Friday, July 13, 2012
Duplication 2.1 Update
Tying up a loose end that has plagued me for years
My wife thinks I need help with my obsession with accuracy. In my original post on Duplication, a Four Part Series, Part 2, I wrote that I wasn’t sure how to position Venn Diagram circles with complete accuracy, or as actually posted:
“I’m still trying to come up with the formula for the accurate distance from the two center points of each circle for a proportionately accurate area of duplication. In the meantime, a good guess should get the point across.”
The ability to position two proportionately accurate circles and the overlap (or duplication between respective data sets) they represent in a diagram has plagued me for years. It has always bothered me that when I created these diagrams, the area of overlap was a visual guesstimate. As an analyst, it always pained me to know I was guessing. Ninety-nine point nine-nine percent of the time, the audience to this kind of diagram could have cared less. In fact, most people were usually surprised that I even made the circles proportionately accurate to the data used. See Exhibit 8.1 for a look at how I last left this diagram.
So for years, I would periodically work on a solution. It ultimately required me to dust off the metaphorical trigonometry textbooks. See Exhibit 8.2 for some of the challenges that I needed to overcome.
I’m not going to post the equations necessary to find the distance simply because it’s so much data and trigonometry that my comfortable status of “geek” would likely elevate to “supreme geek.” Let’s just say your ability to calculate angles, triangle areas, circle segment areas, sector areas, and use pi, sin, cosine or even arc cosines are required. Instead, I’m including a link to an excel document that will calculate the circle dimensions and distance between the circle centers for you (the formulas can be seen within the excel document).
Link to calculator: Excel Document calculating the distance between circles
Below is an example of the calculator.
With this calculator/formula, I can now create diagrams, like the one found in Exhibits 8.3, with complete accuracy.