Posts Tagged ‘scatter Plots’

Scatter Plots for Visualization of Relationships.

Thursday, March 15th, 2012


Scatter plots are one of the Seven Basic QC Tools. They are a graph showing you the relationship between two factors or variables. It can show you if one variable effects another. This can be a very effective tool to find out if you change one thing in a process will it affect another. To see if there is a cause and effect relationship between two factors or variables.

Creating a Scatter Plot:

To create a scatter plot you follow the below steps:

  1. First you need to collect data. This data is called paired data because it will be values from both factors gathered so you can compare one with the other. You can and should collect this paired data with other information (data) that potentially could help understand what is going on.
  2. Next you need to determine which factor you want on the horizontal axis (x) and which to put on the vertical axis (y). This is your choice, but many put the potential cause on the horizontal axis (x) and the effect on the vertical (y) axis.
  3. After you have decided which goes on which axis you need to find the minimum and maximum value of each factor. These will be used to define the each axis scale.
  4. Now we setup the Vertical (y) and Horizontal (x) axis. Both should be the same length but necessarily the same scale. These axis will make the plot (graph) look like square fit the two are the same length.
  5. Mark are each axis scale by starting with the minimum value in the lower left corner for both and the maximum value at the other end. Make sure to divide and label the rest of the axis into equal segments so you will be able to easily plot your data.
  6. Now we plot all of the x, y paired data on the graph. Do this by finding the x value on the horizontal axis and plotting a point above that value that corresponds to the y value on the vertical axis. You continue doing that until all the points are plotted.
  7. Last, but never least, label your graph with a title and a label for the vertical and horizontal axis so everyone who looks at it will be able to under stand what they see.

Interpreting a Scatter Plot:

Now that we have a scatter plot how do we interpret what we see? Is there a relationship or not? Well how we do that is look for patterns. But first, are there any outliers? These are data point that are way out side the pattern of dots that you have plotted. What these point are cause from something other than the relationship of these two variables. Note them and if you can find out what happen that created them. Now let’s look for the patterns.

  • When seeing patterns remember that the tighter together the points are clustered, the stronger the correlation (the effect) between the variables (factors) you have plotted.
  • If you find a pattern that slopes from the lower left to the upper right. This tells you that as x (horizontal axis factor/variable) increases so does the  y (vertical axis factor/variable) increases. This means there is a “Positive” correlation between the two factors/variables.
  • If you find a pattern that slopes from the upper left to the lower right. This tells you that as x (horizontal axis factor/variable) increases, the  y (vertical axis factor/variable) decreases. This means there is a “Negative” correlation between the two factors/variables.

Below is a table of pattern to help you interpret your results:

 

Correlation and Causation

Now that you see a pattern and you have found or not found a correlation between the two factors or variables, please do not assume that one caused the other to happen. That may or may not be true. You see you may very well find a correlation between the number of people using public swimming pools and the number of cooler that break down, but I do not think one caused the other. What you have to do to verify the cause is to conduct a controlled experiment and see if I hold everything else steady will the change in one make the other change as predicted in the scatter plot.

 

But even though you do not have the cause true verified you now see that something is going on and that there is a good chance that one of these factor does effect the other.

Well there you have it. All you need to know about scatter plots. Or at least the basics on how to construct and interpret them. If, you have questions or comments please feel free to contact me by leaving a comment below, emailing me, calling me, or leaving a comment on my website.

Bersbach Consulting
Peter Bersbach
Six Sigma Master Black Belt
http://sixsigmatrainingconsulting.com
peter@bersbach.com
1.520.829.0090