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Monday, February 6, 2012

SCATTER DIAGRAM

Write-up – 9

Understanding Statistical Tools and Techniques

SCATTER DIAGRAM


A scatter diagram is a graphical representation of two variables showing the relationship between them. If variables are correlated, the points will fall along a line or a curve. This diagram is also known as a scatter plot, x-y graph, or correlation chart. It is a problem solving tool.

We can use scatter diagram when we may have paired numerical data and one variable data is dependent on other variable. Scatter diagram can be constructed by plotting two variables against one another on a pair of axes. With the help of scatter diagram, we can try to determine whether two variables are related and potential root causes of problems.



It will be useful to draw scatter diagram after brainstorming causes and effects using a cause and effect diagram to determine whether a particular cause and effect are related. A scatter diagram is used to uncover possible cause-and-effect relationship.

Following procedure will be useful to construct a scatter diagram:
- Decide two variables against which you wish to see the relationship
- Collect pairs of data of these two variables
- Draw a graph with independent variable on the horizontal axis and the dependent variable on the vertical axis
- For each pair of data, put a dot or symbol where x-axis value intersect y-axis value
- Look at the pattern of dots (or symbols) to see if a relationship is obvious
- If data form a line or a curve, it indicates that variables are correlated



When data forms a line or curve, then you may use regression analysis or correlation analysis by using following steps:
- Decide the points from top to bottom by drawing horizontal line
- Divide the points from left to right by drawing a vertical line
- If number of points is odd, you should draw the line through the middle point
- In this way, you will be able to divide points on the graph into four quadrants
- Count the points in each quadrant (leaving the point on the line)
- Add diagonally opposite quadrants
- Find smaller sum and 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
- Look up the limit for N on the trend test table



- If Q is less than the limit, two variables are related
- If q is greater than or equal to the limit, the pattern could have occurred from random chance and we can say that no relationship is demonstrated

How you liked the write-up. Please post your comments. Thanks.

1 comment:

without_one said...

Could you explain how the Trend Test table was constructed?
For example, it starts with values '1-8' and I could not understand why to start with this pair and then why choose to go 9-11, 12-14...an increment by 3 numbers?
Second, I could not understand how the Limit is located? Why 1-8 is 0, 9-11 is 1 ....?
thx.