RUSHI KAPADIA

2013036

GROUP 6

 

SCATTER DIAGRAM

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

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

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.

                                                             Scatter Diagram Example

Source - http://asq.org/learn-about-quality/cause-analysis-tools/overview/scatter.html