of A and B = the smaller of 18 and 6 = 6
N = A + B = 18 + 6 = 24
A = points in upper left + points in lower right = 9 + 9 = 18
B = points in upper right + points in lower left = 3 + 3 = 6
Q = the smaller of A and B = the smaller of 18 and 6 = 6
N = A + B = 18 + 6 = 24
Then they look up the limit
for N on the trend test table. For N = 24, the limit is 6.
Q is equal to the limit. Therefore, the pattern could have occurred from random chance, and no relationship is demonstrated.
Q is equal to the limit. Therefore, the pattern could have occurred from random chance, and no relationship is demonstrated.
Scatter Diagram Example
Source
- http://asq.org/learn-about-quality/cause-analysis-tools/overview/scatter.html
