Graphing Marathon Measures #3
– Scatter Diagram
By: Dr. Adam Stoehr
A Scatter-brain usually refers to a person who makes no sense, who doesn’t employ logic, and who takes irrational approaches toward problem solving. A Scatter-diagram has a similar name but it’s used to do pretty much the exact opposite in understanding relationships between numbers. It’s used to make lots of sense of data, it’s used to employ logic, and it’s used to make rational approaches toward problem solving.
One strategy I’ve been using lately to be less of a scatter-brain is to go for as many runs as possible. I just ran in my second half-marathon this past weekend and it was an amazing time to think and focus. Sometimes I come up with my most important ideas while I’m running around my neighborhood with my music blaring. In this article I’ll use some of my marathon training data to explain a very useful chart called a scatter diagram.
Half Marathon Finish
Before we draw some graphs, let’s set some general ground rules for chart creation.
- Rule 1: Make sure you have a clear purpose for your graph and that it will convey an important message.
- Rule 2: Try to use simple pictures to depict complex data.
- Rule 3: Try to make your data talk and tell interesting stories.
- Rule 4: Remember to adapt your graph to suit the audience.
- Rule 5: Don’t be afraid to experiment with various options and graph styles.
A Scatter Diagram is used to show whether or not a relationship exists between two variables. Scatter diagrams display what happens to one variable when another one changes. The pattern of plots (sometimes scattered) on the diagram suggests the possible relationship.
Figure 1: 100% relationship
In Figure 1 we see a very strong relationship between my Body Mass Index (BMI) and my Weight in pounds. I can say that because the points are not scattered at all. They are tight and linear from the bottom left to the top right. I chose this example because I wanted to show what a perfect relationship between data should look like. As my weight goes up my BMI also goes up. This is however not a ground breaking revelation. Those of you who know how BMI is calculated understand that BMI is a function of weight and height. Since my height is fixed my weight is the only variable that affects my BMI. Hence the perfect relationship.
Figure 2: More Common Scatter
In figure 2 I’m analyzing the relationship between my weight in pounds and my body fat %. This relationship is positively correlated (because generally as one goes up so does the other) but still scattered (because the point don’t climb in a perfect line). This would be a more common outcome for a scatter diagram in the workplace. Based on an output like this you could conclude that a relationship seems to exist.
To draw a scatter diagram you need at least 20 “paired variables” which basically means you need 3 pieces of information about the 20 dots on the chart. You need the first variable like weight in figure 2, a second variable like body fat in figure 2, and something that pairs the two variables together like the date in figure 2. Each single dot on the chart represents a point in time for both weight and body fat. If I was hand drawing this chart I ask myself what was my weight on September 30, and what was my body fat on September 30. My weight on that day was 210 pounds and my body fat was 24%, I look at the Y axis (the one on the left) and find 210 pounds then I look at the X axis and find 24% and draw a dot in the spot that lines up with those 2 measures. I use this exact method at least 20 times for all the data and I end up with my scatter diagram.
You use a scatter diagram whenever you need to study and identify the possible relationship between two different sets of variables. In figure 3 we are looking at the relationship between weight loss and number of km’s run in the previous month.
Figure 3- Inverse relationship
This is referred to as an inverse relationship because as the monthly KM’s goes up the monthly weight goes down. The relationship is not as “tight” as figures 1 and 2 but there still seems to be something tying these two things together.
It’s important that I point out that I’m not saying that any of these relationships are “cause and effect” relationships. Looking at scatter diagrams alone we can never make this claim. To understand cause and effect relationships more work and tools are required. Scatter diagrams show relationship, not cause.
At the end of the day you want the charts to tell stories. For example looking at the three charts we can make the following fact based statements.
Figure 1: There is a very strong positive relationship between my BMI and my weight. As my weight goes up, so does my BMI.
Figure 2: There is a relationship between my weight and my body fat. Generally as my weight goes up my body fat also goes up.
Figure 3: There seems to be an inverse relationship between the number of KM’s I run and the number of pounds I lose. If I run more km’s I seem to lose more weight in the next month.
Common uses for scatter diagrams
- Relationship between customer satisfaction and employee satisfaction
- Relationship between turnaround time and volume of work
- Relationship between employee engagement and commitment to quality
- Relationship between anything and anything…